diff --git a/changelog b/changelog index d1f2faa..bbe9b39 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20100618 tpd src/axiom-website/patches.html 20100619.02.tpd.patch +20100618 tpd src/input/richhyper1000-1098.input rule-based hyper integration 20100618 tpd src/axiom-website/patches.html 20100619.01.tpd.patch 20100619 tpd books/bookvol5 change )version to include *build-version* info 20100618 tpd src/axiom-website/patches.html 20100618.02.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index eaff7b1..6cddd5f 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2920,6 +2920,8 @@ src/input/richlog300-391.input rule-based log integration
src/input/richinvtrig000-092.input rule-based inverse trig int.
20100619.01.tpd.patch books/bookvol5 change )version to include *build-version* info
+20100619.02.tpd.patch +src/input/richhyper1000-1098.input rule-based hyper integration
diff --git a/src/input/richhyper1000-1098.input.pamphlet b/src/input/richhyper1000-1098.input.pamphlet new file mode 100644 index 0000000..cc01870 --- /dev/null +++ b/src/input/richhyper1000-1098.input.pamphlet @@ -0,0 +1,48187 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richhyper1000-1098.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper1000-1098.output +)spool richhyper1000-1098.output +)set message auto off +)clear all + +--S 1 of 531 +t1000:= sech(6*x)*sinh(x) +--R +--R +--R (1) sech(6x)sinh(x) +--R Type: Expression Integer +--E 1 + +--S 2 of 531 +r1000:= -1/12*2^(1/2)*(-2*atanh(2^(1/2)*cosh(x))+atanh(2*cosh(x)*_ + 2^(1/2)/(3^(1/2)-1))*3^(1/2)+atanh(2*cosh(x)*2^(1/2)/(3^(1/2)-1))+_ + atanh(2*cosh(x)*2^(1/2)/(1+3^(1/2)))*3^(1/2)-_ + atanh(2*cosh(x)*2^(1/2)/(1+3^(1/2)))) +--R +--R +--R (2) +--R +-+ +--R +-+ +-+ +-+ +-+ +-+ 2\|2 cosh(x) +--R 2\|2 atanh(\|2 cosh(x)) + (- \|2 \|3 - \|2 )atanh(------------) +--R +-+ +--R \|3 - 1 +--R + +--R +-+ +--R +-+ +-+ +-+ 2\|2 cosh(x) +--R (- \|2 \|3 + \|2 )atanh(------------) +--R +-+ +--R \|3 + 1 +--R / +--R 12 +--R Type: Expression Integer +--E 2 + +--S 3 of 531 +a1000:= integrate(t1000,x) +--R +--R +--R (3) +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 2 +--R ((6\|3 - 12)sinh(x) + (6\|3 - 12)cosh(x)) |--------- + sinh(x) +--R | +-+ +--R \| 36\|3 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((6\|3 + 12)sinh(x) + (6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 2 +-+ 2 +-+ +--R \|2 sinh(x) + \|2 cosh(x) + 4cosh(x) + 2\|2 +--R log(----------------------------------------------) +--R 2 2 +--R sinh(x) + cosh(x) +--R + +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((- 6\|3 - 12)sinh(x) + (- 6\|3 - 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 +--R ((- 6\|3 + 12)sinh(x) + (- 6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R +-+ +--R 6\|2 +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 531 +m1000:= a1000-r1000 +--R +--R +--R (4) +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 2 +--R ((6\|3 - 12)sinh(x) + (6\|3 - 12)cosh(x)) |--------- + sinh(x) +--R | +-+ +--R \| 36\|3 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((6\|3 + 12)sinh(x) + (6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 2 +-+ 2 +-+ +--R \|2 sinh(x) + \|2 cosh(x) + 4cosh(x) + 2\|2 +--R log(----------------------------------------------) +--R 2 2 +--R sinh(x) + cosh(x) +--R + +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((- 6\|3 - 12)sinh(x) + (- 6\|3 - 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 +--R ((- 6\|3 + 12)sinh(x) + (- 6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +--R +-+ +-+ 2\|2 cosh(x) +--R - 2atanh(\|2 cosh(x)) + (\|3 + 1)atanh(------------) +--R +-+ +--R \|3 - 1 +--R + +--R +-+ +--R +-+ 2\|2 cosh(x) +--R (\|3 - 1)atanh(------------) +--R +-+ +--R \|3 + 1 +--R / +--R +-+ +--R 6\|2 +--R Type: Expression Integer +--E 4 + +--S 5 of 531 +d1000:= D(m1000,x) +--R +--R +--R (5) +--R +-+ 13 +-+ 12 +--R - 3\|2 sinh(x) - 24\|2 cosh(x)sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (64\|2 cosh(x) - 96\|2 cosh(x) - 54\|2 cosh(x) - 12cosh(x) - 8\|2 ) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 2 +--R 480\|2 cosh(x) - 720\|2 cosh(x) + 54\|2 cosh(x) - 96cosh(x) +--R + +--R +-+ +--R - 63\|2 cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 3 +--R 1536\|2 cosh(x) - 2272\|2 cosh(x) + 435\|2 cosh(x) - 348cosh(x) +--R + +--R +-+ 2 +-+ +--R - 204\|2 cosh(x) + 2\|2 +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 2592\|2 cosh(x) - 128cosh(x) - 3600\|2 cosh(x) + 192cosh(x) +--R + +--R +-+ 5 4 +-+ 3 2 +--R 498\|2 cosh(x) - 840cosh(x) - 303\|2 cosh(x) + 4cosh(x) +--R + +--R +-+ +--R 3\|2 cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 10 9 +-+ 8 7 +--R 2048\|2 cosh(x) - 768cosh(x) - 2048\|2 cosh(x) + 1024cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R - 1036\|2 cosh(x) - 1416cosh(x) + 20\|2 cosh(x) - 48cosh(x) +--R + +--R +-+ 2 +-+ +--R - 44\|2 cosh(x) + 16cosh(x) + 8\|2 +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 11 10 +-+ 9 8 +--R - 448\|2 cosh(x) - 1792cosh(x) + 2720\|2 cosh(x) + 2048cosh(x) +--R + +--R +-+ 7 6 +-+ 5 4 +--R - 4204\|2 cosh(x) - 1392cosh(x) + 1022\|2 cosh(x) - 304cosh(x) +--R + +--R +-+ 3 2 +-+ +--R - 226\|2 cosh(x) + 68cosh(x) + 35\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 12 11 +-+ 10 +--R - 2688\|2 cosh(x) - 1792cosh(x) + 6784\|2 cosh(x) +--R + +--R 9 +-+ 8 7 +-+ 6 +--R 1280cosh(x) - 6661\|2 cosh(x) + 184cosh(x) + 2036\|2 cosh(x) +--R + +--R 5 +-+ 4 3 +-+ 2 +--R - 1120cosh(x) - 452\|2 cosh(x) + 272cosh(x) + 80\|2 cosh(x) +--R + +--R +-+ +--R - 8cosh(x) - 4\|2 +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 10 +--R - 2624\|2 cosh(x) + 6688\|2 cosh(x) - 1920cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R - 6300\|2 cosh(x) + 3008cosh(x) + 2126\|2 cosh(x) - 2424cosh(x) +--R + +--R +-+ 5 4 +-+ 3 2 +--R - 560\|2 cosh(x) + 660cosh(x) + 153\|2 cosh(x) - 28cosh(x) +--R + +--R +-+ +--R - 5\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 14 13 +-+ 12 +--R - 1088\|2 cosh(x) + 1792cosh(x) + 3680\|2 cosh(x) +--R + +--R 11 +-+ 10 9 +-+ 8 +--R - 4608cosh(x) - 3966\|2 cosh(x) + 4820cosh(x) + 1492\|2 cosh(x) +--R + +--R 7 +-+ 6 5 +-+ 4 +--R - 3184cosh(x) - 468\|2 cosh(x) + 1056cosh(x) + 204\|2 cosh(x) +--R + +--R 3 +-+ 2 +-+ +--R - 112cosh(x) - 30\|2 cosh(x) - 8cosh(x) - 5\|2 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 15 14 +-+ 13 12 +--R - 32\|2 cosh(x) + 1792cosh(x) + 1072\|2 cosh(x) - 4096cosh(x) +--R + +--R +-+ 11 10 +-+ 9 8 +--R - 1738\|2 cosh(x) + 4048cosh(x) + 961\|2 cosh(x) - 2512cosh(x) +--R + +--R +-+ 7 6 +-+ 5 4 +--R - 462\|2 cosh(x) + 860cosh(x) + 233\|2 cosh(x) - 104cosh(x) +--R + +--R +-+ 3 2 +-+ +--R - 42\|2 cosh(x) + 4cosh(x) + 2\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 16 15 +-+ 14 13 +--R 128\|2 cosh(x) + 768cosh(x) + 96\|2 cosh(x) - 1792cosh(x) +--R + +--R +-+ 12 11 +-+ 10 9 +--R - 491\|2 cosh(x) + 1892cosh(x) + 504\|2 cosh(x) - 1280cosh(x) +--R + +--R +-+ 8 7 +-+ 6 5 +--R - 478\|2 cosh(x) + 384cosh(x) + 340\|2 cosh(x) + 104cosh(x) +--R + +--R +-+ 4 3 +-+ 2 +--R - 98\|2 cosh(x) - 80cosh(x) - \|2 cosh(x) + 4cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 17 16 +-+ 15 14 +--R 32\|2 cosh(x) + 128cosh(x) - 16\|2 cosh(x) - 320cosh(x) +--R + +--R +-+ 13 12 +-+ 11 10 +--R - 62\|2 cosh(x) + 392cosh(x) + 97\|2 cosh(x) - 396cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R - 131\|2 cosh(x) + 268cosh(x) + 115\|2 cosh(x) - 76cosh(x) +--R + +--R +-+ 5 4 +-+ 3 +--R - 37\|2 cosh(x) + 4cosh(x) + 2\|2 cosh(x) +--R / +--R +-+ 6 +-+ 4 +-+ 2 +-+ 12 +--R (96\|2 cosh(x) - 144\|2 cosh(x) + 54\|2 cosh(x) - 3\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (768\|2 cosh(x) - 1152\|2 cosh(x) + 432\|2 cosh(x) - 24\|2 cosh(x)) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 8 7 +-+ 6 5 +--R 2880\|2 cosh(x) + 384cosh(x) - 4128\|2 cosh(x) - 576cosh(x) +--R + +--R +-+ 4 3 +-+ 2 +-+ +--R 1332\|2 cosh(x) + 216cosh(x) + 18\|2 cosh(x) - 12cosh(x) - 6\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 6912\|2 cosh(x) + 3072cosh(x) - 8832\|2 cosh(x) - 4608cosh(x) +--R + +--R +-+ 5 4 +-+ 3 2 +--R 1584\|2 cosh(x) + 1728cosh(x) + 648\|2 cosh(x) - 96cosh(x) +--R + +--R +-+ +--R - 48\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 10 9 +-+ 8 +--R 12192\|2 cosh(x) + 11136cosh(x) - 12720\|2 cosh(x) +--R + +--R 7 +-+ 6 5 +-+ 4 +--R - 16704cosh(x) - 1590\|2 cosh(x) + 6264cosh(x) + 2895\|2 cosh(x) +--R + +--R 3 +-+ 2 +-+ +--R - 348cosh(x) - 228\|2 cosh(x) + 3\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 11 10 +-+ 9 +--R 16896\|2 cosh(x) + 24576cosh(x) - 13056\|2 cosh(x) +--R + +--R 8 +-+ 7 6 +-+ 5 +--R - 36864cosh(x) - 9312\|2 cosh(x) + 13824cosh(x) + 6960\|2 cosh(x) +--R + +--R 4 +-+ 3 +-+ +--R - 768cosh(x) - 600\|2 cosh(x) + 12\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 12 11 +-+ 10 +--R 18816\|2 cosh(x) + 37632cosh(x) - 9408\|2 cosh(x) +--R + +--R 9 +-+ 8 7 +--R - 56448cosh(x) - 18408\|2 cosh(x) + 20784cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R 10956\|2 cosh(x) - 600cosh(x) - 732\|2 cosh(x) - 216cosh(x) +--R + +--R +-+ 2 +-+ +--R - 84\|2 cosh(x) + 12cosh(x) + 6\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 13 12 +-+ 11 +--R 16896\|2 cosh(x) + 43008cosh(x) - 3840\|2 cosh(x) +--R + +--R 10 +-+ 9 8 +--R - 64512cosh(x) - 23904\|2 cosh(x) + 22656cosh(x) +--R + +--R +-+ 7 6 +-+ 5 4 +--R 12528\|2 cosh(x) + 960cosh(x) - 168\|2 cosh(x) - 864cosh(x) +--R + +--R +-+ 3 2 +-+ +--R - 396\|2 cosh(x) + 48cosh(x) + 24\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 14 13 +-+ 12 +--R 12192\|2 cosh(x) + 37632cosh(x) + 528\|2 cosh(x) +--R + +--R 11 +-+ 10 9 +--R - 56448cosh(x) - 22710\|2 cosh(x) + 18480cosh(x) +--R + +--R +-+ 8 7 +-+ 6 5 +--R 10875\|2 cosh(x) + 2856cosh(x) + 768\|2 cosh(x) - 1512cosh(x) +--R + +--R +-+ 4 3 +-+ 2 +-+ +--R - 858\|2 cosh(x) + 84cosh(x) + 96\|2 cosh(x) - 3\|2 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 15 14 +-+ 13 +--R 6912\|2 cosh(x) + 24576cosh(x) + 1920\|2 cosh(x) +--R + +--R 12 +-+ 11 10 +--R - 36864cosh(x) - 15696\|2 cosh(x) + 10752cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 6888\|2 cosh(x) + 3840cosh(x) + 1272\|2 cosh(x) - 1728cosh(x) +--R + +--R +-+ 5 4 +-+ 3 +--R - 828\|2 cosh(x) + 96cosh(x) + 48\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 16 15 +-+ 14 +--R 2880\|2 cosh(x) + 11136cosh(x) + 1248\|2 cosh(x) +--R + +--R 13 +-+ 12 11 +--R - 16704cosh(x) - 7500\|2 cosh(x) + 3576cosh(x) +--R + +--R +-+ 10 9 +-+ 8 7 +--R 2850\|2 cosh(x) + 3684cosh(x) + 1602\|2 cosh(x) - 1128cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R - 828\|2 cosh(x) - 492cosh(x) - 138\|2 cosh(x) + 216cosh(x) +--R + +--R +-+ 2 +-+ +--R 102\|2 cosh(x) - 12cosh(x) - 6\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 17 16 +-+ 15 14 +--R 768\|2 cosh(x) + 3072cosh(x) + 384\|2 cosh(x) - 4608cosh(x) +--R + +--R +-+ 13 12 +-+ 11 10 +--R - 2256\|2 cosh(x) + 192cosh(x) + 648\|2 cosh(x) + 2208cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 888\|2 cosh(x) - 864cosh(x) - 420\|2 cosh(x) + 48cosh(x) +--R + +--R +-+ 5 +--R 24\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 18 17 +-+ 16 15 +--R 96\|2 cosh(x) + 384cosh(x) + 48\|2 cosh(x) - 576cosh(x) +--R + +--R +-+ 14 13 +-+ 12 11 +--R - 330\|2 cosh(x) - 168cosh(x) + 57\|2 cosh(x) + 564cosh(x) +--R + +--R +-+ 10 9 +-+ 8 7 +--R 324\|2 cosh(x) + 168cosh(x) - 57\|2 cosh(x) - 564cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R - 228\|2 cosh(x) + 216cosh(x) + 105\|2 cosh(x) - 12cosh(x) +--R + +--R +-+ 2 +--R - 6\|2 cosh(x) +--R Type: Expression Integer +--E 5 + +--S 6 of 531 +t1001:= csch(2*x)*sinh(x) +--R +--R +--R (6) csch(2x)sinh(x) +--R Type: Expression Integer +--E 6 + +--S 7 of 531 +r1001:= 1/2*atan(sinh(x)) +--R +--R +--R atan(sinh(x)) +--R (7) ------------- +--R 2 +--R Type: Expression Integer +--E 7 + +--S 8 of 531 +a1001:= integrate(t1001,x) +--R +--R +--R (8) atan(sinh(x) + cosh(x)) +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 531 +m1001:= a1001-r1001 +--R +--R +--R 2atan(sinh(x) + cosh(x)) - atan(sinh(x)) +--R (9) ---------------------------------------- +--R 2 +--R Type: Expression Integer +--E 9 + +--S 10 of 531 +d1001:= D(m1001,x) +--R +--R +--R (10) +--R 3 2 2 3 +--R 2sinh(x) + cosh(x)sinh(x) + (- 2cosh(x) + 2)sinh(x) - cosh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) + 4)sinh(x) + 4cosh(x)sinh(x) +--R + +--R 2 +--R 2cosh(x) + 2 +--R Type: Expression Integer +--E 10 + +--S 11 of 531 +t1002:= csch(3*x)*sinh(x) +--R +--R +--R (11) csch(3x)sinh(x) +--R Type: Expression Integer +--E 11 + +--S 12 of 531 +r1002:= 1/3*atan(1/3*tanh(x)*3^(1/2))*3^(1/2) +--R +--R +--R +-+ +--R +-+ \|3 tanh(x) +--R \|3 atan(-----------) +--R 3 +--R (12) --------------------- +--R 3 +--R Type: Expression Integer +--E 12 + +--S 13 of 531 +a1002:= integrate(t1002,x) +--R +--R +--R +-+ +-+ +--R \|3 sinh(x) + 3\|3 cosh(x) +--R atan(--------------------------) +--R 3sinh(x) - 3cosh(x) +--R (13) - -------------------------------- +--R +-+ +--R \|3 +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 531 +m1002:= a1002-r1002 +--R +--R +--R +-+ +-+ +-+ +--R \|3 tanh(x) \|3 sinh(x) + 3\|3 cosh(x) +--R - atan(-----------) - atan(--------------------------) +--R 3 3sinh(x) - 3cosh(x) +--R (14) ------------------------------------------------------ +--R +-+ +--R \|3 +--R Type: Expression Integer +--E 14 + +--S 15 of 531 +d1002:= D(m1002,x) +--R +--R +--R 2 2 2 +--R 4cosh(x) tanh(x) - 4sinh(x) +--R (15) ------------------------------------------------------ +--R 2 2 2 2 2 +--R (sinh(x) + 3cosh(x) )tanh(x) + 3sinh(x) + 9cosh(x) +--R Type: Expression Integer +--E 15 + +--S 16 of 531 +t1003:= csch(4*x)*sinh(x) +--R +--R +--R (16) csch(4x)sinh(x) +--R Type: Expression Integer +--E 16 + +--S 17 of 531 +r1003:= -1/4*atan(sinh(x))+1/4*atan(2^(1/2)*sinh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 atan(\|2 sinh(x)) - atan(sinh(x)) +--R (17) ------------------------------------- +--R 4 +--R Type: Expression Integer +--E 17 + +--S 18 of 531 +a1003:= integrate(t1003,x) +--R +--R +--R (18) +--R +-+ +-+ +--R \|2 sinh(x) + \|2 cosh(x) +-+ +--R atan(-------------------------) - \|2 atan(sinh(x) + cosh(x)) +--R 2 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R - atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 531 +m1003:= a1003-r1003 +--R +--R +--R (19) +--R +-+ +-+ +--R +-+ \|2 sinh(x) + \|2 cosh(x) +--R - 2atan(\|2 sinh(x)) + 2atan(-------------------------) +--R 2 +--R + +--R +-+ +-+ +--R - 2\|2 atan(sinh(x) + cosh(x)) + \|2 atan(sinh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R - 2atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression Integer +--E 19 + +--S 20 of 531 +d1003:= D(m1003,x) +--R +--R +--R (20) +--R 11 10 2 9 +--R - 12sinh(x) - 60cosh(x)sinh(x) + (- 108cosh(x) - 62)sinh(x) +--R + +--R 3 8 +--R (- 60cosh(x) - 231cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (60cosh(x) - 290cosh(x) - 124)sinh(x) +--R + +--R 5 3 6 +--R (108cosh(x) - 78cosh(x) - 299cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (60cosh(x) + 134cosh(x) - 248cosh(x) - 112)sinh(x) +--R + +--R 7 5 3 4 +--R (12cosh(x) + 128cosh(x) - 23cosh(x) - 159cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (34cosh(x) + 88cosh(x) - 66cosh(x) - 44)sinh(x) +--R + +--R 7 5 3 2 +--R (- 10cosh(x) + 35cosh(x) + 8cosh(x) - 31cosh(x))sinh(x) +--R + +--R 8 6 4 2 9 +--R (- 8cosh(x) - 4cosh(x) + 14cosh(x) + 4cosh(x) - 6)sinh(x) - cosh(x) +--R + +--R 7 5 3 +--R - cosh(x) + 3cosh(x) - cosh(x) +--R / +--R 12 11 2 10 +--R 8sinh(x) + 64cosh(x)sinh(x) + (224cosh(x) + 68)sinh(x) +--R + +--R 3 9 +--R (448cosh(x) + 368cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (560cosh(x) + 920cosh(x) + 208)sinh(x) +--R + +--R 5 3 7 +--R (448cosh(x) + 1408cosh(x) + 728cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (224cosh(x) + 1424cosh(x) + 1324cosh(x) + 296)sinh(x) +--R + +--R 7 5 3 5 +--R (64cosh(x) + 944cosh(x) + 1616cosh(x) + 616cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (8cosh(x) + 392cosh(x) + 1276cosh(x) + 884cosh(x) + 208)sinh(x) +--R + +--R 7 5 3 3 +--R (96cosh(x) + 632cosh(x) + 800cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (12cosh(x) + 196cosh(x) + 472cosh(x) + 300cosh(x) + 68)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 136cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 28cosh(x) + 60cosh(x) + 44cosh(x) + 8 +--R Type: Expression Integer +--E 20 + +--S 21 of 531 +t1004:= csch(5*x)*sinh(x) +--R +--R +--R (21) csch(5x)sinh(x) +--R Type: Expression Integer +--E 21 + +--S 22 of 531 +r1004:= -1/10*(10+2*5^(1/2))^(1/2)*atan(1/5*(25-10*5^(1/2))^(1/2)*tanh(x))+_ + 1/10*(10-2*5^(1/2))^(1/2)*atan(1/5*(25+10*5^(1/2))^(1/2)*tanh(x)) +--R +--R +--R (22) +--R +-----------+ +--R +------------+ | +-+ +--R | +-+ tanh(x)\|10\|5 + 25 +--R \|- 2\|5 + 10 atan(---------------------) +--R 5 +--R + +--R +-------------+ +--R +----------+ | +-+ +--R | +-+ tanh(x)\|- 10\|5 + 25 +--R - \|2\|5 + 10 atan(-----------------------) +--R 5 +--R / +--R 10 +--R Type: Expression Integer +--E 22 + +--S 23 of 531 +a1004:= integrate(t1004,x) +--R +--R +--R (23) +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 1 +--R |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 1 +--R (5\|5 - 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 + 5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 1 +--R |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 1 +--R (5\|5 + 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 - 5 +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 531 +m1004:= a1004-r1004 +--R +--R +--R (24) +--R +-----------+ +--R +------------+ | +-+ +--R | +-+ tanh(x)\|10\|5 + 25 +--R - \|- 2\|5 + 10 atan(---------------------) +--R 5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 1 +--R 10 |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 1 +--R (5\|5 - 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 + 5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 1 +--R 10 |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 1 +--R (5\|5 + 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 - 5 +--R + +--R +-------------+ +--R +----------+ | +-+ +--R | +-+ tanh(x)\|- 10\|5 + 25 +--R \|2\|5 + 10 atan(-----------------------) +--R 5 +--R / +--R 10 +--R Type: Expression Integer +--E 24 + +--S 25 of 531 +d1004:= D(m1004,x) +--R +--R +--R (25) +--R +-+ 8 +-+ 7 +--R (- 2\|5 + 5)sinh(x) + (- 16\|5 + 40)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R ((- 56\|5 + 140)cosh(x) - 2\|5 + 5)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 112\|5 + 280)cosh(x) + (- 12\|5 + 30)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 140\|5 + 350)cosh(x) + (- 30\|5 + 75)cosh(x) - 2\|5 +--R + +--R 5 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 112\|5 + 280)cosh(x) + (- 40\|5 + 100)cosh(x) +--R + +--R +-+ +--R (- 8\|5 + 20)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 56\|5 + 140)cosh(x) + (- 30\|5 + 75)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 12\|5 + 30)cosh(x) - 2\|5 + 5 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 16\|5 + 40)cosh(x) + (- 12\|5 + 30)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8\|5 + 20)cosh(x) + (- 4\|5 + 10)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 2\|5 + 5)cosh(x) + (- 2\|5 + 5)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 2\|5 + 5)cosh(x) + (- 2\|5 + 5)cosh(x) - 2\|5 + 5 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 2\|5 sinh(x) + 16\|5 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (56\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (112\|5 cosh(x) + 12\|5 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (140\|5 cosh(x) + 30\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (112\|5 cosh(x) + 40\|5 cosh(x) + 8\|5 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (56\|5 cosh(x) + 30\|5 cosh(x) + 12\|5 cosh(x) + 2\|5 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 16\|5 cosh(x) + 12\|5 cosh(x) + 8\|5 cosh(x) +--R + +--R +-+ +--R 4\|5 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) +--R + +--R +-+ +--R 2\|5 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 5sinh(x) - 40cosh(x)sinh(x) + (- 140cosh(x) - 5)sinh(x) +--R + +--R 3 5 +--R (- 280cosh(x) - 30cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 350cosh(x) - 75cosh(x) - 5)sinh(x) +--R + +--R 5 3 3 +--R (- 280cosh(x) - 100cosh(x) - 20cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 140cosh(x) - 75cosh(x) - 30cosh(x) - 5)sinh(x) +--R + +--R 7 5 3 +--R (- 40cosh(x) - 30cosh(x) - 20cosh(x) - 10cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 5cosh(x) - 5cosh(x) - 5cosh(x) - 5cosh(x) - 5 +--R * +--R +------------+ +-----------+ +--R | +-+ | +-+ +--R \|- 2\|5 + 10 \|10\|5 + 25 +--R + +--R +-+ 8 +-+ 7 +--R (- 2\|5 - 5)sinh(x) + (- 16\|5 - 40)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R ((- 56\|5 - 140)cosh(x) - 2\|5 - 5)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 112\|5 - 280)cosh(x) + (- 12\|5 - 30)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 140\|5 - 350)cosh(x) + (- 30\|5 - 75)cosh(x) - 2\|5 +--R + +--R - 5 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 112\|5 - 280)cosh(x) + (- 40\|5 - 100)cosh(x) +--R + +--R +-+ +--R (- 8\|5 - 20)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 56\|5 - 140)cosh(x) + (- 30\|5 - 75)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 12\|5 - 30)cosh(x) - 2\|5 - 5 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 16\|5 - 40)cosh(x) + (- 12\|5 - 30)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8\|5 - 20)cosh(x) + (- 4\|5 - 10)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 2\|5 - 5)cosh(x) + (- 2\|5 - 5)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 2\|5 - 5)cosh(x) + (- 2\|5 - 5)cosh(x) - 2\|5 - 5 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 2\|5 sinh(x) + 16\|5 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (56\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (112\|5 cosh(x) + 12\|5 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (140\|5 cosh(x) + 30\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (112\|5 cosh(x) + 40\|5 cosh(x) + 8\|5 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (56\|5 cosh(x) + 30\|5 cosh(x) + 12\|5 cosh(x) + 2\|5 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 16\|5 cosh(x) + 12\|5 cosh(x) + 8\|5 cosh(x) +--R + +--R +-+ +--R 4\|5 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) +--R + +--R +-+ +--R 2\|5 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 5sinh(x) + 40cosh(x)sinh(x) + (140cosh(x) + 5)sinh(x) +--R + +--R 3 5 +--R (280cosh(x) + 30cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (350cosh(x) + 75cosh(x) + 5)sinh(x) +--R + +--R 5 3 3 +--R (280cosh(x) + 100cosh(x) + 20cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (140cosh(x) + 75cosh(x) + 30cosh(x) + 5)sinh(x) +--R + +--R 7 5 3 8 +--R (40cosh(x) + 30cosh(x) + 20cosh(x) + 10cosh(x))sinh(x) + 5cosh(x) +--R + +--R 6 4 2 +--R 5cosh(x) + 5cosh(x) + 5cosh(x) + 5 +--R * +--R +-------------+ +----------+ +--R | +-+ | +-+ +--R \|- 10\|5 + 25 \|2\|5 + 10 +--R + +--R 4 3 2 2 +--R 50sinh(x) + 200cosh(x)sinh(x) + 300cosh(x) sinh(x) +--R + +--R 3 4 +--R 200cosh(x) sinh(x) + 50cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 4 3 2 2 +--R 500sinh(x) + 2000cosh(x)sinh(x) + 3000cosh(x) sinh(x) +--R + +--R 3 4 +--R 2000cosh(x) sinh(x) + 500cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R 250sinh(x) + 1000cosh(x)sinh(x) + 1500cosh(x) sinh(x) +--R + +--R 3 4 +--R 1000cosh(x) sinh(x) + 250cosh(x) +--R / +--R 8 7 2 6 +--R 50sinh(x) + 400cosh(x)sinh(x) + (1400cosh(x) + 50)sinh(x) +--R + +--R 3 5 +--R (2800cosh(x) + 300cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (3500cosh(x) + 750cosh(x) + 50)sinh(x) +--R + +--R 5 3 3 +--R (2800cosh(x) + 1000cosh(x) + 200cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (1400cosh(x) + 750cosh(x) + 300cosh(x) + 50)sinh(x) +--R + +--R 7 5 3 +--R (400cosh(x) + 300cosh(x) + 200cosh(x) + 100cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 50cosh(x) + 50cosh(x) + 50cosh(x) + 50cosh(x) + 50 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 500sinh(x) + 4000cosh(x)sinh(x) + (14000cosh(x) + 500)sinh(x) +--R + +--R 3 5 +--R (28000cosh(x) + 3000cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (35000cosh(x) + 7500cosh(x) + 500)sinh(x) +--R + +--R 5 3 3 +--R (28000cosh(x) + 10000cosh(x) + 2000cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (14000cosh(x) + 7500cosh(x) + 3000cosh(x) + 500)sinh(x) +--R + +--R 7 5 3 +--R (4000cosh(x) + 3000cosh(x) + 2000cosh(x) + 1000cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 500cosh(x) + 500cosh(x) + 500cosh(x) + 500cosh(x) + 500 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 250sinh(x) + 2000cosh(x)sinh(x) + (7000cosh(x) + 250)sinh(x) +--R + +--R 3 5 +--R (14000cosh(x) + 1500cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (17500cosh(x) + 3750cosh(x) + 250)sinh(x) +--R + +--R 5 3 3 +--R (14000cosh(x) + 5000cosh(x) + 1000cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (7000cosh(x) + 3750cosh(x) + 1500cosh(x) + 250)sinh(x) +--R + +--R 7 5 3 +--R (2000cosh(x) + 1500cosh(x) + 1000cosh(x) + 500cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 250cosh(x) + 250cosh(x) + 250cosh(x) + 250cosh(x) + 250 +--R Type: Expression Integer +--E 25 + +--S 26 of 531 +t1005:= csch(6*x)*sinh(x) +--R +--R +--R (26) csch(6x)sinh(x) +--R Type: Expression Integer +--E 26 + +--S 27 of 531 +r1005:= 1/6*atan(sinh(x))+1/6*atan(2*sinh(x))-_ + 1/6*atan(2/3*sinh(x)*3^(1/2))*3^(1/2) +--R +--R +--R +-+ +--R +-+ 2\|3 sinh(x) +--R - \|3 atan(------------) + atan(2sinh(x)) + atan(sinh(x)) +--R 3 +--R (27) --------------------------------------------------------- +--R 6 +--R Type: Expression Integer +--E 27 + +--S 28 of 531 +a1005:= integrate(t1005,x) +--R +--R +--R (28) +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R - 3atan(-------------------------) +--R 3 +--R + +--R 2 2 +--R +-+ sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R - \|3 atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +-+ +--R 3\|3 atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R 3atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 531 +m1005:= a1005-r1005 +--R +--R +--R (29) +--R +-+ +-+ +-+ +--R 2\|3 sinh(x) \|3 sinh(x) + \|3 cosh(x) +--R 3atan(------------) - 3atan(-------------------------) +--R 3 3 +--R + +--R 2 2 +--R +-+ +-+ sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R - \|3 atan(2sinh(x)) - \|3 atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +-+ +-+ +--R 3\|3 atan(sinh(x) + cosh(x)) - \|3 atan(sinh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R 3atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R / +--R +-+ +--R 6\|3 +--R Type: Expression Integer +--E 29 + +--S 30 of 531 +d1005:= D(m1005,x) +--R +--R +--R (30) +--R 17 16 2 15 +--R 32sinh(x) + 288cosh(x)sinh(x) + (1120cosh(x) + 192)sinh(x) +--R + +--R 3 14 +--R (2400cosh(x) + 1536cosh(x))sinh(x) +--R + +--R 4 2 13 +--R (2880cosh(x) + 5312cosh(x) + 486)sinh(x) +--R + +--R 5 3 12 +--R (1344cosh(x) + 10176cosh(x) + 3093cosh(x))sinh(x) +--R + +--R 6 4 2 11 +--R (- 1344cosh(x) + 11136cosh(x) + 9318cosh(x) + 670)sinh(x) +--R + +--R 7 5 3 10 +--R (- 2880cosh(x) + 5376cosh(x) + 16800cosh(x) + 2142cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 2400cosh(x) - 2688cosh(x) + 18368cosh(x) + 7722cosh(x) + 540) +--R * +--R 9 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 1120cosh(x) - 6528cosh(x) + 10253cosh(x) + 15126cosh(x) +--R + +--R - 894cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 288cosh(x) - 5184cosh(x) - 660cosh(x) + 16428cosh(x) +--R + +--R 2 +--R 3380cosh(x) + 252 +--R * +--R 7 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 32cosh(x) - 2304cosh(x) - 5560cosh(x) + 9948cosh(x) +--R + +--R 3 +--R 8748cosh(x) - 1968cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 576cosh(x) - 4410cosh(x) + 1300cosh(x) + 8372cosh(x) +--R + +--R 2 +--R 1148cosh(x) + 62 +--R * +--R 5 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 64cosh(x) - 1953cosh(x) - 2436cosh(x) + 4712cosh(x) +--R + +--R 3 +--R 3268cosh(x) - 903cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 562cosh(x) - 1898cosh(x) + 844cosh(x) + 2324cosh(x) +--R + +--R 2 +--R 454cosh(x) + 6 +--R * +--R 3 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 104cosh(x) - 698cosh(x) - 476cosh(x) + 1016cosh(x) +--R + +--R 3 +--R 604cosh(x) - 126cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 12cosh(x) - 158cosh(x) - 336cosh(x) + 116cosh(x) +--R + +--R 4 2 +--R 300cosh(x) + 90cosh(x) +--R * +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R - cosh(x) - 18cosh(x) - 58cosh(x) - 12cosh(x) + 59cosh(x) +--R + +--R 3 +--R 30cosh(x) +--R / +--R 18 17 2 16 +--R 32sinh(x) + 384cosh(x)sinh(x) + (2112cosh(x) + 448)sinh(x) +--R + +--R 3 15 +--R (7040cosh(x) + 4096cosh(x))sinh(x) +--R + +--R 4 2 14 +--R (15840cosh(x) + 17408cosh(x) + 2278)sinh(x) +--R + +--R 5 3 13 +--R (25344cosh(x) + 45824cosh(x) + 15560cosh(x))sinh(x) +--R + +--R 6 4 2 12 +--R (29568cosh(x) + 83648cosh(x) + 51660cosh(x) + 5710)sinh(x) +--R + +--R 7 5 3 11 +--R (25344cosh(x) + 111616cosh(x) + 110504cosh(x) + 27576cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 15840cosh(x) + 111104cosh(x) + 168442cosh(x) + 73652cosh(x) +--R + +--R 7996 +--R * +--R 10 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 7040cosh(x) + 82432cosh(x) + 190608cosh(x) + 131688cosh(x) +--R + +--R 24352cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 2112cosh(x) + 44864cosh(x) + 161832cosh(x) + 168106cosh(x) +--R + +--R 2 +--R 55832cosh(x) + 6532 +--R * +--R 8 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 384cosh(x) + 17408cosh(x) + 102032cosh(x) + 161072cosh(x) +--R + +--R 3 +--R 82960cosh(x) + 9488cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 32cosh(x) + 4608cosh(x) + 46650cosh(x) + 115128cosh(x) +--R + +--R 4 2 +--R 89640cosh(x) + 23424cosh(x) + 3062 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 768cosh(x) + 15016cosh(x) + 59344cosh(x) + 70640cosh(x) +--R + +--R 3 +--R 26256cosh(x) + 168cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 64cosh(x) + 3276cosh(x) + 21570cosh(x) + 41408cosh(x) +--R + +--R 4 2 +--R 25992cosh(x) + 5684cosh(x) + 750 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 456cosh(x) + 5272cosh(x) + 15984cosh(x) + 15152cosh(x) +--R + +--R 3 +--R 3336cosh(x) - 840cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 38cosh(x) + 852cosh(x) + 4220cosh(x) + 7008cosh(x) +--R + +--R 4 2 +--R 4118cosh(x) + 876cosh(x) + 72 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R 72cosh(x) + 624cosh(x) + 1584cosh(x) + 1248cosh(x) + 72cosh(x) +--R + +--R - 144cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 6cosh(x) + 72cosh(x) + 276cosh(x) + 432cosh(x) + 294cosh(x) +--R + +--R 2 +--R 72cosh(x) +--R Type: Expression Integer +--E 30 + +--S 31 of 531 +t1006:= x*cosh(2*x)*sech(x)^2 +--R +--R +--R 2 +--R (31) x cosh(2x)sech(x) +--R Type: Expression Integer +--E 31 + +--S 32 of 531 +r1006:= x^2+log(cosh(x))-x*tanh(x) +--R +--R +--R 2 +--R (32) log(cosh(x)) - x tanh(x) + x +--R Type: Expression Integer +--E 32 + +--S 33 of 531 +a1006:= integrate(t1006,x) +--R +--R +--R (33) +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (x - 2x)sinh(x) + (2x - 4x)cosh(x)sinh(x) + (x - 2x)cosh(x) + x +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 531 +m1006:= a1006-r1006 +--R +--R +--R (34) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)log(cosh(x)) +--R + +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) + x)tanh(x) - 2x sinh(x) +--R + +--R 2 +--R - 4x cosh(x)sinh(x) - 2x cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Expression Integer +--E 34 + +--S 35 of 531 +d1006:= D(m1006,x) +--R +--R +--R (35) +--R 4 3 2 2 +--R - x sinh(x) - 4x cosh(x)sinh(x) + (- 6x cosh(x) - 2x)sinh(x) +--R + +--R 3 4 2 +--R (- 4x cosh(x) - 4x cosh(x))sinh(x) - x cosh(x) - 2x cosh(x) - x +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R (x - 1)sinh(x) + (4x - 4)cosh(x)sinh(x) +--R + +--R 2 2 3 +--R ((6x - 6)cosh(x) - 2x)sinh(x) + ((4x - 4)cosh(x) - 4x cosh(x))sinh(x) +--R + +--R 4 2 +--R (x - 1)cosh(x) - 2x cosh(x) + x + 1 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Expression Integer +--E 35 + +--S 36 of 531 +t1007:= x*cosh(2*x)*sech(x)^3 +--R +--R +--R 3 +--R (36) x cosh(2x)sech(x) +--R Type: Expression Integer +--E 36 + +--S 37 of 531 +r1007:= 3*x*atan(exp(x))-3/2*%i*polylog(2,-%i*exp(x))+_ + 3/2*%i*polylog(2,%i*exp(x))-1/2*sech(x)-1/2*x*sech(x)*tanh(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 531 +a1007:= integrate(t1007,x) +--R +--R +--R x +--R ++ 3 +--R (37) | %Q cosh(2%Q)sech(%Q) d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 531 +--m1007:= a1007-r1007 +--E 39 + +--S 40 of 531 +--d1007:= D(m1007,x) +--E 40 + +--S 41 of 531 +t1008:= sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R \|sinh(b x + a) +--R (38) ---------------- +--R +-------------+ +--R \|cosh(b x + a) +--R Type: Expression Integer +--E 41 + +--S 42 of 531 +r1008:= -(atan(sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2))-_ + atanh(sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2)))/b +--R +--R +--R +-------------+ +-------------+ +--R \|sinh(b x + a) \|sinh(b x + a) +--R atanh(----------------) - atan(----------------) +--R +-------------+ +-------------+ +--R \|cosh(b x + a) \|cosh(b x + a) +--R (39) ------------------------------------------------ +--R b +--R Type: Expression Integer +--E 42 + +--S 43 of 531 +a1008:= integrate(t1008,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 531 +--m1008:= a1008-r1008 +--E 44 + +--S 45 of 531 +--d1008:= D(m1008,x) +--E 45 + +--S 46 of 531 +t1009:= cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R \|cosh(b x + a) +--R (40) ---------------- +--R +-------------+ +--R \|sinh(b x + a) +--R Type: Expression Integer +--E 46 + +--S 47 of 531 +r1009:= -(atan(cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2))-_ + atanh(cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2)))/b +--R +--R +--R +-------------+ +-------------+ +--R \|cosh(b x + a) \|cosh(b x + a) +--R atanh(----------------) - atan(----------------) +--R +-------------+ +-------------+ +--R \|sinh(b x + a) \|sinh(b x + a) +--R (41) ------------------------------------------------ +--R b +--R Type: Expression Integer +--E 47 + +--S 48 of 531 +a1009:= integrate(t1009,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 48 + +--S 49 of 531 +--m1009:= a1009-r1009 +--E 49 + +--S 50 of 531 +--d1009:= D(m1009,x) +--E 50 + +--S 51 of 531 +t1010:= sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3) +--R +--R +--R 3+-------------+ +--R \|sinh(b x + a) +--R (42) ---------------- +--R 3+-------------+ +--R \|cosh(b x + a) +--R Type: Expression Integer +--E 51 + +--S 52 of 531 +r1010:= -1/2*3^(1/2)*atan(1/3*(1+2*sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))*_ + 3^(1/2))/b-1/2*log(1-sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/4*_ + log(1+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3)+_ + sinh(a+b*x)^(4/3)/cosh(a+b*x)^(4/3))/b +--R +--R +--R (43) +--R log +--R 3+-------------+2 +--R cosh(b x + a)\|sinh(b x + a) +--R + +--R 3+-------------+3+-------------+ +--R sinh(b x + a)\|cosh(b x + a) \|sinh(b x + a) +--R + +--R 3+-------------+2 +--R cosh(b x + a)\|cosh(b x + a) +--R / +--R 3+-------------+2 +--R cosh(b x + a)\|cosh(b x + a) +--R + +--R 3+-------------+2 3+-------------+2 +--R - \|sinh(b x + a) + \|cosh(b x + a) +--R - 2log(---------------------------------------) +--R 3+-------------+2 +--R \|cosh(b x + a) +--R + +--R +-+3+-------------+2 +-+3+-------------+2 +--R +-+ 2\|3 \|sinh(b x + a) + \|3 \|cosh(b x + a) +--R - 2\|3 atan(----------------------------------------------) +--R 3+-------------+2 +--R 3\|cosh(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 52 + +--S 53 of 531 +a1010:= integrate(t1010,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 53 + +--S 54 of 531 +--m1010:= a1010-r1010 +--E 54 + +--S 55 of 531 +--d1010:= D(m1010,x) +--E 55 + +--S 56 of 531 +t1011:= cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3) +--R +--R +--R 3+-------------+ +--R \|cosh(b x + a) +--R (44) ---------------- +--R 3+-------------+ +--R \|sinh(b x + a) +--R Type: Expression Integer +--E 56 + +--S 57 of 531 +r1011:= -1/2*3^(1/2)*atan(1/3*(1+2*cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))*_ + 3^(1/2))/b-1/2*log(1-cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b+1/4*_ + log(1+cosh(a+b*x)^(4/3)/sinh(a+b*x)^(4/3)+_ + cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b +--R +--R +--R (45) +--R log +--R 3+-------------+2 +--R sinh(b x + a)\|sinh(b x + a) +--R + +--R 3+-------------+3+-------------+ +--R cosh(b x + a)\|cosh(b x + a) \|sinh(b x + a) +--R + +--R 3+-------------+2 +--R sinh(b x + a)\|cosh(b x + a) +--R / +--R 3+-------------+2 +--R sinh(b x + a)\|sinh(b x + a) +--R + +--R 3+-------------+2 3+-------------+2 +--R \|sinh(b x + a) - \|cosh(b x + a) +--R - 2log(-------------------------------------) +--R 3+-------------+2 +--R \|sinh(b x + a) +--R + +--R +-+3+-------------+2 +-+3+-------------+2 +--R +-+ \|3 \|sinh(b x + a) + 2\|3 \|cosh(b x + a) +--R - 2\|3 atan(----------------------------------------------) +--R 3+-------------+2 +--R 3\|sinh(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 57 + +--S 58 of 531 +a1011:= integrate(t1011,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 58 + +--S 59 of 531 +--m1011:= a1011-r1011 +--E 59 + +--S 60 of 531 +--d1011:= D(m1011,x) +--E 60 + +--S 61 of 531 +t1012:= cosh(x)^(2/3)/sinh(x)^(8/3) +--R +--R +--R 3+-------+2 +--R \|cosh(x) +--R (46) ------------------- +--R 2 3+-------+2 +--R sinh(x) \|sinh(x) +--R Type: Expression Integer +--E 61 + +--S 62 of 531 +r1012:= -3/5*cosh(x)^(5/3)/sinh(x)^(5/3) +--R +--R +--R 3+-------+2 +--R 3cosh(x)\|cosh(x) +--R (47) - ------------------- +--R 3+-------+2 +--R 5sinh(x)\|sinh(x) +--R Type: Expression Integer +--E 62 + +--S 63 of 531 +a1012:= integrate(t1012,x) +--R +--R +--R (48) +--R 3 2 +--R - 9234sinh(x) - 27702cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 27702cosh(x) - 9234)sinh(x) - 9234cosh(x) - 9234cosh(x) +--R * +--R 3+-------+2 3+-------+ +--R \|cosh(x) \|sinh(x) +--R + +--R 4 3 2 2 +--R 1745sinh(x) + 6980cosh(x)sinh(x) + (10470cosh(x) - 3490)sinh(x) +--R + +--R 3 4 2 +--R (6980cosh(x) - 6980cosh(x))sinh(x) + 1745cosh(x) - 3490cosh(x) + 1745 +--R / +--R 4 3 2 2 +--R 7695sinh(x) + 30780cosh(x)sinh(x) + (46170cosh(x) - 15390)sinh(x) +--R + +--R 3 4 2 +--R (30780cosh(x) - 30780cosh(x))sinh(x) + 7695cosh(x) - 15390cosh(x) + 7695 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 531 +m1012:= a1012-r1012 +--R +--R +--R (49) +--R 5 4 2 3 +--R 1745sinh(x) + 6980cosh(x)sinh(x) + (10470cosh(x) - 3490)sinh(x) +--R + +--R 3 2 +--R (6980cosh(x) - 6980cosh(x))sinh(x) +--R + +--R 4 2 +--R (1745cosh(x) - 3490cosh(x) + 1745)sinh(x) +--R * +--R 3+-------+2 +--R \|sinh(x) +--R + +--R 5 4 +--R - 9234sinh(x) - 23085cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 9234cosh(x) - 9234)sinh(x) +--R + +--R 3 2 +--R (18468cosh(x) - 18468cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (18468cosh(x) - 18468cosh(x) )sinh(x) + 4617cosh(x) - 9234cosh(x) +--R + +--R 4617cosh(x) +--R * +--R 3+-------+2 +--R \|cosh(x) +--R / +--R 5 4 2 3 +--R 7695sinh(x) + 30780cosh(x)sinh(x) + (46170cosh(x) - 15390)sinh(x) +--R + +--R 3 2 +--R (30780cosh(x) - 30780cosh(x))sinh(x) +--R + +--R 4 2 +--R (7695cosh(x) - 15390cosh(x) + 7695)sinh(x) +--R * +--R 3+-------+2 +--R \|sinh(x) +--R Type: Expression Integer +--E 64 + +--S 65 of 531 +d1012:= D(m1012,x) +--R +--R +--R (50) +--R 9 8 2 7 +--R - 4sinh(x) - 9cosh(x)sinh(x) + 18cosh(x) sinh(x) +--R + +--R 3 6 4 2 5 +--R (80cosh(x) + 21cosh(x))sinh(x) + (90cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 4 +--R (6cosh(x) + 33cosh(x) + 25cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (- 74cosh(x) + 36cosh(x) + 38cosh(x) )sinh(x) +--R + +--R 7 5 3 2 +--R (- 72cosh(x) + 75cosh(x) + 2cosh(x) - 5cosh(x))sinh(x) +--R + +--R 8 6 4 9 7 +--R (- 30cosh(x) + 60cosh(x) - 30cosh(x) )sinh(x) - 5cosh(x) + 15cosh(x) +--R + +--R 5 3 +--R - 15cosh(x) + 5cosh(x) +--R / +--R 8 7 2 6 +--R 5sinh(x) + 30cosh(x)sinh(x) + (75cosh(x) - 15)sinh(x) +--R + +--R 3 5 +--R (100cosh(x) - 60cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (75cosh(x) - 90cosh(x) + 15)sinh(x) +--R + +--R 5 3 3 +--R (30cosh(x) - 60cosh(x) + 30cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (5cosh(x) - 15cosh(x) + 15cosh(x) - 5)sinh(x) +--R * +--R 3+-------+3+-------+2 +--R \|cosh(x) \|sinh(x) +--R Type: Expression Integer +--E 65 + +--S 66 of 531 +t1013:= sinh(x)^(2/3)/cosh(x)^(8/3) +--R +--R +--R 3+-------+2 +--R \|sinh(x) +--R (51) ------------------- +--R 2 3+-------+2 +--R cosh(x) \|cosh(x) +--R Type: Expression Integer +--E 66 + +--S 67 of 531 +r1013:= 3/5*sinh(x)^(5/3)/cosh(x)^(5/3) +--R +--R +--R 3+-------+2 +--R 3sinh(x)\|sinh(x) +--R (52) ------------------- +--R 3+-------+2 +--R 5cosh(x)\|cosh(x) +--R Type: Expression Integer +--E 67 + +--S 68 of 531 +a1013:= integrate(t1013,x) +--R +--R +--R (53) +--R 3 2 2 +--R 14250sinh(x) + 42750cosh(x)sinh(x) + (42750cosh(x) - 14250)sinh(x) +--R + +--R 3 +--R 14250cosh(x) - 14250cosh(x) +--R * +--R 3+-------+3+-------+2 +--R \|cosh(x) \|sinh(x) +--R + +--R 4 3 2 2 +--R - 5869sinh(x) - 23476cosh(x)sinh(x) + (- 35214cosh(x) - 11738)sinh(x) +--R + +--R 3 4 2 +--R (- 23476cosh(x) - 23476cosh(x))sinh(x) - 5869cosh(x) - 11738cosh(x) +--R + +--R - 5869 +--R / +--R 4 3 2 2 +--R 11875sinh(x) + 47500cosh(x)sinh(x) + (71250cosh(x) + 23750)sinh(x) +--R + +--R 3 4 2 +--R (47500cosh(x) + 47500cosh(x))sinh(x) + 11875cosh(x) + 23750cosh(x) +--R + +--R 11875 +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 531 +m1013:= a1013-r1013 +--R +--R +--R (54) +--R 5 4 +--R - 7125sinh(x) - 28500cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 28500cosh(x) - 14250)sinh(x) +--R + +--R 3 2 +--R (14250cosh(x) - 28500cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (35625cosh(x) - 28500cosh(x) - 7125)sinh(x) + 14250cosh(x) +--R + +--R 3 +--R - 14250cosh(x) +--R * +--R 3+-------+2 +--R \|sinh(x) +--R + +--R 4 2 3 +--R - 5869cosh(x)sinh(x) - 23476cosh(x) sinh(x) +--R + +--R 3 2 +--R (- 35214cosh(x) - 11738cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (- 23476cosh(x) - 23476cosh(x) )sinh(x) - 5869cosh(x) +--R + +--R 3 +--R - 11738cosh(x) - 5869cosh(x) +--R * +--R 3+-------+2 +--R \|cosh(x) +--R / +--R 4 2 3 +--R 11875cosh(x)sinh(x) + 47500cosh(x) sinh(x) +--R + +--R 3 2 +--R (71250cosh(x) + 23750cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (47500cosh(x) + 47500cosh(x) )sinh(x) + 11875cosh(x) + 23750cosh(x) +--R + +--R 11875cosh(x) +--R * +--R 3+-------+2 +--R \|cosh(x) +--R Type: Expression Integer +--E 69 + +--S 70 of 531 +d1013:= D(m1013,x) +--R +--R +--R (55) +--R 9 8 2 7 +--R 5sinh(x) + 30cosh(x)sinh(x) + (72cosh(x) + 15)sinh(x) +--R + +--R 3 6 +--R (74cosh(x) + 60cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (- 6cosh(x) + 75cosh(x) + 15)sinh(x) +--R + +--R 5 3 4 +--R (- 90cosh(x) + 36cosh(x) + 30cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (- 80cosh(x) + 33cosh(x) - 2cosh(x) + 5)sinh(x) +--R + +--R 7 5 3 2 +--R (- 18cosh(x) + 48cosh(x) - 38cosh(x) )sinh(x) +--R + +--R 8 6 4 2 9 +--R (9cosh(x) + 21cosh(x) - 25cosh(x) - 5cosh(x) )sinh(x) + 4cosh(x) +--R + +--R 5 +--R - 4cosh(x) +--R / +--R 2 6 3 5 +--R 5cosh(x) sinh(x) + 30cosh(x) sinh(x) +--R + +--R 4 2 4 5 3 3 +--R (75cosh(x) + 15cosh(x) )sinh(x) + (100cosh(x) + 60cosh(x) )sinh(x) +--R + +--R 6 4 2 2 +--R (75cosh(x) + 90cosh(x) + 15cosh(x) )sinh(x) +--R + +--R 7 5 3 8 6 +--R (30cosh(x) + 60cosh(x) + 30cosh(x) )sinh(x) + 5cosh(x) + 15cosh(x) +--R + +--R 4 2 +--R 15cosh(x) + 5cosh(x) +--R * +--R 3+-------+2 3+-------+ +--R \|cosh(x) \|sinh(x) +--R Type: Expression Integer +--E 70 + +--S 71 of 531 +t1014:= cosh(x)*csch(x)^(7/3) +--R +--R +--R 2 3+-------+ +--R (56) cosh(x)csch(x) \|csch(x) +--R Type: Expression Integer +--E 71 + +--S 72 of 531 +r1014:= -3/4*csch(x)^(4/3) +--R +--R +--R 3+-------+ +--R 3csch(x)\|csch(x) +--R (57) - ------------------ +--R 4 +--R Type: Expression Integer +--E 72 + +--S 73 of 531 +a1014:= integrate(t1014,x) +--R +--R +--R (58) +--R +-----------------------------------------+ +--R | 2sinh(x) + 2cosh(x) +--R (- 3sinh(x) - 3cosh(x)) |----------------------------------------- +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 6)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) - 24cosh(x))sinh(x) + (30cosh(x) - 36cosh(x) + 6)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 24cosh(x) + 12cosh(x))sinh(x) + 2cosh(x) - 6cosh(x) +--R + +--R 2 +--R 6cosh(x) - 2 +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 531 +m1014:= a1014-r1014 +--R +--R +--R (59) +--R 6 5 +--R 3csch(x)sinh(x) + 18cosh(x)csch(x)sinh(x) +--R + +--R 2 4 +--R (45cosh(x) - 9)csch(x)sinh(x) +--R + +--R 3 3 +--R (60cosh(x) - 36cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (45cosh(x) - 54cosh(x) + 9)csch(x)sinh(x) +--R + +--R 5 3 +--R (18cosh(x) - 36cosh(x) + 18cosh(x))csch(x)sinh(x) +--R + +--R 6 4 2 +--R (3cosh(x) - 9cosh(x) + 9cosh(x) - 3)csch(x) +--R * +--R 3+-------+ +--R \|csch(x) +--R + +--R +-----------------------------------------+ +--R | 2sinh(x) + 2cosh(x) +--R (- 6sinh(x) - 6cosh(x)) |----------------------------------------- +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 12)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 48cosh(x))sinh(x) + (60cosh(x) - 72cosh(x) + 12)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 48cosh(x) + 24cosh(x))sinh(x) + 4cosh(x) - 12cosh(x) +--R + +--R 2 +--R 12cosh(x) - 4 +--R Type: Expression Integer +--E 74 + +--S 75 of 531 +d1014:= D(m1014,x) +--R +--R +--R (60) +--R 4 3 2 2 +--R 16sinh(x) + 64cosh(x)sinh(x) + (96cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (64cosh(x) + 8cosh(x))sinh(x) + 16cosh(x) + 4cosh(x) +--R * +--R 3+-------+2 +--R \|csch(x) +--R + +--R 2 10 2 9 +--R - coth(x)csch(x) sinh(x) - 10cosh(x)coth(x)csch(x) sinh(x) +--R + +--R 2 2 8 +--R (- 45cosh(x) + 5)coth(x)csch(x) sinh(x) +--R + +--R 3 2 7 +--R (- 120cosh(x) + 40cosh(x))coth(x)csch(x) sinh(x) +--R + +--R 4 2 2 6 +--R (- 210cosh(x) + 140cosh(x) - 10)coth(x)csch(x) sinh(x) +--R + +--R 5 3 2 5 +--R (- 252cosh(x) + 280cosh(x) - 60cosh(x))coth(x)csch(x) sinh(x) +--R + +--R 6 4 2 2 +--R (- 210cosh(x) + 350cosh(x) - 150cosh(x) + 10)coth(x)csch(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 120cosh(x) + 280cosh(x) - 200cosh(x) + 40cosh(x))coth(x) +--R * +--R 2 3 +--R csch(x) sinh(x) +--R + +--R 8 6 4 2 +--R (- 45cosh(x) + 140cosh(x) - 150cosh(x) + 60cosh(x) - 5)coth(x) +--R * +--R 2 2 +--R csch(x) sinh(x) +--R + +--R 9 7 5 3 +--R (- 10cosh(x) + 40cosh(x) - 60cosh(x) + 40cosh(x) - 10cosh(x)) +--R * +--R 2 +--R coth(x)csch(x) sinh(x) +--R + +--R 10 8 6 4 2 +--R (- cosh(x) + 5cosh(x) - 10cosh(x) + 10cosh(x) - 5cosh(x) + 1) +--R * +--R 2 +--R coth(x)csch(x) +--R * +--R +-----------------------------------------+2 +--R | 2sinh(x) + 2cosh(x) +--R |----------------------------------------- +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 10 9 2 8 +--R sinh(x) + 10cosh(x)sinh(x) + (45cosh(x) - 5)sinh(x) +--R + +--R 3 7 +--R (120cosh(x) - 40cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (210cosh(x) - 140cosh(x) + 10)sinh(x) +--R + +--R 5 3 5 +--R (252cosh(x) - 280cosh(x) + 60cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (210cosh(x) - 350cosh(x) + 150cosh(x) - 10)sinh(x) +--R + +--R 7 5 3 3 +--R (120cosh(x) - 280cosh(x) + 200cosh(x) - 40cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (45cosh(x) - 140cosh(x) + 150cosh(x) - 60cosh(x) + 5)sinh(x) +--R + +--R 9 7 5 3 +--R (10cosh(x) - 40cosh(x) + 60cosh(x) - 40cosh(x) + 10cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 5cosh(x) + 10cosh(x) - 10cosh(x) + 5cosh(x) - 1 +--R * +--R +-----------------------------------------+2 +--R | 2sinh(x) + 2cosh(x) 3+-------+2 +--R |----------------------------------------- \|csch(x) +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression Integer +--E 75 + +--S 76 of 531 +t1015:= (1+coth(x))^(1/2)*sech(x)^2 +--R +--R +--R 2 +-----------+ +--R (61) sech(x) \|coth(x) + 1 +--R Type: Expression Integer +--E 76 + +--S 77 of 531 +r1015:= atanh((1+coth(x))^(1/2))+(1+coth(x))^(1/2)*tanh(x) +--R +--R +--R +-----------+ +-----------+ +--R (62) atanh(\|coth(x) + 1 ) + tanh(x)\|coth(x) + 1 +--R Type: Expression Integer +--E 77 + +--S 78 of 531 +a1015:= integrate(t1015,x) +--R +--R +--R (63) +--R 12 11 2 10 +--R sinh(x) + 12cosh(x)sinh(x) + (66cosh(x) + 8)sinh(x) +--R + +--R 3 9 +--R (220cosh(x) + 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (495cosh(x) + 360cosh(x) - 16)sinh(x) +--R + +--R 5 3 7 +--R (792cosh(x) + 960cosh(x) - 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (924cosh(x) + 1680cosh(x) - 448cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 5 +--R (792cosh(x) + 2016cosh(x) - 896cosh(x) + 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (495cosh(x) + 1680cosh(x) - 1120cosh(x) + 360cosh(x) - 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 220cosh(x) + 960cosh(x) - 896cosh(x) + 480cosh(x) +--R + +--R - 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 66cosh(x) + 360cosh(x) - 448cosh(x) + 360cosh(x) +--R + +--R 2 +--R - 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 12cosh(x) + 80cosh(x) - 128cosh(x) + 144cosh(x) +--R + +--R 3 +--R - 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R cosh(x) + 8cosh(x) - 16cosh(x) + 24cosh(x) - 32cosh(x) + 16 +--R * +--R log +--R 5 4 2 3 +--R 4sinh(x) + 20cosh(x)sinh(x) + (40cosh(x) - 4)sinh(x) +--R + +--R 3 2 +--R (40cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (20cosh(x) - 12cosh(x) )sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 +--R - sinh(x) - 12cosh(x)sinh(x) + (- 66cosh(x) - 8)sinh(x) +--R + +--R 3 9 +--R (- 220cosh(x) - 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 495cosh(x) - 360cosh(x) + 16)sinh(x) +--R + +--R 5 3 7 +--R (- 792cosh(x) - 960cosh(x) + 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 924cosh(x) - 1680cosh(x) + 448cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 5 +--R (- 792cosh(x) - 2016cosh(x) + 896cosh(x) - 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 495cosh(x) - 1680cosh(x) + 1120cosh(x) - 360cosh(x) + 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 220cosh(x) - 960cosh(x) + 896cosh(x) - 480cosh(x) +--R + +--R 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 66cosh(x) - 360cosh(x) + 448cosh(x) - 360cosh(x) +--R + +--R 2 +--R 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 12cosh(x) - 80cosh(x) + 128cosh(x) - 144cosh(x) +--R + +--R 3 +--R 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - cosh(x) - 8cosh(x) + 16cosh(x) - 24cosh(x) + 32cosh(x) - 16 +--R * +--R log +--R 5 4 2 3 +--R - 4sinh(x) - 20cosh(x)sinh(x) + (- 40cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R (- 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (- 20cosh(x) + 12cosh(x) )sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 11 10 2 9 +--R - 8sinh(x) - 88cosh(x)sinh(x) + (- 440cosh(x) + 104)sinh(x) +--R + +--R 3 8 +--R (- 1320cosh(x) + 936cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (- 2640cosh(x) + 3744cosh(x) - 224)sinh(x) +--R + +--R 5 3 6 +--R (- 3696cosh(x) + 8736cosh(x) - 1568cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (- 3696cosh(x) + 13104cosh(x) - 4704cosh(x) + 160)sinh(x) +--R + +--R 7 5 3 4 +--R (- 2640cosh(x) + 13104cosh(x) - 7840cosh(x) + 800cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1320cosh(x) + 8736cosh(x) - 7840cosh(x) + 1600cosh(x) - 32) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 440cosh(x) + 3744cosh(x) - 4704cosh(x) + 1600cosh(x) +--R + +--R - 96cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 88cosh(x) + 936cosh(x) - 1568cosh(x) + 800cosh(x) +--R + +--R 2 +--R - 96cosh(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R - 8cosh(x) + 104cosh(x) - 224cosh(x) + 160cosh(x) - 32cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 12 11 2 10 +--R 4sinh(x) + 48cosh(x)sinh(x) + (264cosh(x) + 32)sinh(x) +--R + +--R 3 9 +--R (880cosh(x) + 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (1980cosh(x) + 1440cosh(x) - 64)sinh(x) +--R + +--R 5 3 7 +--R (3168cosh(x) + 3840cosh(x) - 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (3696cosh(x) + 6720cosh(x) - 1792cosh(x) + 96)sinh(x) +--R + +--R 7 5 3 5 +--R (3168cosh(x) + 8064cosh(x) - 3584cosh(x) + 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (1980cosh(x) + 6720cosh(x) - 4480cosh(x) + 1440cosh(x) - 128)sinh(x) +--R + +--R 9 7 5 3 +--R (880cosh(x) + 3840cosh(x) - 3584cosh(x) + 1920cosh(x) - 512cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 264cosh(x) + 1440cosh(x) - 1792cosh(x) + 1440cosh(x) +--R + +--R 2 +--R - 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (48cosh(x) + 320cosh(x) - 512cosh(x) + 576cosh(x) - 512cosh(x) ) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 4cosh(x) + 32cosh(x) - 64cosh(x) + 96cosh(x) - 128cosh(x) + 64 +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 531 +m1015:= a1015-r1015 +--R +--R +--R (64) +--R 12 11 2 10 +--R sinh(x) + 12cosh(x)sinh(x) + (66cosh(x) + 8)sinh(x) +--R + +--R 3 9 +--R (220cosh(x) + 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (495cosh(x) + 360cosh(x) - 16)sinh(x) +--R + +--R 5 3 7 +--R (792cosh(x) + 960cosh(x) - 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (924cosh(x) + 1680cosh(x) - 448cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 5 +--R (792cosh(x) + 2016cosh(x) - 896cosh(x) + 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (495cosh(x) + 1680cosh(x) - 1120cosh(x) + 360cosh(x) - 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 220cosh(x) + 960cosh(x) - 896cosh(x) + 480cosh(x) +--R + +--R - 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 66cosh(x) + 360cosh(x) - 448cosh(x) + 360cosh(x) +--R + +--R 2 +--R - 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 12cosh(x) + 80cosh(x) - 128cosh(x) + 144cosh(x) +--R + +--R 3 +--R - 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R cosh(x) + 8cosh(x) - 16cosh(x) + 24cosh(x) - 32cosh(x) + 16 +--R * +--R log +--R 5 4 2 3 +--R 4sinh(x) + 20cosh(x)sinh(x) + (40cosh(x) - 4)sinh(x) +--R + +--R 3 2 +--R (40cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (20cosh(x) - 12cosh(x) )sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 +--R - sinh(x) - 12cosh(x)sinh(x) + (- 66cosh(x) - 8)sinh(x) +--R + +--R 3 9 +--R (- 220cosh(x) - 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 495cosh(x) - 360cosh(x) + 16)sinh(x) +--R + +--R 5 3 7 +--R (- 792cosh(x) - 960cosh(x) + 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 924cosh(x) - 1680cosh(x) + 448cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 5 +--R (- 792cosh(x) - 2016cosh(x) + 896cosh(x) - 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 495cosh(x) - 1680cosh(x) + 1120cosh(x) - 360cosh(x) + 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 220cosh(x) - 960cosh(x) + 896cosh(x) - 480cosh(x) +--R + +--R 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 66cosh(x) - 360cosh(x) + 448cosh(x) - 360cosh(x) +--R + +--R 2 +--R 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 12cosh(x) - 80cosh(x) + 128cosh(x) - 144cosh(x) +--R + +--R 3 +--R 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - cosh(x) - 8cosh(x) + 16cosh(x) - 24cosh(x) + 32cosh(x) - 16 +--R * +--R log +--R 5 4 2 3 +--R - 4sinh(x) - 20cosh(x)sinh(x) + (- 40cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R (- 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (- 20cosh(x) + 12cosh(x) )sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 +--R - 4sinh(x) - 48cosh(x)sinh(x) + (- 264cosh(x) - 32)sinh(x) +--R + +--R 3 9 +--R (- 880cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 1980cosh(x) - 1440cosh(x) + 64)sinh(x) +--R + +--R 5 3 7 +--R (- 3168cosh(x) - 3840cosh(x) + 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 3696cosh(x) - 6720cosh(x) + 1792cosh(x) - 96)sinh(x) +--R + +--R 7 5 3 5 +--R (- 3168cosh(x) - 8064cosh(x) + 3584cosh(x) - 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1980cosh(x) - 6720cosh(x) + 4480cosh(x) - 1440cosh(x) + 128) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 880cosh(x) - 3840cosh(x) + 3584cosh(x) - 1920cosh(x) +--R + +--R 512cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 264cosh(x) - 1440cosh(x) + 1792cosh(x) - 1440cosh(x) +--R + +--R 2 +--R 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) + 512cosh(x) - 576cosh(x) +--R + +--R 3 +--R 512cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 4cosh(x) - 32cosh(x) + 64cosh(x) - 96cosh(x) + 128cosh(x) - 64 +--R * +--R +-----------+ +--R atanh(\|coth(x) + 1 ) +--R + +--R 12 11 2 10 +--R - 4sinh(x) - 48cosh(x)sinh(x) + (- 264cosh(x) - 32)sinh(x) +--R + +--R 3 9 +--R (- 880cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 1980cosh(x) - 1440cosh(x) + 64)sinh(x) +--R + +--R 5 3 7 +--R (- 3168cosh(x) - 3840cosh(x) + 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 3696cosh(x) - 6720cosh(x) + 1792cosh(x) - 96)sinh(x) +--R + +--R 7 5 3 5 +--R (- 3168cosh(x) - 8064cosh(x) + 3584cosh(x) - 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1980cosh(x) - 6720cosh(x) + 4480cosh(x) - 1440cosh(x) + 128) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 880cosh(x) - 3840cosh(x) + 3584cosh(x) - 1920cosh(x) +--R + +--R 512cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 264cosh(x) - 1440cosh(x) + 1792cosh(x) - 1440cosh(x) +--R + +--R 2 +--R 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) + 512cosh(x) - 576cosh(x) +--R + +--R 3 +--R 512cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 4cosh(x) - 32cosh(x) + 64cosh(x) - 96cosh(x) + 128cosh(x) - 64 +--R * +--R +-----------+ +--R tanh(x)\|coth(x) + 1 +--R + +--R 11 10 2 9 +--R - 8sinh(x) - 88cosh(x)sinh(x) + (- 440cosh(x) + 104)sinh(x) +--R + +--R 3 8 +--R (- 1320cosh(x) + 936cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (- 2640cosh(x) + 3744cosh(x) - 224)sinh(x) +--R + +--R 5 3 6 +--R (- 3696cosh(x) + 8736cosh(x) - 1568cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (- 3696cosh(x) + 13104cosh(x) - 4704cosh(x) + 160)sinh(x) +--R + +--R 7 5 3 4 +--R (- 2640cosh(x) + 13104cosh(x) - 7840cosh(x) + 800cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1320cosh(x) + 8736cosh(x) - 7840cosh(x) + 1600cosh(x) - 32) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 440cosh(x) + 3744cosh(x) - 4704cosh(x) + 1600cosh(x) +--R + +--R - 96cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 88cosh(x) + 936cosh(x) - 1568cosh(x) + 800cosh(x) +--R + +--R 2 +--R - 96cosh(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R - 8cosh(x) + 104cosh(x) - 224cosh(x) + 160cosh(x) - 32cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 12 11 2 10 +--R 4sinh(x) + 48cosh(x)sinh(x) + (264cosh(x) + 32)sinh(x) +--R + +--R 3 9 +--R (880cosh(x) + 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (1980cosh(x) + 1440cosh(x) - 64)sinh(x) +--R + +--R 5 3 7 +--R (3168cosh(x) + 3840cosh(x) - 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (3696cosh(x) + 6720cosh(x) - 1792cosh(x) + 96)sinh(x) +--R + +--R 7 5 3 5 +--R (3168cosh(x) + 8064cosh(x) - 3584cosh(x) + 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (1980cosh(x) + 6720cosh(x) - 4480cosh(x) + 1440cosh(x) - 128)sinh(x) +--R + +--R 9 7 5 3 +--R (880cosh(x) + 3840cosh(x) - 3584cosh(x) + 1920cosh(x) - 512cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 264cosh(x) + 1440cosh(x) - 1792cosh(x) + 1440cosh(x) +--R + +--R 2 +--R - 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (48cosh(x) + 320cosh(x) - 512cosh(x) + 576cosh(x) - 512cosh(x) ) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 4cosh(x) + 32cosh(x) - 64cosh(x) + 96cosh(x) - 128cosh(x) + 64 +--R Type: Expression Integer +--E 79 + +--S 80 of 531 +--d1015:= D(m1015,x) +--E 80 + +--S 81 of 531 +t1016:= sinh(x)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R sinh(x) +--R (65) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 81 + +--S 82 of 531 +r1016:= (-b*x+a*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) +--R +--R +--R - a log(b sinh(x) + a cosh(x)) + b x +--R (66) ------------------------------------ +--R 2 2 +--R b - a +--R Type: Expression Integer +--E 82 + +--S 83 of 531 +a1016:= integrate(t1016,x) +--R +--R +--R - 2b sinh(x) - 2a cosh(x) +--R - a log(-------------------------) + (b + a)x +--R sinh(x) - cosh(x) +--R (67) --------------------------------------------- +--R 2 2 +--R b - a +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 531 +m1016:= a1016-r1016 +--R +--R +--R - 2b sinh(x) - 2a cosh(x) +--R a log(b sinh(x) + a cosh(x)) - a log(-------------------------) + a x +--R sinh(x) - cosh(x) +--R (68) --------------------------------------------------------------------- +--R 2 2 +--R b - a +--R Type: Expression Integer +--E 84 + +--S 85 of 531 +d1016:= D(m1016,x) +--R +--R +--R (69) 0 +--R Type: Expression Integer +--E 85 + +--S 86 of 531 +t1017:= sinh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (70) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 86 + +--S 87 of 531 +r1017:= -a^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) +--R +--R +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R a atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (71) --------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression Integer +--E 87 + +--S 88 of 531 +a1017:= integrate(t1017,x) +--R +--R +--R (72) +--R [ +--R 2 2 +--R (2a sinh(x) + 2a cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4a sinh(x) - 4a cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 88 + +--S 89 of 531 +m1017a:= a1017.1-r1017 +--R +--R +--R (73) +--R +---------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R 2 2 | 2 2 a sinh(x) + b cosh(x) +--R (- 2a sinh(x) - 2a cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression Integer +--E 89 + +--S 90 of 531 +d1017a:= D(m1017a,x) +--R +--R +--R (74) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- b - 6a b - 9a b - 4a b)cosh(x) + b + 2a b - 2a b - 6a b +--R + +--R 4 +--R a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 4a b - 12a b - 12a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 6a b - 14a b - 2a b - 2a )cosh(x) + 2a b + a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 4b - 12a b + 4a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 6a b - 6a b - 6a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 4 +--R (b + 2a b + a b )cosh(x) + (- 3b - 4a b + 4a b - a )cosh(x) +--R + +--R 4 3 2 2 4 2 4 2 2 4 +--R (3b + 2a b - 7a b + 2a )cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 90 + +--S 91 of 531 +m1017b:= a1017.2-r1017 +--R +--R +--R (75) +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4a sinh(x) - 4a cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 a sinh(x) + b cosh(x) +--R (- 2a sinh(x) - 2a cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression Integer +--E 91 + +--S 92 of 531 +d1017b:= D(m1017b,x) +--R +--R +--R (76) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- b - 6a b - 9a b - 4a b)cosh(x) + b + 2a b - 2a b - 6a b +--R + +--R 4 +--R a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 4a b - 12a b - 12a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 6a b - 14a b - 2a b - 2a )cosh(x) + 2a b + a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 4b - 12a b + 4a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 6a b - 6a b - 6a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 4 +--R (b + 2a b + a b )cosh(x) + (- 3b - 4a b + 4a b - a )cosh(x) +--R + +--R 4 3 2 2 4 2 4 2 2 4 +--R (3b + 2a b - 7a b + 2a )cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 92 + +--S 93 of 531 +t1018:= sinh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R sinh(x) +--R (77) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 93 + +--S 94 of 531 +r1018:= -1/2*(-3*a^2*b*x+b^3*x+2*a^3*log(a*cosh(x)+_ + b*sinh(x))+a^2*cosh(x)*b*sinh(x)-b^3*cosh(x)*sinh(x)+_ + a^3-cosh(x)^2*a^3-b^2*a+cosh(x)^2*b^2*a)/(a^2-b^2)^2 +--R +--R +--R (78) +--R 3 3 2 +--R - 2a log(b sinh(x) + a cosh(x)) + (b - a b)cosh(x)sinh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- a b + a )cosh(x) + (- b + 3a b)x + a b - a +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression Integer +--E 94 + +--S 95 of 531 +a1018:= integrate(t1018,x) +--R +--R +--R (79) +--R 3 2 3 3 2 +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 4b + 12a b + 8a )x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 8b + 24a b + 16a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 4b + 12a b + 8a )x cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression Integer,...) +--E 95 + +--S 96 of 531 +m1018:= a1018-r1018 +--R +--R +--R (80) +--R 3 2 3 3 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 3 3 2 +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (b - a b - a b + a )sinh(x) + (- 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((- 2b - 2a b + 2a b + 2a )cosh(x) + 8a x - 4a b + 4a )sinh(x) +--R + +--R 2 3 3 3 2 3 +--R ((4a b - 4a )cosh(x) + (16a x - 8a b + 8a )cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b + 3a b - a b - 3a )cosh(x) + (8a x - 4a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression Integer +--E 96 + +--S 97 of 531 +d1018:= D(m1018,x) +--R +--R +--R 4 2 2 4 +--R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 +--R (81) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression Integer +--E 97 + +--S 98 of 531 +t1019:= sinh(x)/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R sinh(x) +--R (82) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 98 + +--S 99 of 531 +r1019:= -b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R (b sinh(x) + a b cosh(x))atan(---------------------) + a\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (83) -------------------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a +--R Type: Expression Integer +--E 99 + +--S 100 of 531 +a1019:= integrate(t1019,x) +--R +--R +--R (84) +--R [ +--R 2 2 2 +--R (b + a b)sinh(x) + (2b + 2a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (b + a b)cosh(x) - b + a b +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R +-------+ +--R | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b - a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 2 2 +--R (- 2b - 2a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 2b - 2a b)cosh(x) + 2b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R +---------+ +--R | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 100 + +--S 101 of 531 +m1019a:= a1019.1-r1019 +--R +--R +--R (85) +--R 3 2 3 3 2 2 2 +--R (b + a b )sinh(x) + (2b + 3a b + a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((b + 3a b + 2a b)cosh(x) - b + a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (a b + a b)cosh(x) + (- a b + a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 3 2 3 3 2 2 2 +--R (- b - a b )sinh(x) + (- 2b - 3a b - a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((- b - 3a b - 2a b)cosh(x) + b - a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (- a b - a b)cosh(x) + (a b - a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((a b - a )sinh(x) + (- a b + a )cosh(x) + a b - a )\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 101 + +--S 102 of 531 +d1019a:= D(m1019a,x) +--R +--R +--R (86) +--R 4 3 3 4 7 +--R (- b - 2a b - 2a b - a )sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 2 3 4 +--R ((- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) - a b - 2a b - 3a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 3a b - 2a b - 15a b - 8a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (- 6b - 8a b - 18a b - 20a b - 8a )cosh(x) + b + 2a b - 2a b +--R + +--R 3 4 +--R 2a b - 3a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 4b - 18a b - 28a b - 10a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 3a b + 8a b - 9a b - 4a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (8a b + 14a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 16a b - 17a b - 2a b + 5a )cosh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 4 +--R (8a b + 4a b - 8a b - 4a )cosh(x) - a b + 2a b - a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 3 2 2 3 4 5 +--R (a b + 4a b + a b)cosh(x) + (- 3a b - 6a b + a b + 2a )cosh(x) +--R + +--R 3 3 4 3 3 2 2 3 +--R (3a b - a b - 2a )cosh(x) + (- a b + 2a b - a b)cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression Integer +--E 102 + +--S 103 of 531 +m1019b:= a1019.2-r1019 +--R +--R +--R (87) +--R 3 2 3 3 2 2 2 +--R (- 2b - 2a b )sinh(x) + (- 4b - 6a b - 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((- 2b - 6a b - 4a b)cosh(x) + 2b - 2a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (- 2a b - 2a b)cosh(x) + (2a b - 2a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 3 3 2 2 2 +--R (- b - a b )sinh(x) + (- 2b - 3a b - a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((- b - 3a b - 2a b)cosh(x) + b - a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (- a b - a b)cosh(x) + (a b - a b)cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((a b - a )sinh(x) + (- a b + a )cosh(x) + a b - a )\|- b + a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 103 + +--S 104 of 531 +d1019b:= D(m1019b,x) +--R +--R +--R (88) +--R 4 3 3 4 7 +--R (- b - 2a b - 2a b - a )sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 2 3 4 +--R ((- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) - a b - 2a b - 3a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 3a b - 2a b - 15a b - 8a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (- 6b - 8a b - 18a b - 20a b - 8a )cosh(x) + b + 2a b - 2a b +--R + +--R 3 4 +--R 2a b - 3a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 4b - 18a b - 28a b - 10a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 3a b + 8a b - 9a b - 4a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (8a b + 14a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 16a b - 17a b - 2a b + 5a )cosh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 4 +--R (8a b + 4a b - 8a b - 4a )cosh(x) - a b + 2a b - a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 3 2 2 3 4 5 +--R (a b + 4a b + a b)cosh(x) + (- 3a b - 6a b + a b + 2a )cosh(x) +--R + +--R 3 3 4 3 3 2 2 3 +--R (3a b - a b - 2a )cosh(x) + (- a b + 2a b - a b)cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression Integer +--E 104 + +--S 105 of 531 +t1020:= sinh(x)^2/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R 2 +--R sinh(x) +--R (89) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 105 + +--S 106 of 531 +r1020:= (a^2+b^2)*x/(a^2-b^2)^2-a/(a^2-b^2)/(b+a*coth(x))-_ + 2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2 +--R +--R +--R (90) +--R 2 2 2 3 +--R (- 2a b coth(x) - 2a b )log(b sinh(x) + a cosh(x)) + (a b + a )x coth(x) +--R + +--R 3 2 2 3 +--R (b + a b)x + a b - a +--R / +--R 4 3 2 5 5 2 3 4 +--R (a b - 2a b + a )coth(x) + b - 2a b + a b +--R Type: Expression Integer +--E 106 + +--S 107 of 531 +a1020:= integrate(t1020,x) +--R +--R +--R (91) +--R 2 2 2 2 2 +--R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 2a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 2 +--R (b + 3a b + 3a b + a )x sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 6a b + 6a b + 2a )x cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 2 3 +--R (b + 3a b + 3a b + a )x cosh(x) + (- b - a b + a b + a )x - 2a b + 2a +--R / +--R 5 4 2 3 3 2 4 5 2 +--R (b + a b - 2a b - 2a b + a b + a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 2 3 +--R (b + a b - 2a b - 2a b + a b + a )cosh(x) - b + a b + 2a b +--R + +--R 3 2 4 5 +--R - 2a b - a b + a +--R Type: Union(Expression Integer,...) +--E 107 + +--S 108 of 531 +m1020:= a1020-r1020 +--R +--R +--R (92) +--R 2 2 3 3 2 2 2 +--R ((2a b + 2a b)coth(x) + 2a b + 2a b )sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((4a b + 4a b)cosh(x)coth(x) + (4a b + 4a b )cosh(x))sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((2a b + 2a b)cosh(x) - 2a b + 2a b)coth(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )cosh(x) - 2a b + 2a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2a b - 2a b)coth(x) - 2a b - 2a b )sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((- 4a b - 4a b)cosh(x)coth(x) + (- 4a b - 4a b )cosh(x))sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 2a b - 2a b)cosh(x) + 2a b - 2a b)coth(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2a b - 2a b )cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 2 3 4 +--R ((2a b + 2a b)x coth(x) + (2a b + 2a b )x - a b - a b + a b + a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 +--R (4a b + 4a b)x cosh(x)coth(x) +--R + +--R 3 2 2 3 2 2 3 4 +--R ((4a b + 4a b )x - 2a b - 2a b + 2a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 2 2 2 3 3 4 +--R ((2a b + 2a b)x cosh(x) + (- 2a b + 2a b)x - 2a b + 2a )coth(x) +--R + +--R 3 2 2 3 2 2 3 4 2 3 2 2 +--R ((2a b + 2a b )x - a b - a b + a b + a )cosh(x) + (- 2a b + 2a b )x +--R + +--R 3 2 2 3 4 +--R a b - 3a b + a b + a +--R / +--R 5 2 4 3 3 4 2 5 6 6 5 2 4 +--R (a b + a b - 2a b - 2a b + a b + a )coth(x) + b + a b - 2a b +--R + +--R 3 3 4 2 5 +--R - 2a b + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)coth(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 5 2 4 +--R (a b + a b - 2a b - 2a b + a b + a )cosh(x) - a b + a b +--R + +--R 3 3 4 2 5 6 +--R 2a b - 2a b - a b + a +--R * +--R coth(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 5 2 4 +--R (b + a b - 2a b - 2a b + a b + a b)cosh(x) - b + a b + 2a b +--R + +--R 3 3 4 2 5 +--R - 2a b - a b + a b +--R Type: Expression Integer +--E 108 + +--S 109 of 531 +d1020:= D(m1020,x) +--R +--R +--R (93) +--R 2 2 3 4 2 2 2 3 4 4 +--R ((- a b - 2a b - a )coth(x) + a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 4 2 2 2 3 4 +--R ((- 4a b - 8a b - 4a )cosh(x)coth(x) + (4a b + 8a b + 4a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 2 2 2 4 2 +--R ((- 6a b - 12a b - 6a )cosh(x) + 2a b + 2a )coth(x) +--R + +--R 3 2 2 3 4 2 2 2 4 +--R 8a b coth(x) + (6a b + 12a b + 6a )cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 4 3 2 2 4 2 +--R ((- 4a b - 8a b - 4a )cosh(x) + (4a b + 4a )cosh(x))coth(x) +--R + +--R 3 2 2 3 4 3 +--R 16a b cosh(x)coth(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 4 +--R (4a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 4 2 2 4 2 2 2 3 +--R (- a b - 2a b - a )cosh(x) + (2a b + 2a )cosh(x) - a b + 2a b +--R + +--R 4 +--R - a +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 2 3 4 4 2 2 4 2 +--R 8a b cosh(x) coth(x) + (a b + 2a b + a )cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 4 +--R a b - 2a b + a +--R / +--R 2 4 3 3 5 6 2 +--R (a b + 2a b - 2a b - a )coth(x) +--R + +--R 5 2 4 4 2 5 6 5 3 3 4 2 +--R (2a b + 4a b - 4a b - 2a b)coth(x) + b + 2a b - 2a b - a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (4a b + 8a b - 8a b - 4a )cosh(x)coth(x) +--R + +--R 5 2 4 4 2 5 +--R (8a b + 16a b - 16a b - 8a b)cosh(x)coth(x) +--R + +--R 6 5 3 3 4 2 +--R (4b + 8a b - 8a b - 4a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 5 6 2 2 4 4 2 6 +--R ((6a b + 12a b - 12a b - 6a )cosh(x) - 2a b + 4a b - 2a ) +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 4 4 2 5 2 5 3 3 5 +--R ((12a b + 24a b - 24a b - 12a b)cosh(x) - 4a b + 8a b - 4a b) +--R * +--R coth(x) +--R + +--R 6 5 3 3 4 2 2 6 2 4 4 2 +--R (6b + 12a b - 12a b - 6a b )cosh(x) - 2b + 4a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 5 6 3 +--R (4a b + 8a b - 8a b - 4a )cosh(x) +--R + +--R 2 4 4 2 6 +--R (- 4a b + 8a b - 4a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 4 4 2 5 3 +--R (8a b + 16a b - 16a b - 8a b)cosh(x) +--R + +--R 5 3 3 5 +--R (- 8a b + 16a b - 8a b)cosh(x) +--R * +--R coth(x) +--R + +--R 6 5 3 3 4 2 3 6 2 4 4 2 +--R (4b + 8a b - 8a b - 4a b )cosh(x) + (- 4b + 8a b - 4a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 5 6 4 2 4 4 2 6 2 +--R (a b + 2a b - 2a b - a )cosh(x) + (- 2a b + 4a b - 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 +--R a b - 2a b + 2a b - a +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 4 4 2 5 4 +--R (2a b + 4a b - 4a b - 2a b)cosh(x) +--R + +--R 5 3 3 5 2 5 2 4 4 2 5 +--R (- 4a b + 8a b - 4a b)cosh(x) + 2a b - 4a b + 4a b - 2a b +--R * +--R coth(x) +--R + +--R 6 5 3 3 4 2 4 6 2 4 4 2 2 +--R (b + 2a b - 2a b - a b )cosh(x) + (- 2b + 4a b - 2a b )cosh(x) +--R + +--R 6 5 3 3 4 2 +--R b - 2a b + 2a b - a b +--R Type: Expression Integer +--E 109 + +--S 110 of 531 +t1021:= sinh(x)/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R sinh(x) +--R (94) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 110 + +--S 111 of 531 +r1021:= -1/2*a/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2-_ + b*sinh(x)/a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R (95) +--R 2 2 2 +--R 2b sinh(x) + 2a b cosh(x)sinh(x) + a +--R / +--R 4 3 2 2 2 3 4 +--R (2a b - 2a b )sinh(x) + (4a b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 5 2 +--R (2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 111 + +--S 112 of 531 +a1021:= integrate(t1021,x) +--R +--R +--R (96) +--R (- 4b - 2a)sinh(x) - 2a cosh(x) +--R / +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x) - 3b - 4a b + 2a b +--R + +--R 3 4 +--R 4a b + a +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - 4a b - 2a b + 4a b + 3a )cosh(x) +--R Type: Union(Expression Integer,...) +--E 112 + +--S 113 of 531 +m1021:= a1021-r1021 +--R +--R +--R (97) +--R 5 4 2 3 3 2 5 +--R (- 2b - 6a b - 6a b - 2a b )sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 6b - 20a b - 24a b - 12a b - 2a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 4 +--R (- 6b - 24a b - 36a b - 24a b - 6a b)cosh(x) + 6b - 6a b +--R + +--R 2 3 3 2 4 5 +--R - 3a b - a b - 3a b - a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 2b - 12a b - 24a b - 20a b - 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 12a b - 23a b - 9a b - 3a b - 3a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 2a b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 2 3 3 2 4 5 +--R (2a b + 3a b - 27a b - 3a b + a )cosh(x) + 3a b + a b - 3a b - a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 5 3 2 3 3 2 4 5 +--R (- a b - 3a b - 7a b + 3a )cosh(x) + (a b + 3a b - a b - 3a )cosh(x) +--R / +--R 7 2 6 3 5 4 4 5 3 6 2 5 +--R (2a b + 6a b + 4a b - 4a b - 6a b - 2a b )sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 4 +--R (6a b + 22a b + 24a b - 4a b - 26a b - 18a b - 4a b)cosh(x)sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R (6a b + 30a b + 50a b + 18a b - 38a b - 46a b - 18a b - 2a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 6a b - 2a b + 12a b + 4a b - 6a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R (2a b + 18a b + 46a b + 38a b - 18a b - 50a b - 30a b - 6a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 7 2 6 4 4 5 3 6 2 7 +--R (- 2a b - 18a b + 36a b + 6a b - 18a b - 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 4 +--R (4a b + 18a b + 26a b + 4a b - 24a b - 22a b - 6a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 7 8 2 +--R (- 4a b - 18a b + 6a b + 36a b - 18a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 5 +--R (2a b + 6a b + 4a b - 4a b - 6a b - 2a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- 2a b - 6a b + 4a b + 12a b - 2a b - 6a )cosh(x) +--R Type: Expression Integer +--E 113 + +--S 114 of 531 +d1021:= D(m1021,x) +--R +--R +--R (98) +--R 6 5 2 4 3 3 4 2 9 +--R (b + 4a b + 6a b + 4a b + a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (6b + 25a b + 40a b + 30a b + 10a b + a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 +--R (14b + 62a b + 108a b + 92a b + 38a b + 6a b)cosh(x) + 6b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 4a b - 7a b + 8a b + 8a b + 4a b + a +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (14b + 70a b + 140a b + 140a b + 70a b + 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (12b + 15a b - 10a b + 14a b + 48a b + 27a b + 6a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (14a b + 56a b + 84a b + 56a b + 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6b + 66a b + 63a b + 36a b + 84a b + 66a b + 15a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 5b - 8a b - 4a b - 8a b + 5a b + 8a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 14b - 56a b - 84a b - 56a b - 14a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (8b + 85a b + 192a b + 138a b + 64a b + 57a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (6b - a b - 56a b - 10a b + 14a b + 35a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 14b - 70a b - 140a b - 140a b - 70a b - 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b + 72a b + 215a b + 224a b + 48a b - 16a b - a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 4b - 2a b - 64a b - 68a b + 60a b + 54a b + 24a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R 9a b - 12a b - 2a b + 4a b + a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 6b - 38a b - 92a b - 108a b - 62a b - 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (12b + 57a b + 126a b + 162a b + 48a b - 51a b - 18a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (- 6b - 28a b - 28a b - 56a b + 34a b + 68a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (9a b - 6a b + 6a b - 24a b + 9a b + 6a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (- b - 10a b - 30a b - 40a b - 25a b - 6a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (2b + 26a b + 49a b + 52a b + 20a b - 22a b - 15a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- b - 22a b - 28a b + 12a b - a b + 34a b + 6a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (6a b + 9a b - 24a b + 6a b - 6a b + 9a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 9 +--R (- a b - 4a b - 6a b - 4a b - a b)cosh(x) +--R + +--R 5 2 4 3 3 5 6 7 +--R (3a b + 12a b + 6a b - a b - 4a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 3a b - 12a b + 2a b + 16a b - 7a b + 4a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (a b + 4a b - 2a b - 12a b + 9a b)cosh(x) +--R / +--R 9 8 2 7 4 5 5 4 6 3 9 +--R (b + 4a b + 5a b - 5a b - 4a b - a b )sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 27a b + 42a b + 15a b - 30a b - 39a b - 18a b - 3a b ) +--R * +--R 8 +--R cosh(x)sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 78a b + 150a b + 102a b - 60a b - 150a b - 102a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 6b - 8a b + 10a b + 16a b - 2a b - 8a b - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 20b + 125a b + 298a b + 298a b - 6a b - 300a b - 290a b +--R + +--R 7 2 8 9 +--R - 122a b - 22a b - a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 20b - 50a b + 4a b + 94a b + 52a b - 38a b - 36a b +--R + +--R 7 2 +--R - 6a b +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 120a b + 360a b + 486a b + 174a b - 330a b - 480a b +--R + +--R 7 2 8 9 +--R - 270a b - 69a b - 6a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 24b - 108a b - 90a b + 156a b + 246a b + 12a b - 126a b +--R + +--R 7 2 8 +--R - 60a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 9b - 12a b - 11a b + 16a b + 3a b - 4a b - a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b + 69a b + 270a b + 480a b + 330a b - 174a b - 486a b +--R + +--R 7 2 8 9 +--R - 360a b - 120a b - 15a +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 12b - 104a b - 200a b + 34a b + 392a b + 242a b - 136a b +--R + +--R 7 2 8 9 +--R - 170a b - 44a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 35a b - 70a b - 33a b + 82a b + a b - 18a b - 3a b ) +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 122a b + 290a b + 300a b + 6a b - 298a b +--R + +--R 7 2 8 9 +--R - 298a b - 125a b - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 2b - 44a b - 170a b - 136a b + 242a b + 392a b + 34a b +--R + +--R 7 2 8 9 +--R - 200a b - 104a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 48a b - 154a b - 22a b + 162a b - 24a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 102a b + 150a b + 60a b - 102a b - 150a b +--R + +--R 8 9 +--R - 78a b - 15a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 6a b - 60a b - 126a b + 12a b + 246a b + 156a b - 90a b +--R + +--R 8 9 +--R - 108a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 24a b - 162a b + 22a b + 154a b - 48a b +--R + +--R 8 9 +--R - 22a b - a +--R * +--R 3 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b + 39a b + 30a b - 15a b - 42a b - 27a b - 6a ) +--R * +--R 8 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 6a b - 36a b - 38a b + 52a b + 94a b + 4a b - 50a b +--R + +--R 9 +--R - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b - a b - 82a b + 33a b + 70a b - 35a b - 6a ) +--R * +--R 4 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 4 5 5 4 7 2 8 9 9 +--R (a b + 4a b + 5a b - 5a b - 4a b - a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 7 +--R (- 2a b - 8a b - 2a b + 16a b + 10a b - 8a b - 6a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 5 +--R (a b + 4a b - 3a b - 16a b + 11a b + 12a b - 9a )cosh(x) +--R Type: Expression Integer +--E 114 + +--S 115 of 531 +t1022:= sinh(x)^3/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R 3 +--R sinh(x) +--R (99) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 115 + +--S 116 of 531 +r1022:= -b*(3*a^2+b^2)*x/(a^2-b^2)^3-1/2*a/(a^2-b^2)/(b+a*coth(x))^2+_ + 2*a*b/(a^2-b^2)^2/(b+a*coth(x))+a*(a^2+3*b^2)*_ + log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3 +--R +--R +--R (100) +--R 3 2 5 2 2 3 4 4 3 2 +--R ((- 6a b - 2a )coth(x) + (- 12a b - 4a b)coth(x) - 6a b - 2a b ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 3 4 2 4 3 2 2 3 4 +--R (2a b + 6a b)x coth(x) + ((4a b + 12a b )x + 4a b - 4a b)coth(x) +--R + +--R 5 2 3 4 3 2 5 +--R (2b + 6a b )x + 5a b - 6a b + a +--R / +--R 2 6 4 4 6 2 8 2 +--R (2a b - 6a b + 6a b - 2a )coth(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 6 2 +--R (4a b - 12a b + 12a b - 4a b)coth(x) + 2b - 6a b + 6a b - 2a b +--R Type: Expression Integer +--E 116 + +--S 117 of 531 +a1022:= integrate(t1022,x) +--R +--R +--R (101) +--R 4 2 3 3 2 4 5 4 +--R (- 3a b - 6a b - 4a b - 2a b - a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 12a b - 24a b - 16a b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (- 18a b - 36a b - 24a b - 12a b - 6a )cosh(x) + 6a b +--R + +--R 3 2 5 +--R - 4a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 12a b - 24a b - 16a b - 8a b - 4a )cosh(x) +--R + +--R 4 3 2 5 +--R (12a b - 8a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 3a b - 6a b - 4a b - 2a b - a )cosh(x) +--R + +--R 4 3 2 5 2 4 2 3 3 2 4 5 +--R (6a b - 4a b - 2a )cosh(x) - 3a b + 6a b - 4a b + 2a b - a +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (b + 5a b + 10a b + 10a b + 5a b + a )x sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (4b + 20a b + 40a b + 40a b + 20a b + 4a )x cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (6b + 30a b + 60a b + 60a b + 30a b + 6a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 4 +--R (- 2b - 6a b - 4a b + 4a b + 6a b + 2a )x - 6a b + 2a b + 6a b +--R + +--R 5 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (4b + 20a b + 40a b + 40a b + 20a b + 4a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 +--R (- 4b - 12a b - 8a b + 8a b + 12a b + 4a )x - 12a b + 4a b +--R + +--R 4 5 +--R 12a b - 4a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (b + 5a b + 10a b + 10a b + 5a b + a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 4 +--R (- 2b - 6a b - 4a b + 4a b + 6a b + 2a )x - 6a b + 2a b + 6a b +--R + +--R 5 +--R - 2a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 4 +--R (b + a b - 2a b - 2a b + a b + a )x + 6a b - 12a b + 6a b +--R / +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (6b + 12a b - 12a b - 36a b + 36a b + 12a b - 12a b - 6a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R - 2b + 8a b - 12a b + 8a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 3 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 4b + 16a b - 24a b + 16a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 7 2 6 +--R (- 2b + 8a b - 12a b + 8a b - 2a )cosh(x) + b - 2a b - 2a b +--R + +--R 3 5 5 3 6 2 7 8 +--R 6a b - 6a b + 2a b + 2a b - a +--R Type: Union(Expression Integer,...) +--E 117 + +--S 118 of 531 +m1022:= a1022-r1022 +--R +--R +--R (102) +--R 3 4 4 3 5 2 6 7 2 +--R (6a b + 12a b + 8a b + 4a b + 2a )coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 2 5 +--R (12a b + 24a b + 16a b + 8a b + 4a b)coth(x) + 6a b + 12a b +--R + +--R 3 4 4 3 5 2 +--R 8a b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (24a b + 48a b + 32a b + 16a b + 8a )cosh(x)coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (48a b + 96a b + 64a b + 32a b + 16a b)cosh(x)coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24a b + 48a b + 32a b + 16a b + 8a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 3 4 +--R (36a b + 72a b + 48a b + 24a b + 12a )cosh(x) - 12a b +--R + +--R 5 2 7 +--R 8a b + 4a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 2 5 +--R (72a b + 144a b + 96a b + 48a b + 24a b)cosh(x) - 24a b +--R + +--R 4 3 6 +--R 16a b + 8a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 6 +--R (36a b + 72a b + 48a b + 24a b + 12a b )cosh(x) - 12a b +--R + +--R 3 4 5 2 +--R 8a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (24a b + 48a b + 32a b + 16a b + 8a )cosh(x) +--R + +--R 3 4 5 2 7 +--R (- 24a b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (48a b + 96a b + 64a b + 32a b + 16a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (- 48a b + 32a b + 16a b)cosh(x) +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (24a b + 48a b + 32a b + 16a b + 8a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (- 24a b + 16a b + 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (6a b + 12a b + 8a b + 4a b + 2a )cosh(x) +--R + +--R 3 4 5 2 7 2 3 4 4 3 5 2 6 +--R (- 12a b + 8a b + 4a )cosh(x) + 6a b - 12a b + 8a b - 4a b +--R + +--R 7 +--R 2a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (12a b + 24a b + 16a b + 8a b + 4a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 +--R (- 24a b + 16a b + 8a b)cosh(x) + 12a b - 24a b + 16a b +--R + +--R 5 2 6 +--R - 8a b + 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (6a b + 12a b + 8a b + 4a b + 2a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 4 3 +--R (- 12a b + 8a b + 4a b )cosh(x) + 6a b - 12a b + 8a b - 4a b +--R + +--R 5 2 +--R 2a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (- 6a b - 12a b - 8a b - 4a b - 2a )coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 12a b - 24a b - 16a b - 8a b - 4a b)coth(x) - 6a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 12a b - 8a b - 4a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (- 24a b - 48a b - 32a b - 16a b - 8a )cosh(x)coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 48a b - 96a b - 64a b - 32a b - 16a b)cosh(x)coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (- 24a b - 48a b - 32a b - 16a b - 8a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 3 4 +--R (- 36a b - 72a b - 48a b - 24a b - 12a )cosh(x) + 12a b +--R + +--R 5 2 7 +--R - 8a b - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (- 72a b - 144a b - 96a b - 48a b - 24a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R 24a b - 16a b - 8a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 6 +--R (- 36a b - 72a b - 48a b - 24a b - 12a b )cosh(x) + 12a b +--R + +--R 3 4 5 2 +--R - 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- 24a b - 48a b - 32a b - 16a b - 8a )cosh(x) +--R + +--R 3 4 5 2 7 +--R (24a b - 16a b - 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 48a b - 96a b - 64a b - 32a b - 16a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (48a b - 32a b - 16a b)cosh(x) +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 24a b - 48a b - 32a b - 16a b - 8a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (24a b - 16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 6a b - 12a b - 8a b - 4a b - 2a )cosh(x) +--R + +--R 3 4 5 2 7 2 3 4 4 3 5 2 6 +--R (12a b - 8a b - 4a )cosh(x) - 6a b + 12a b - 8a b + 4a b +--R + +--R 7 +--R - 2a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 12a b - 24a b - 16a b - 8a b - 4a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 +--R (24a b - 16a b - 8a b)cosh(x) - 12a b + 24a b - 16a b +--R + +--R 5 2 6 +--R 8a b - 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 6a b - 12a b - 8a b - 4a b - 2a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 4 3 +--R (12a b - 8a b - 4a b )cosh(x) - 6a b + 12a b - 8a b + 4a b +--R + +--R 5 2 +--R - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (6a b + 12a b + 8a b + 4a b + 2a )x coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (12a b + 24a b + 16a b + 8a b + 4a b)x - 4a b - 8a b +--R + +--R 5 2 6 +--R 8a b + 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (6a b + 12a b + 8a b + 4a b + 2a b )x - 5a b - 10a b + a b +--R + +--R 4 3 5 2 6 7 +--R 12a b + 5a b - 2a b - a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (24a b + 48a b + 32a b + 16a b + 8a )x cosh(x)coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (48a b + 96a b + 64a b + 32a b + 16a b)x - 16a b - 32a b +--R + +--R 5 2 6 +--R 32a b + 16a b +--R * +--R cosh(x)coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (24a b + 48a b + 32a b + 16a b + 8a b )x - 20a b - 40a b +--R + +--R 3 4 4 3 5 2 6 7 +--R 4a b + 48a b + 20a b - 8a b - 4a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (36a b + 72a b + 48a b + 24a b + 12a )x cosh(x) +--R + +--R 3 4 5 2 7 4 3 5 2 6 7 +--R (- 12a b + 8a b + 4a )x - 12a b + 4a b + 12a b - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 +--R (72a b + 144a b + 96a b + 48a b + 24a b)x - 24a b +--R + +--R 3 4 5 2 6 +--R - 48a b + 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 4 3 6 2 5 3 4 4 3 5 2 +--R (- 24a b + 16a b + 8a b)x + 8a b - 24a b - 8a b + 24a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (36a b + 72a b + 48a b + 24a b + 12a b )x - 30a b - 60a b +--R + +--R 3 4 4 3 5 2 6 7 +--R 6a b + 72a b + 30a b - 12a b - 6a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 3 4 5 2 6 2 5 3 4 4 3 +--R (- 12a b + 8a b + 4a b )x + 10a b - 12a b - 18a b + 12a b +--R + +--R 5 2 7 +--R 10a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (24a b + 48a b + 32a b + 16a b + 8a )x cosh(x) +--R + +--R 3 4 5 2 7 4 3 5 2 6 7 +--R ((- 24a b + 16a b + 8a )x - 24a b + 8a b + 24a b - 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 +--R (48a b + 96a b + 64a b + 32a b + 16a b)x - 16a b +--R + +--R 3 4 5 2 6 +--R - 32a b + 32a b + 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 5 4 3 6 2 5 3 4 4 3 +--R (- 48a b + 32a b + 16a b)x + 16a b - 48a b - 16a b +--R + +--R 5 2 +--R 48a b +--R * +--R cosh(x) +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (24a b + 48a b + 32a b + 16a b + 8a b )x - 20a b - 40a b +--R + +--R 3 4 4 3 5 2 6 7 +--R 4a b + 48a b + 20a b - 8a b - 4a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 3 4 5 2 6 2 5 3 4 4 3 +--R (- 24a b + 16a b + 8a b )x + 20a b - 24a b - 36a b + 24a b +--R + +--R 5 2 7 +--R 20a b - 4a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (6a b + 12a b + 8a b + 4a b + 2a )x cosh(x) +--R + +--R 3 4 5 2 7 4 3 5 2 6 7 2 +--R ((- 12a b + 8a b + 4a )x - 12a b + 4a b + 12a b - 4a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 3 5 2 6 +--R (6a b - 12a b + 8a b - 4a b + 2a )x + 12a b - 24a b + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (12a b + 24a b + 16a b + 8a b + 4a b)x - 4a b - 8a b +--R + +--R 5 2 6 +--R 8a b + 4a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 5 4 3 6 2 5 3 4 4 3 5 2 +--R ((- 24a b + 16a b + 8a b)x + 8a b - 24a b - 8a b + 24a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 4 3 +--R (12a b - 24a b + 16a b - 8a b + 4a b)x - 4a b + 32a b - 48a b +--R + +--R 5 2 6 +--R 16a b + 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (6a b + 12a b + 8a b + 4a b + 2a b )x - 5a b - 10a b + a b +--R + +--R 4 3 5 2 6 7 +--R 12a b + 5a b - 2a b - a +--R * +--R 4 +--R cosh(x) +--R + +--R 6 3 4 5 2 6 2 5 3 4 4 3 +--R (- 12a b + 8a b + 4a b )x + 10a b - 12a b - 18a b + 12a b +--R + +--R 5 2 7 +--R 10a b - 2a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (6a b - 12a b + 8a b - 4a b + 2a b )x - 5a b + 22a b - 23a b +--R + +--R 5 2 6 7 +--R 5a b + 2a b - a +--R / +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a ) +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 +--R 2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b - 8a ) +--R * +--R 2 +--R cosh(x)coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R cosh(x)coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 +--R 12a b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 10 +--R - 12a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R - 4a b + 16a b - 24a b + 16a b - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 +--R 24a b + 48a b - 48a b - 144a b + 144a b + 48a b +--R + +--R 8 2 9 +--R - 48a b - 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R - 8a b + 32a b - 48a b + 32a b - 8a b +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 12b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 8 2 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R - 4b + 16a b - 24a b + 16a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 +--R 8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 10 +--R - 8a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R (- 8a b + 32a b - 48a b + 32a b - 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R (- 16a b + 64a b - 96a b + 64a b - 16a b)cosh(x) +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R (- 8b + 32a b - 48a b + 32a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 2 8 3 7 +--R (- 4a b + 16a b - 24a b + 16a b - 4a )cosh(x) + 2a b - 4a b +--R + +--R 4 6 5 5 7 3 8 2 9 10 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 9 2 8 +--R (- 8a b + 32a b - 48a b + 32a b - 8a b)cosh(x) + 4a b - 8a b +--R + +--R 3 7 4 6 6 4 7 3 8 2 9 +--R - 8a b + 24a b - 24a b + 8a b + 8a b - 4a b +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 4 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 10 9 +--R (- 4b + 16a b - 24a b + 16a b - 4a b )cosh(x) + 2b - 4a b +--R + +--R 2 8 3 7 5 5 6 4 7 3 8 2 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a b +--R Type: Expression Integer +--E 118 + +--S 119 of 531 +--d1022:= D(m1022,x) +--E 119 + +--S 120 of 531 +t1023:= cosh(x)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R cosh(x) +--R (103) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 120 + +--S 121 of 531 +r1023:= -(-a*x+b*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) +--R +--R +--R b log(b sinh(x) + a cosh(x)) - a x +--R (104) ---------------------------------- +--R 2 2 +--R b - a +--R Type: Expression Integer +--E 121 + +--S 122 of 531 +a1023:= integrate(t1023,x) +--R +--R +--R - 2b sinh(x) - 2a cosh(x) +--R b log(-------------------------) + (- b - a)x +--R sinh(x) - cosh(x) +--R (105) --------------------------------------------- +--R 2 2 +--R b - a +--R Type: Union(Expression Integer,...) +--E 122 + +--S 123 of 531 +m1023:= a1023-r1023 +--R +--R +--R (106) +--R - 2b sinh(x) - 2a cosh(x) +--R - b log(b sinh(x) + a cosh(x)) + b log(-------------------------) - b x +--R sinh(x) - cosh(x) +--R ----------------------------------------------------------------------- +--R 2 2 +--R b - a +--R Type: Expression Integer +--E 123 + +--S 124 of 531 +d1023:= D(m1023,x) +--R +--R +--R (107) 0 +--R Type: Expression Integer +--E 124 + +--S 125 of 531 +t1024:= cosh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (108) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 125 + +--S 126 of 531 +r1024:= -b^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) +--R +--R +--R (109) +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R b atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R --------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression Integer +--E 126 + +--S 127 of 531 +a1024:= integrate(t1024,x) +--R +--R +--R (110) +--R [ +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 127 + +--S 128 of 531 +m1024a:= a1024.1-r1024 +--R +--R +--R (111) +--R +---------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R 2 2 | 2 2 a sinh(x) + b cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression Integer +--E 128 + +--S 129 of 531 +d1024a:= D(m1024a,x) +--R +--R +--R (112) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 4 +--R ((- b - 6a b - 9a b - 4a b)cosh(x) - b + 4a b - 4a b - 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 4b + 4a b - 12a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 +--R (- 2b - 2a b - 14a b - 6a b)cosh(x) - 2b + 7a b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 12a b - 12a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 4 4 +--R (b + 2a b + a b )cosh(x) + (b - 6a b - 2a b + 2a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (- b + 4a b - a b - 2a b)cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 129 + +--S 130 of 531 +m1024b:= a1024.2-r1024 +--R +--R +--R (113) +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 a sinh(x) + b cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression Integer +--E 130 + +--S 131 of 531 +d1024b:= D(m1024b,x) +--R +--R +--R (114) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 4 +--R ((- b - 6a b - 9a b - 4a b)cosh(x) - b + 4a b - 4a b - 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 4b + 4a b - 12a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 +--R (- 2b - 2a b - 14a b - 6a b)cosh(x) - 2b + 7a b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 12a b - 12a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 4 4 +--R (b + 2a b + a b )cosh(x) + (b - 6a b - 2a b + 2a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (- b + 4a b - a b - 2a b)cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 131 + +--S 132 of 531 +t1025:= cosh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R cosh(x) +--R (115) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 132 + +--S 133 of 531 +r1025:= 1/2/(a^2-b^2)^2*(-3*a*b^2*x+a^3*x+2*log(a*cosh(x)+_ + b*sinh(x))*b^3+a^3*cosh(x)*sinh(x)-cosh(x)*b^2*a*sinh(x)+a^2*b-_ + a^2*b*cosh(x)^2-b^3+cosh(x)^2*b^3) +--R +--R +--R (116) +--R 3 2 3 +--R 2b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b - a b)cosh(x) + (- 3a b + a )x - b + a b +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression Integer +--E 133 + +--S 134 of 531 +a1025:= integrate(t1025,x) +--R +--R +--R (117) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 8b - 12a b + 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 16b - 24a b + 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 8b - 12a b + 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression Integer,...) +--E 134 + +--S 135 of 531 +m1025:= a1025-r1025 +--R +--R +--R (118) +--R 3 2 3 3 2 +--R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 3 2 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) - 8b x + 4b - 4a b)sinh(x) +--R + +--R 3 2 3 3 3 2 +--R ((- 4b + 4a b)cosh(x) + (- 16b x + 8b - 8a b)cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) + (- 8b x + 4b - 4a b)cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression Integer +--E 135 + +--S 136 of 531 +d1025:= D(m1025,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (119) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression Integer +--E 136 + +--S 137 of 531 +t1026:= cosh(x)/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R cosh(x) +--R (120) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 137 + +--S 138 of 531 +r1026:= a*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ + b/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R (121) +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R (- a b sinh(x) - a cosh(x))atan(---------------------) - b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a +--R Type: Expression Integer +--E 138 + +--S 139 of 531 +a1026:= integrate(t1026,x) +--R +--R +--R (122) +--R [ +--R 2 2 2 +--R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (a b + a )cosh(x) - a b + a +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R +-------+ +--R | 2 2 +--R (- 2b sinh(x) - 2b cosh(x))\|b - a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 2 2 +--R (2a b + 2a )sinh(x) + (4a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) - 2a b + 2a +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R +---------+ +--R | 2 2 +--R (- 2b sinh(x) - 2b cosh(x))\|- b + a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 139 + +--S 140 of 531 +m1026a:= a1026.1-r1026 +--R +--R +--R (123) +--R 2 2 3 2 2 3 2 +--R (a b + a b)sinh(x) + (2a b + 3a b + a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((a b + 3a b + 2a )cosh(x) - a b + a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (a b + a )cosh(x) + (- a b + a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 2 2 3 2 2 3 2 +--R (a b + a b)sinh(x) + (2a b + 3a b + a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((a b + 3a b + 2a )cosh(x) - a b + a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (a b + a )cosh(x) + (- a b + a )cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((- b + a b)sinh(x) + (b - a b)cosh(x) - b + a b)\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 140 + +--S 141 of 531 +d1026a:= D(m1026a,x) +--R +--R +--R (124) +--R 3 2 2 3 7 3 2 2 3 6 +--R (a b + 4a b + a b)sinh(x) + (8a b + 14a b + 8a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) - 2b - a b + 6a b +--R + +--R 3 +--R 3a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 5b + 2a b + 17a b + 16a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 4 3 3 +--R (10a b + 28a b + 18a b + 4a )cosh(x) - 2b - a b + 3a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (8b + 20a b + 18a b + 8a b + 6a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 4b - 8a b + 4a b + 8a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (8b + 15a b + 2a b + 3a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 2 2 3 +--R (- 4b - 9a b + 8a b + 3a b + 2a )cosh(x) + a b - 2a b + a b +--R * +--R sinh(x) +--R + +--R 4 3 3 4 7 4 3 2 2 5 +--R (- b - 2a b - 2a b - a )cosh(x) + (3b + 2a b + a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 3 2 2 +--R (- 3b + 2a b - 2a b + 2a b + a )cosh(x) + (b - 2a b + a b )cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression Integer +--E 141 + +--S 142 of 531 +m1026b:= a1026.2-r1026 +--R +--R +--R (125) +--R 2 2 3 2 2 3 2 +--R (2a b + 2a b)sinh(x) + (4a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((2a b + 6a b + 4a )cosh(x) - 2a b + 2a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (2a b + 2a )cosh(x) + (- 2a b + 2a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 2 2 3 2 2 3 2 +--R (a b + a b)sinh(x) + (2a b + 3a b + a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((a b + 3a b + 2a )cosh(x) - a b + a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (a b + a )cosh(x) + (- a b + a )cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((- b + a b)sinh(x) + (b - a b)cosh(x) - b + a b)\|- b + a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 142 + +--S 143 of 531 +d1026b:= D(m1026b,x) +--R +--R +--R (126) +--R 3 2 2 3 7 3 2 2 3 6 +--R (a b + 4a b + a b)sinh(x) + (8a b + 14a b + 8a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) - 2b - a b + 6a b +--R + +--R 3 +--R 3a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 5b + 2a b + 17a b + 16a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 4 3 3 +--R (10a b + 28a b + 18a b + 4a )cosh(x) - 2b - a b + 3a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (8b + 20a b + 18a b + 8a b + 6a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 4b - 8a b + 4a b + 8a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (8b + 15a b + 2a b + 3a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 2 2 3 +--R (- 4b - 9a b + 8a b + 3a b + 2a )cosh(x) + a b - 2a b + a b +--R * +--R sinh(x) +--R + +--R 4 3 3 4 7 4 3 2 2 5 +--R (- b - 2a b - 2a b - a )cosh(x) + (3b + 2a b + a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 3 2 2 +--R (- 3b + 2a b - 2a b + 2a b + a )cosh(x) + (b - 2a b + a b )cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression Integer +--E 143 + +--S 144 of 531 +t1027:= cosh(x)^2/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R 2 +--R cosh(x) +--R (127) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 144 + +--S 145 of 531 +r1027:= (a^2+b^2)*x/(a^2-b^2)^2-2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+_ + b/(a^2-b^2)/(a+b*tanh(x)) +--R +--R +--R (128) +--R 2 2 3 2 +--R (- 2a b tanh(x) - 2a b)log(b sinh(x) + a cosh(x)) + (b + a b)x tanh(x) +--R + +--R 2 3 3 2 +--R (a b + a )x - b + a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b - 2a b + a b)tanh(x) + a b - 2a b + a +--R Type: Expression Integer +--E 145 + +--S 146 of 531 +a1027:= integrate(t1027,x) +--R +--R +--R (129) +--R 2 2 2 2 2 +--R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 2a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 2 +--R (b + 3a b + 3a b + a )x sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 6a b + 6a b + 2a )x cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 3 +--R (b + 3a b + 3a b + a )x cosh(x) + (- b - a b + a b + a )x - 2b +--R + +--R 2 +--R 2a b +--R / +--R 5 4 2 3 3 2 4 5 2 +--R (b + a b - 2a b - 2a b + a b + a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 2 3 +--R (b + a b - 2a b - 2a b + a b + a )cosh(x) - b + a b + 2a b +--R + +--R 3 2 4 5 +--R - 2a b - a b + a +--R Type: Union(Expression Integer,...) +--E 146 + +--S 147 of 531 +m1027:= a1027-r1027 +--R +--R +--R (130) +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )sinh(x) + (4a b + 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )cosh(x) - 2a b + 2a b +--R * +--R tanh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 2a b)sinh(x) + (4a b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 2a b)cosh(x) - 2a b + 2a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2a b - 2a b )sinh(x) + (- 4a b - 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2a b - 2a b )cosh(x) + 2a b - 2a b +--R * +--R tanh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 2a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )x sinh(x) + (4a b + 4a b )x cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 3 +--R (2a b + 2a b )x cosh(x) + (- 2a b + 2a b )x - 2b + 2a b +--R * +--R tanh(x) +--R + +--R 2 2 3 4 3 2 2 3 2 +--R ((2a b + 2a b)x + b + a b - a b - a b)sinh(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R ((4a b + 4a b)x + 2b + 2a b - 2a b - 2a b)cosh(x)sinh(x) +--R + +--R 2 2 3 4 3 2 2 3 2 2 2 3 +--R ((2a b + 2a b)x + b + a b - a b - a b)cosh(x) + (- 2a b + 2a b)x +--R + +--R 4 3 2 2 3 +--R - b - a b + 3a b - a b +--R / +--R 6 5 2 4 3 3 4 2 5 2 +--R (b + a b - 2a b - 2a b + a b + a b)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 5 2 4 +--R (b + a b - 2a b - 2a b + a b + a b)cosh(x) - b + a b + 2a b +--R + +--R 3 3 4 2 5 +--R - 2a b - a b + a b +--R * +--R tanh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (a b + a b - 2a b - 2a b + a b + a )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 5 2 4 3 3 +--R (a b + a b - 2a b - 2a b + a b + a )cosh(x) - a b + a b + 2a b +--R + +--R 4 2 5 6 +--R - 2a b - a b + a +--R Type: Expression Integer +--E 147 + +--S 148 of 531 +d1027:= D(m1027,x) +--R +--R +--R (131) +--R 4 3 2 2 4 4 3 2 2 3 +--R (b + 2a b + a b )sinh(x) + (4b + 8a b + 4a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 2 2 2 +--R ((6b + 12a b + 6a b )cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R ((4b + 8a b + 4a b )cosh(x) + (4b + 4a b )cosh(x))sinh(x) +--R + +--R 4 3 2 2 4 4 2 2 2 4 3 2 2 +--R (b + 2a b + a b )cosh(x) + (2b + 2a b )cosh(x) + b - 2a b + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 3 3 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) )tanh(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- b - 2a b - a b )sinh(x) + (- 4b - 8a b - 4a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 2 2 2 +--R ((- 6b - 12a b - 6a b )cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R ((- 4b - 8a b - 4a b )cosh(x) + (4b + 4a b )cosh(x))sinh(x) +--R + +--R 4 3 2 2 4 4 2 2 2 4 3 2 2 +--R (- b - 2a b - a b )cosh(x) + (2b + 2a b )cosh(x) - b + 2a b - a b +--R / +--R 6 5 3 3 4 2 4 +--R (b + 2a b - 2a b - a b )sinh(x) +--R + +--R 6 5 3 3 4 2 3 +--R (4b + 8a b - 8a b - 4a b )cosh(x)sinh(x) +--R + +--R 6 5 3 3 4 2 2 6 2 4 4 2 +--R ((6b + 12a b - 12a b - 6a b )cosh(x) - 2b + 4a b - 2a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 3 3 4 2 3 +--R (4b + 8a b - 8a b - 4a b )cosh(x) +--R + +--R 6 2 4 4 2 +--R (- 4b + 8a b - 4a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 3 3 4 2 4 6 2 4 4 2 2 +--R (b + 2a b - 2a b - a b )cosh(x) + (- 2b + 4a b - 2a b )cosh(x) +--R + +--R 6 5 3 3 4 2 +--R b - 2a b + 2a b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 5 2 4 4 2 5 4 +--R (2a b + 4a b - 4a b - 2a b)sinh(x) +--R + +--R 5 2 4 4 2 5 3 +--R (8a b + 16a b - 16a b - 8a b)cosh(x)sinh(x) +--R + +--R 5 2 4 4 2 5 2 5 3 3 5 +--R ((12a b + 24a b - 24a b - 12a b)cosh(x) - 4a b + 8a b - 4a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 4 2 5 3 +--R (8a b + 16a b - 16a b - 8a b)cosh(x) +--R + +--R 5 3 3 5 +--R (- 8a b + 16a b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 4 2 5 4 +--R (2a b + 4a b - 4a b - 2a b)cosh(x) +--R + +--R 5 3 3 5 2 5 2 4 4 2 5 +--R (- 4a b + 8a b - 4a b)cosh(x) + 2a b - 4a b + 4a b - 2a b +--R * +--R tanh(x) +--R + +--R 2 4 3 3 5 6 4 +--R (a b + 2a b - 2a b - a )sinh(x) +--R + +--R 2 4 3 3 5 6 3 +--R (4a b + 8a b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 4 3 3 5 6 2 2 4 4 2 6 2 +--R ((6a b + 12a b - 12a b - 6a )cosh(x) - 2a b + 4a b - 2a )sinh(x) +--R + +--R 2 4 3 3 5 6 3 2 4 4 2 6 +--R ((4a b + 8a b - 8a b - 4a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 5 6 4 2 4 4 2 6 2 +--R (a b + 2a b - 2a b - a )cosh(x) + (- 2a b + 4a b - 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 +--R a b - 2a b + 2a b - a +--R Type: Expression Integer +--E 148 + +--S 149 of 531 +t1028:= cosh(x)/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R (132) +--R cosh(x) +--R --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 149 + +--S 150 of 531 +r1028:= 1/2*b/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2+_ + sinh(x)/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R (133) +--R 2 +--R - 2b sinh(x) - 2a cosh(x)sinh(x) - b +--R ---------------------------------------------------------------------------- +--R 4 2 2 2 3 3 2 2 4 2 +--R (2b - 2a b )sinh(x) + (4a b - 4a b)cosh(x)sinh(x) + (2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 150 + +--S 151 of 531 +a1028:= integrate(t1028,x) +--R +--R +--R (134) +--R - 2b sinh(x) + (- 2b - 4a)cosh(x) +--R / +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x) - 3b - 4a b + 2a b +--R + +--R 3 4 +--R 4a b + a +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - 4a b - 2a b + 4a b + 3a )cosh(x) +--R Type: Union(Expression Integer,...) +--E 151 + +--S 152 of 531 +m1028:= a1028-r1028 +--R +--R +--R (135) +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b + 20a b + 24a b + 12a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (6b + 24a b + 36a b + 24a b + 6a )cosh(x) - 9b + 5a b + 9a b +--R + +--R 3 +--R 3a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b + 12a b + 24a b + 20a b + 6a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 3b - 15a b + 25a b + 15a b + 2a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 6a b + 6a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R (3b - a b - 9a b + 25a b + 6a )cosh(x) - 3b - a b + 3a b + a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + 3a b - a b - 3a b + 8a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- b - 3a b + a b + 3a b)cosh(x) +--R / +--R 7 6 2 5 3 4 4 3 5 2 5 +--R (2b + 6a b + 4a b - 4a b - 6a b - 2a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 4 +--R (6b + 22a b + 24a b - 4a b - 26a b - 18a b - 4a b)cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (6b + 30a b + 50a b + 18a b - 38a b - 46a b - 18a b - 2a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 6b - 2a b + 12a b + 4a b - 6a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (2b + 18a b + 46a b + 38a b - 18a b - 50a b - 30a b - 6a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (- 2b - 18a b + 36a b + 6a b - 18a b - 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 4 +--R (4a b + 18a b + 26a b + 4a b - 24a b - 22a b - 6a )cosh(x) +--R + +--R 6 2 5 3 4 4 3 6 7 2 +--R (- 4a b - 18a b + 6a b + 36a b - 18a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 5 +--R (2a b + 6a b + 4a b - 4a b - 6a b - 2a )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 3 +--R (- 2a b - 6a b + 4a b + 12a b - 2a b - 6a )cosh(x) +--R Type: Expression Integer +--E 152 + +--S 153 of 531 +d1028:= D(m1028,x) +--R +--R +--R (136) +--R 5 2 4 3 3 4 2 5 9 +--R (- a b - 4a b - 6a b - 4a b - a b)sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 8 +--R (- 6a b - 25a b - 40a b - 30a b - 10a b - a )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 6 +--R (- 14a b - 62a b - 108a b - 92a b - 38a b - 6a )cosh(x) + 4b +--R + +--R 5 3 3 4 2 5 +--R a b - 6a b - 12a b - 3a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 14a b - 70a b - 140a b - 140a b - 70a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (15b + 22a b - 20a b - 52a b - 49a b - 26a b - 2a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 14a b - 56a b - 84a b - 56a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (18b + 51a b - 48a b - 162a b - 126a b - 57a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 4b - 7a b + 16a b + 2a b - 12a b - 3a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (14a b + 56a b + 84a b + 56a b + 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (b + 16a b - 48a b - 224a b - 215a b - 72a b - 18a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (6b + 34a b - a b + 12a b - 28a b - 22a b - a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (14a b + 70a b + 140a b + 140a b + 70a b + 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 16b - 57a b - 64a b - 138a b - 192a b - 85a b - 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (16b + 68a b + 34a b - 56a b - 28a b - 28a b - 6a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 9a b + 12a b + 2a b - 4a b - a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (6a b + 38a b + 92a b + 108a b + 62a b + 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 15b - 66a b - 84a b - 36a b - 63a b - 66a b - 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (24b + 54a b + 60a b - 68a b - 64a b - 2a b - 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 9b + 6a b - 6a b + 24a b - 9a b - 6a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 8 +--R (a b + 10a b + 30a b + 40a b + 25a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 6b - 27a b - 48a b - 14a b + 10a b - 15a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (12b + 35a b + 14a b - 10a b - 56a b - a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 6b - 9a b + 24a b - 6a b + 6a b - 9a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (a b + 4a b + 6a b + 4a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (- b - 4a b - 8a b - 8a b + 7a b + 4a b - 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (2b + 8a b + 5a b - 8a b - 4a b - 8a b + 5a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- b - 4a b + 2a b + 12a b - 9a b )cosh(x) +--R / +--R 9 8 2 7 4 5 5 4 6 3 9 +--R (b + 4a b + 5a b - 5a b - 4a b - a b )sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 27a b + 42a b + 15a b - 30a b - 39a b - 18a b - 3a b ) +--R * +--R 8 +--R cosh(x)sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 78a b + 150a b + 102a b - 60a b - 150a b - 102a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 6b - 8a b + 10a b + 16a b - 2a b - 8a b - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 20b + 125a b + 298a b + 298a b - 6a b - 300a b - 290a b +--R + +--R 7 2 8 9 +--R - 122a b - 22a b - a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 20b - 50a b + 4a b + 94a b + 52a b - 38a b - 36a b +--R + +--R 7 2 +--R - 6a b +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 120a b + 360a b + 486a b + 174a b - 330a b - 480a b +--R + +--R 7 2 8 9 +--R - 270a b - 69a b - 6a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 24b - 108a b - 90a b + 156a b + 246a b + 12a b - 126a b +--R + +--R 7 2 8 +--R - 60a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 9b - 12a b - 11a b + 16a b + 3a b - 4a b - a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b + 69a b + 270a b + 480a b + 330a b - 174a b - 486a b +--R + +--R 7 2 8 9 +--R - 360a b - 120a b - 15a +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 12b - 104a b - 200a b + 34a b + 392a b + 242a b - 136a b +--R + +--R 7 2 8 9 +--R - 170a b - 44a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 35a b - 70a b - 33a b + 82a b + a b - 18a b - 3a b ) +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 122a b + 290a b + 300a b + 6a b - 298a b +--R + +--R 7 2 8 9 +--R - 298a b - 125a b - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 2b - 44a b - 170a b - 136a b + 242a b + 392a b + 34a b +--R + +--R 7 2 8 9 +--R - 200a b - 104a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 48a b - 154a b - 22a b + 162a b - 24a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 102a b + 150a b + 60a b - 102a b - 150a b +--R + +--R 8 9 +--R - 78a b - 15a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 6a b - 60a b - 126a b + 12a b + 246a b + 156a b - 90a b +--R + +--R 8 9 +--R - 108a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 24a b - 162a b + 22a b + 154a b - 48a b +--R + +--R 8 9 +--R - 22a b - a +--R * +--R 3 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b + 39a b + 30a b - 15a b - 42a b - 27a b - 6a ) +--R * +--R 8 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 6a b - 36a b - 38a b + 52a b + 94a b + 4a b - 50a b +--R + +--R 9 +--R - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b - a b - 82a b + 33a b + 70a b - 35a b - 6a ) +--R * +--R 4 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 4 5 5 4 7 2 8 9 9 +--R (a b + 4a b + 5a b - 5a b - 4a b - a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 7 +--R (- 2a b - 8a b - 2a b + 16a b + 10a b - 8a b - 6a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 5 +--R (a b + 4a b - 3a b - 16a b + 11a b + 12a b - 9a )cosh(x) +--R Type: Expression Integer +--E 153 + +--S 154 of 531 +t1029:= cosh(x)^3/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R (137) +--R 3 +--R cosh(x) +--R --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 154 + +--S 155 of 531 +r1029:= a*(a^2+3*b^2)*x/(a^2-b^2)^3-b*(3*a^2+b^2)*log(a*cosh(x)+_ + b*sinh(x))/(a^2-b^2)^3+1/2*b/(a^2-b^2)/(a+b*tanh(x))^2+_ + 2*a*b/(a^2-b^2)^2/(a+b*tanh(x)) +--R +--R +--R (138) +--R 5 2 3 2 4 3 2 2 3 4 +--R ((2b + 6a b )tanh(x) + (4a b + 12a b )tanh(x) + 2a b + 6a b) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b - 2a b )x tanh(x) + ((- 12a b - 4a b)x + 4a b - 4a b )tanh(x) +--R + +--R 3 2 5 5 2 3 4 +--R (- 6a b - 2a )x - b + 6a b - 5a b +--R / +--R 8 2 6 4 4 6 2 2 +--R (2b - 6a b + 6a b - 2a b )tanh(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 8 +--R (4a b - 12a b + 12a b - 4a b)tanh(x) + 2a b - 6a b + 6a b - 2a +--R Type: Expression Integer +--E 155 + +--S 156 of 531 +a1029:= integrate(t1029,x) +--R +--R +--R (139) +--R 5 4 2 3 3 2 4 4 +--R (b + 2a b + 4a b + 6a b + 3a b)sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b + 8a b + 16a b + 24a b + 12a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 2 3 +--R (6b + 12a b + 24a b + 36a b + 18a b)cosh(x) - 2b - 4a b +--R + +--R 4 +--R 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b + 8a b + 16a b + 24a b + 12a b)cosh(x) +--R + +--R 5 2 3 4 +--R (- 4b - 8a b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (b + 2a b + 4a b + 6a b + 3a b)cosh(x) +--R + +--R 5 2 3 4 2 5 4 2 3 3 2 4 +--R (- 2b - 4a b + 6a b)cosh(x) + b - 2a b + 4a b - 6a b + 3a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- b - 5a b - 10a b - 10a b - 5a b - a )x sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 4b - 20a b - 40a b - 40a b - 20a b - 4a )x cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 6b - 30a b - 60a b - 60a b - 30a b - 6a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b + 6a b + 4a b - 4a b - 6a b - 2a )x - 2b + 6a b + 2a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 4b - 20a b - 40a b - 40a b - 20a b - 4a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 +--R (4b + 12a b + 8a b - 8a b - 12a b - 4a )x - 4b + 12a b +--R + +--R 2 3 3 2 +--R 4a b - 12a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- b - 5a b - 10a b - 10a b - 5a b - a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b + 6a b + 4a b - 4a b - 6a b - 2a )x - 2b + 6a b + 2a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (- b - a b + 2a b + 2a b - a b - a )x - 6a b + 12a b - 6a b +--R / +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (6b + 12a b - 12a b - 36a b + 36a b + 12a b - 12a b - 6a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R - 2b + 8a b - 12a b + 8a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 3 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 4b + 16a b - 24a b + 16a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 7 2 6 +--R (- 2b + 8a b - 12a b + 8a b - 2a )cosh(x) + b - 2a b - 2a b +--R + +--R 3 5 5 3 6 2 7 8 +--R 6a b - 6a b + 2a b + 2a b - a +--R Type: Union(Expression Integer,...) +--E 156 + +--S 157 of 531 +m1029:= a1029-r1029 +--R +--R +--R (140) +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 7 +--R (- 12b - 24a b - 48a b - 72a b - 36a b )cosh(x) + 4b +--R + +--R 2 5 4 3 +--R 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )cosh(x) +--R + +--R 7 2 5 4 3 +--R (8b + 16a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )cosh(x) +--R + +--R 7 2 5 4 3 2 7 6 2 5 3 4 +--R (4b + 8a b - 12a b )cosh(x) - 2b + 4a b - 8a b + 12a b +--R + +--R 4 3 +--R - 6a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (- 24a b - 48a b - 96a b - 144a b - 72a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R 8a b + 16a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (16a b + 32a b - 48a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 +--R (8a b + 16a b - 24a b )cosh(x) - 4a b + 8a b - 16a b +--R + +--R 4 3 5 2 +--R 24a b - 12a b +--R * +--R tanh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)cosh(x)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 2 5 +--R (- 12a b - 24a b - 48a b - 72a b - 36a b)cosh(x) + 4a b +--R + +--R 4 3 6 +--R 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (8a b + 16a b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 5 2 6 +--R (4a b + 8a b - 12a b)cosh(x) - 2a b + 4a b - 8a b + 12a b - 6a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (2b + 4a b + 8a b + 12a b + 6a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (8b + 16a b + 32a b + 48a b + 24a b )cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 7 +--R (12b + 24a b + 48a b + 72a b + 36a b )cosh(x) - 4b +--R + +--R 2 5 4 3 +--R - 8a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (8b + 16a b + 32a b + 48a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 +--R (- 8b - 16a b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (2b + 4a b + 8a b + 12a b + 6a b )cosh(x) +--R + +--R 7 2 5 4 3 2 7 6 2 5 3 4 +--R (- 4b - 8a b + 12a b )cosh(x) + 2b - 4a b + 8a b - 12a b +--R + +--R 4 3 +--R 6a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (4a b + 8a b + 16a b + 24a b + 12a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (16a b + 32a b + 64a b + 96a b + 48a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 6 +--R (24a b + 48a b + 96a b + 144a b + 72a b )cosh(x) - 8a b +--R + +--R 3 4 5 2 +--R - 16a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (16a b + 32a b + 64a b + 96a b + 48a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (- 16a b - 32a b + 48a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (4a b + 8a b + 16a b + 24a b + 12a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 +--R (- 8a b - 16a b + 24a b )cosh(x) + 4a b - 8a b + 16a b +--R + +--R 4 3 5 2 +--R - 24a b + 12a b +--R * +--R tanh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (2a b + 4a b + 8a b + 12a b + 6a b)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (8a b + 16a b + 32a b + 48a b + 24a b)cosh(x)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 2 5 +--R (12a b + 24a b + 48a b + 72a b + 36a b)cosh(x) - 4a b +--R + +--R 4 3 6 +--R - 8a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (8a b + 16a b + 32a b + 48a b + 24a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (- 8a b - 16a b + 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (2a b + 4a b + 8a b + 12a b + 6a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 5 2 +--R (- 4a b - 8a b + 12a b)cosh(x) + 2a b - 4a b + 8a b - 12a b +--R + +--R 6 +--R 6a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )x sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )x cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 +--R (- 12b - 24a b - 48a b - 72a b - 36a b )x cosh(x) +--R + +--R 7 2 5 4 3 7 6 2 5 3 4 +--R (4b + 8a b - 12a b )x - 4b + 12a b + 4a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )x cosh(x) +--R + +--R 7 2 5 4 3 7 6 2 5 3 4 +--R ((8b + 16a b - 24a b )x - 8b + 24a b + 8a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )x cosh(x) +--R + +--R 7 2 5 4 3 7 6 2 5 3 4 2 +--R ((4b + 8a b - 12a b )x - 4b + 12a b + 4a b - 12a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 6 2 5 3 4 +--R (- 2b + 4a b - 8a b + 12a b - 6a b )x - 12a b + 24a b - 12a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )x - 4a b - 8a b +--R + +--R 4 3 5 2 +--R 8a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )x - 16a b - 32a b +--R + +--R 4 3 5 2 +--R 32a b + 16a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 24a b - 48a b - 96a b - 144a b - 72a b )x - 24a b +--R + +--R 2 5 4 3 5 2 +--R - 48a b + 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 3 4 5 2 2 5 3 4 4 3 5 2 +--R (8a b + 16a b - 24a b )x + 24a b - 8a b - 24a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )x - 16a b +--R + +--R 2 5 4 3 5 2 +--R - 32a b + 32a b + 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 3 4 5 2 2 5 3 4 4 3 +--R (16a b + 32a b - 48a b )x + 48a b - 16a b - 48a b +--R + +--R 5 2 +--R 16a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )x - 4a b - 8a b +--R + +--R 4 3 5 2 +--R 8a b + 4a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 3 4 5 2 2 5 3 4 4 3 5 2 +--R ((8a b + 16a b - 24a b )x + 24a b - 8a b - 24a b + 8a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 4a b + 8a b - 16a b + 24a b - 12a b )x - 4a b - 16a b +--R + +--R 3 4 4 3 5 2 +--R 48a b - 32a b + 4a b +--R * +--R tanh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)x + b + 2a b - 5a b +--R + +--R 3 4 4 3 5 2 6 +--R - 12a b - a b + 10a b + 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)x + 4b + 8a b - 20a b +--R + +--R 3 4 4 3 5 2 6 +--R - 48a b - 4a b + 40a b + 20a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 +--R (- 12a b - 24a b - 48a b - 72a b - 36a b)x + 6b + 12a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 30a b - 72a b - 6a b + 60a b + 30a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 4 3 6 7 2 5 3 4 4 3 5 2 +--R (4a b + 8a b - 12a b)x - 2b + 10a b + 12a b - 18a b - 12a b +--R + +--R 6 +--R 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)x + 4b + 8a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 20a b - 48a b - 4a b + 40a b + 20a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 5 4 3 6 7 2 5 3 4 4 3 +--R (8a b + 16a b - 24a b)x - 4b + 20a b + 24a b - 36a b +--R + +--R 5 2 6 +--R - 24a b + 20a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)x + b + 2a b - 5a b +--R + +--R 3 4 4 3 5 2 6 +--R - 12a b - a b + 10a b + 5a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 5 4 3 6 7 2 5 3 4 4 3 5 2 +--R (4a b + 8a b - 12a b)x - 2b + 10a b + 12a b - 18a b - 12a b +--R + +--R 6 +--R 10a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 4 3 +--R (- 2a b + 4a b - 8a b + 12a b - 6a b)x + b - 2a b - 5a b + 23a b +--R + +--R 5 2 6 +--R - 22a b + 5a b +--R / +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 12b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 8 2 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R - 4b + 16a b - 24a b + 16a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R (- 8b + 32a b - 48a b + 32a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 10 9 +--R (- 4b + 16a b - 24a b + 16a b - 4a b )cosh(x) + 2b - 4a b +--R + +--R 2 8 3 7 5 5 6 4 7 3 8 2 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 +--R 24a b + 48a b - 48a b - 144a b + 144a b + 48a b +--R + +--R 8 2 9 +--R - 48a b - 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R - 8a b + 32a b - 48a b + 32a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R (- 16a b + 64a b - 96a b + 64a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 9 2 8 +--R (- 8a b + 32a b - 48a b + 32a b - 8a b)cosh(x) + 4a b - 8a b +--R + +--R 3 7 4 6 6 4 7 3 8 2 9 +--R - 8a b + 24a b - 24a b + 8a b + 8a b - 4a b +--R * +--R tanh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 4 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a )sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b - 8a ) +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 +--R 12a b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 10 +--R - 12a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R - 4a b + 16a b - 24a b + 16a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b - 8a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R (- 8a b + 32a b - 48a b + 32a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 4 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 2 8 3 7 +--R (- 4a b + 16a b - 24a b + 16a b - 4a )cosh(x) + 2a b - 4a b +--R + +--R 4 6 5 5 7 3 8 2 9 10 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a +--R Type: Expression Integer +--E 157 + +--S 158 of 531 +d1029:= D(m1029,x) +--R +--R +--R (141) +--R 6 2 5 3 4 4 3 6 +--R (- 2a b - 6a b - 6a b - 2a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (- 12a b - 36a b - 36a b - 12a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 2 7 6 +--R (- 30a b - 90a b - 90a b - 30a b )cosh(x) + 4b - 2a b +--R + +--R 2 5 3 4 4 3 +--R - 6a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (- 40a b - 120a b - 120a b - 40a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R (16b - 8a b - 24a b - 24a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (- 30a b - 90a b - 90a b - 30a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 7 6 +--R (24b - 12a b - 36a b - 36a b - 36a b )cosh(x) + 4b + 2a b +--R + +--R 2 5 3 4 4 3 +--R - 6a b + 6a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (- 12a b - 36a b - 36a b - 12a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (16b - 8a b - 24a b - 24a b - 24a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R (8b + 4a b - 12a b + 12a b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (- 2a b - 6a b - 6a b - 2a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (4b - 2a b - 6a b - 6a b - 6a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 6 2 5 3 4 +--R (4b + 2a b - 6a b + 6a b - 6a b )cosh(x) + 2a b - 6a b + 6a b +--R + +--R 4 3 +--R - 2a b +--R * +--R 3 +--R tanh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (b + 3a b - 8a b - 9a b - 3a b )sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (6b + 18a b - 48a b - 54a b - 18a b )cosh(x)sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 2 7 +--R (15b + 45a b - 120a b - 135a b - 45a b )cosh(x) - 3b +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 9a b - 12a b - 24a b - 9a b - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 3 +--R (20b + 60a b - 160a b - 180a b - 60a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (- 12b + 36a b - 48a b - 96a b - 36a b - 36a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 4 +--R (15b + 45a b - 120a b - 135a b - 45a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 +--R (- 18b + 54a b - 72a b - 144a b - 54a b - 54a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 3b + 9a b + 12a b - 24a b + 9a b - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (6b + 18a b - 48a b - 54a b - 18a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (- 12b + 36a b - 48a b - 96a b - 36a b - 36a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (6b + 18a b + 24a b - 48a b + 18a b - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (b + 3a b - 8a b - 9a b - 3a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (- 3b + 9a b - 12a b - 24a b - 9a b - 9a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 7 6 +--R (3b + 9a b + 12a b - 24a b + 9a b - 9a b )cosh(x) - b + 3a b +--R + +--R 3 4 4 3 5 2 +--R - 8a b + 9a b - 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b + 6a b + 6a b + 2a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (12a b + 36a b + 36a b + 12a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 2 6 2 5 +--R (30a b + 90a b + 90a b + 30a b )cosh(x) - 6a b + 6a b +--R + +--R 3 4 4 3 +--R - 18a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (40a b + 120a b + 120a b + 40a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (- 24a b + 24a b - 72a b - 120a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (30a b + 90a b + 90a b + 30a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 6 2 5 +--R (- 36a b + 36a b - 108a b - 180a b )cosh(x) + 6a b + 6a b +--R + +--R 3 4 4 3 +--R 18a b - 30a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (12a b + 36a b + 36a b + 12a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (- 24a b + 24a b - 72a b - 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (12a b + 12a b + 36a b - 60a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b + 6a b + 6a b + 2a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (- 6a b + 6a b - 18a b - 30a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 6 2 5 3 4 +--R (6a b + 6a b + 18a b - 30a b )cosh(x) - 2a b + 6a b - 6a b +--R + +--R 4 3 +--R 2a b +--R * +--R tanh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (- b - 3a b + 8a b + 9a b + 3a b )sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (- 6b - 18a b + 48a b + 54a b + 18a b )cosh(x)sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 2 7 6 +--R (- 15b - 45a b + 120a b + 135a b + 45a b )cosh(x) + 3b + 3a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 12a b - 8a b + a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 3 +--R (- 20b - 60a b + 160a b + 180a b + 60a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (12b + 12a b - 48a b - 32a b + 4a b - 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 4 +--R (- 15b - 45a b + 120a b + 135a b + 45a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 7 +--R (18b + 18a b - 72a b - 48a b + 6a b - 18a b )cosh(x) - 3b +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 3a b + 12a b - 8a b - a b - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (- 6b - 18a b + 48a b + 54a b + 18a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (12b + 12a b - 48a b - 32a b + 4a b - 12a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (- 6b + 6a b + 24a b - 16a b - 2a b - 6a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (- b - 3a b + 8a b + 9a b + 3a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (3b + 3a b - 12a b - 8a b + a b - 3a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 7 6 +--R (- 3b + 3a b + 12a b - 8a b - a b - 3a b )cosh(x) + b - 3a b +--R + +--R 3 4 4 3 5 2 +--R 8a b - 9a b + 3a b +--R / +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 6 +--R (b + 3a b + a b - 5a b - 5a b + a b + 3a b + a b )sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R (6b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b + 6a b ) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 15b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 7 3 +--R 15a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 3b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 20b + 60a b + 20a b - 100a b - 100a b + 20a b + 60a b +--R + +--R 7 3 +--R 20a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 12b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 7 3 +--R 12a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 15b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 7 3 +--R 15a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 18b - 18a b + 54a b + 54a b - 54a b - 54a b + 18a b +--R + +--R 7 3 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 3b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 6b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b +--R + +--R 7 3 +--R 6a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 12b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 7 3 +--R 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 6b - 6a b - 18a b + 18a b + 18a b - 18a b - 6a b +--R + +--R 7 3 +--R 6a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 6 +--R (b + 3a b + a b - 5a b - 5a b + a b + 3a b + a b )cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R (- 3b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R (3b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - b + 3a b - a b - 5a b + 5a b + a b - 3a b + a b +--R * +--R 3 +--R tanh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 8 2 +--R 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 7 3 8 2 +--R 135a b + 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 60a b + 180a b + 60a b - 300a b - 300a b + 60a b +--R + +--R 7 3 8 2 +--R 180a b + 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 7 3 8 2 +--R 36a b + 36a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 7 3 8 2 +--R 135a b + 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 54a b - 54a b + 162a b + 162a b - 162a b - 162a b +--R + +--R 7 3 8 2 +--R 54a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 8 2 +--R 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 7 3 8 2 +--R 36a b + 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 18a b - 18a b - 54a b + 54a b + 54a b - 54a b - 18a b +--R + +--R 8 2 +--R 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b ) +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b +--R + +--R 8 2 +--R 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 3a b + 9a b - 3a b - 15a b + 15a b + 3a b - 9a b + 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 9 +--R 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 8 2 9 +--R 135a b + 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 60a b + 180a b + 60a b - 300a b - 300a b + 60a b +--R + +--R 8 2 9 +--R 180a b + 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 8 2 9 +--R 36a b + 36a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 8 2 9 +--R 135a b + 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 54a b - 54a b + 162a b + 162a b - 162a b - 162a b +--R + +--R 8 2 9 +--R 54a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 9 +--R 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 8 2 9 +--R 36a b + 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b - 18a b - 54a b + 54a b + 54a b - 54a b - 18a b +--R + +--R 9 +--R 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b +--R + +--R 9 +--R 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 3a b + 9a b - 3a b - 15a b + 15a b + 3a b - 9a b + 3a b +--R * +--R tanh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 6 +--R (a b + 3a b + a b - 5a b - 5a b + a b + 3a b + a )sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (6a b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b + 6a ) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 15a b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 10 +--R 15a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R - 3a b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 20a b + 60a b + 20a b - 100a b - 100a b + 20a b + 60a b +--R + +--R 10 +--R 20a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 12a b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 10 +--R 12a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 15a b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 10 +--R 15a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 18a b - 18a b + 54a b + 54a b - 54a b - 54a b + 18a b +--R + +--R 10 +--R 18a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R 3a b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (6a b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b + 6a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 12a b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 10 +--R 12a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (6a b - 6a b - 18a b + 18a b + 18a b - 18a b - 6a b + 6a ) +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 6 +--R (a b + 3a b + a b - 5a b - 5a b + a b + 3a b + a )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 4 +--R (- 3a b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 2 +--R (3a b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R - a b + 3a b - a b - 5a b + 5a b + a b - 3a b + a +--R Type: Expression Integer +--E 158 + +--S 159 of 531 +t1030:= cosh(x)*sinh(x)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R cosh(x)sinh(x) +--R (142) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 159 + +--S 160 of 531 +r1030:= a*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ + a*cosh(x)/(a^2-b^2)-b*sinh(x)/(a^2-b^2) +--R +--R +--R (143) +--R +---------+ +--R a sinh(x) + b cosh(x) | 2 2 +--R - a b atan(---------------------) + (b sinh(x) - a cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression Integer +--E 160 + +--S 161 of 531 +a1030:= integrate(t1030,x) +--R +--R +--R (144) +--R [ +--R (2a b sinh(x) + 2a b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R (4a b sinh(x) + 4a b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 161 + +--S 162 of 531 +m1030a:= a1030.1-r1030 +--R +--R +--R (145) +--R +---------+ +--R | 2 2 +--R (2a b sinh(x) + 2a b cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R (2a b sinh(x) + 2a b cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression Integer +--E 162 + +--S 163 of 531 +d1030a:= D(m1030a,x) +--R +--R +--R (146) +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 4 +--R ((b + 6a b + 9a b + 4a b)cosh(x) - b + 2a b + 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (2b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 2a b + 6a b + 6a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 4a b - 9a b - 6a b - a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 4 +--R (8a b + 8a b + 8a b)cosh(x) - a b - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 4 +--R (4b + 6a b + 6a b + 2a b - 2a )cosh(x) + (- 2b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 2 2 4 4 +--R (- b - 2a b - a b )cosh(x) + (3b + 2a b - a )cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 4 +--R (- 3b + 2a b + a b )cosh(x) + b - 2a b + a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 163 + +--S 164 of 531 +m1030b:= a1030.2-r1030 +--R +--R +--R (147) +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R (4a b sinh(x) + 4a b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R a sinh(x) + b cosh(x) +--R (2a b sinh(x) + 2a b cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression Integer +--E 164 + +--S 165 of 531 +d1030b:= D(m1030b,x) +--R +--R +--R (148) +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 4 +--R ((b + 6a b + 9a b + 4a b)cosh(x) - b + 2a b + 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (2b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 2a b + 6a b + 6a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 4a b - 9a b - 6a b - a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 4 +--R (8a b + 8a b + 8a b)cosh(x) - a b - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 4 +--R (4b + 6a b + 6a b + 2a b - 2a )cosh(x) + (- 2b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 2 2 4 4 +--R (- b - 2a b - a b )cosh(x) + (3b + 2a b - a )cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 4 +--R (- 3b + 2a b + a b )cosh(x) + b - 2a b + a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 165 + +--S 166 of 531 +t1031:= cosh(x)*sinh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R cosh(x)sinh(x) +--R (149) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 166 + +--S 167 of 531 +r1031:= 1/2/(a^2-b^2)^2*(-a^3*x-a*b^2*x+2*a^2*b*log(a*cosh(x)+b*sinh(x))+_ + a^3*cosh(x)*sinh(x)-a*cosh(x)*sinh(x)*b^2+a^2*b-_ + a^2*b*cosh(x)^2-b^3+cosh(x)^2*b^3) +--R +--R +--R (150) +--R 2 2 3 +--R 2a b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b - a b)cosh(x) + (- a b - a )x - b + a b +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression Integer +--E 167 + +--S 168 of 531 +a1031:= integrate(t1031,x) +--R +--R +--R (151) +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 4a b - 8a b - 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 8a b - 16a b - 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 4a b - 8a b - 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 531 +m1031:= a1031-r1031 +--R +--R +--R (152) +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 2 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) - 8a b x + 4b - 4a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R ((- 4b + 4a b)cosh(x) + (- 16a b x + 8b - 8a b)cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) + (- 8a b x + 4b - 4a b)cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression Integer +--E 169 + +--S 170 of 531 +d1031:= D(m1031,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (153) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression Integer +--E 170 + +--S 171 of 531 +t1032:= cosh(x)*sinh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R cosh(x)sinh(x) +--R (154) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 171 + +--S 172 of 531 +r1032:= -a^3*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ + a^3*cosh(x)/(a^2-b^2)^2+a*cosh(x)^3/(3*a^2-3*b^2)+_ + a^4*sinh(x)/b/(a^2-b^2)^2-a^2*sinh(x)/b/(a^2-b^2)-_ + b*sinh(x)^3/(3*a^2-3*b^2) +--R +--R +--R (155) +--R 3 a sinh(x) + b cosh(x) +--R - 3a b atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 3 +--R (b - a b)sinh(x) + 3a b sinh(x) + (- a b + a )cosh(x) +--R + +--R 3 +--R - 3a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 | 2 2 +--R (3b - 6a b + 3a )\|- b + a +--R Type: Expression Integer +--E 172 + +--S 173 of 531 +a1032:= integrate(t1032,x) +--R +--R +--R (156) +--R [ +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) - 3b - 3a b + 15a b +--R + +--R 3 +--R - 9a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 90a b - 54a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) - 3b - 3a b + 15a b +--R + +--R 3 +--R - 9a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 90a b - 54a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 173 + +--S 174 of 531 +m1032a:= a1032.1-r1032 +--R +--R +--R (157) +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((- 9b - 15a b + 9a b + 15a )cosh(x) - 3b - 3a b - 9a b - 9a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b - 12a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 36a b + 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + 7a b - a b - 7a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 174 + +--S 175 of 531 +d1032a:= D(m1032a,x) +--R +--R +--R (158) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + a b +--R + +--R 4 2 5 6 +--R a b + 8a b + 7a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (4a b + 4a b - 16a b + 8a b + 60a b + 36a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (10b + 24a b - 22a b - 72a b + 62a b + 160a b + 62a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R 2b - 6a b + 6a b + 14a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (20b + 20a b - 104a b - 80a b + 164a b + 172a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b + 8a b - 12a b - 8a b + 20a b + 32a b + 52a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 64a b - 144a b + 40a b + 164a b + 24a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6b + 32a b - 10a b - 16a b + 50a b + 112a b + 66a )cosh(x) +--R + +--R 2 4 4 2 5 6 +--R 2a b - 4a b - 8a b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 32b - 132a b - 68a b + 112a b + 24a b - 92a b - 36a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (16b + 48a b - 8a b + 96a b + 144a b + 24a )cosh(x) +--R + +--R 5 2 4 4 2 5 6 +--R (4a b - 4a b - 8a b - 20a b + 28a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 42b - 88a b + 6a b + 40a b - 62a b - 64a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (22b + 32a b + 6a b + 16a b + 98a b + 80a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (2b + 8a b - 26a b + 8a b - 2a b - 16a b + 26a )cosh(x) - 2b +--R + +--R 2 4 4 2 6 +--R 5a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 20b - 20a b + 8a b - 16a b - 36a b - 12a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (12b + 8a b + 20a b + 8a b + 44a b + 16a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 4a b - 32a b + 16a b + 4a b - 4a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 4b - 2a b + 12a b + 4a b - 12a b - 2a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 +--R (b - 2a b + a b )cosh(x) +--R + +--R 6 2 4 3 3 4 2 6 8 +--R (- 3b - a b - 8a b - 5a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 4 +--R (2b - 12a b + 8a b + 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- 3b + 8a b - 7a b + 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression Integer +--E 175 + +--S 176 of 531 +m1032b:= a1032.2-r1032 +--R +--R +--R (159) +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((- 9b - 15a b + 9a b + 15a )cosh(x) - 3b - 3a b - 9a b - 9a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b - 12a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 36a b + 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + 7a b - a b - 7a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 176 + +--S 177 of 531 +d1032b:= D(m1032b,x) +--R +--R +--R (160) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + a b +--R + +--R 4 2 5 6 +--R a b + 8a b + 7a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (4a b + 4a b - 16a b + 8a b + 60a b + 36a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (10b + 24a b - 22a b - 72a b + 62a b + 160a b + 62a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R 2b - 6a b + 6a b + 14a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (20b + 20a b - 104a b - 80a b + 164a b + 172a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b + 8a b - 12a b - 8a b + 20a b + 32a b + 52a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 64a b - 144a b + 40a b + 164a b + 24a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6b + 32a b - 10a b - 16a b + 50a b + 112a b + 66a )cosh(x) +--R + +--R 2 4 4 2 5 6 +--R 2a b - 4a b - 8a b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 32b - 132a b - 68a b + 112a b + 24a b - 92a b - 36a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (16b + 48a b - 8a b + 96a b + 144a b + 24a )cosh(x) +--R + +--R 5 2 4 4 2 5 6 +--R (4a b - 4a b - 8a b - 20a b + 28a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 42b - 88a b + 6a b + 40a b - 62a b - 64a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (22b + 32a b + 6a b + 16a b + 98a b + 80a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (2b + 8a b - 26a b + 8a b - 2a b - 16a b + 26a )cosh(x) - 2b +--R + +--R 2 4 4 2 6 +--R 5a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 20b - 20a b + 8a b - 16a b - 36a b - 12a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (12b + 8a b + 20a b + 8a b + 44a b + 16a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 4a b - 32a b + 16a b + 4a b - 4a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 4b - 2a b + 12a b + 4a b - 12a b - 2a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 +--R (b - 2a b + a b )cosh(x) +--R + +--R 6 2 4 3 3 4 2 6 8 +--R (- 3b - a b - 8a b - 5a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 4 +--R (2b - 12a b + 8a b + 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- 3b + 8a b - 7a b + 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression Integer +--E 177 + +--S 178 of 531 +t1033:= sinh(x)*cosh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R cosh(x) sinh(x) +--R (161) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 178 + +--S 179 of 531 +r1033:= -1/2*(-b^3*x-a^2*b*x+2*a*b^2*log(a*cosh(x)+b*sinh(x))+_ + a^2*b*sinh(x)*cosh(x)-b^3*sinh(x)*cosh(x)+a^3-cosh(x)^2*a^3-_ + b^2*a+cosh(x)^2*b^2*a)/(a^2-b^2)^2 +--R +--R +--R (162) +--R 2 3 2 +--R - 2a b log(b sinh(x) + a cosh(x)) + (b - a b)cosh(x)sinh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- a b + a )cosh(x) + (b + a b)x + a b - a +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression Integer +--E 179 + +--S 180 of 531 +a1033:= integrate(t1033,x) +--R +--R +--R (163) +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (4b + 8a b + 4a b)x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 2 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (8b + 16a b + 8a b)x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 2 3 +--R (b - a b - a b + a )cosh(x) + (4b + 8a b + 4a b)x cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression Integer,...) +--E 180 + +--S 181 of 531 +m1033:= a1033-r1033 +--R +--R +--R (164) +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (b - a b - a b + a )sinh(x) + (- 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R ((- 2b - 2a b + 2a b + 2a )cosh(x) + 8a b x - 4a b + 4a )sinh(x) +--R + +--R 2 3 3 2 2 3 +--R ((4a b - 4a )cosh(x) + (16a b x - 8a b + 8a )cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 3 +--R (b + 3a b - a b - 3a )cosh(x) + (8a b x - 4a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression Integer +--E 181 + +--S 182 of 531 +d1033:= D(m1033,x) +--R +--R +--R 4 2 2 4 +--R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 +--R (165) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression Integer +--E 182 + +--S 183 of 531 +t1034:= sinh(x)*cosh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R cosh(x) sinh(x) +--R (166) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression Integer +--E 183 + +--S 184 of 531 +r1034:= -a*b^3*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ + a*b^2*cosh(x)/(a^2-b^2)^2+a*cosh(x)^3/(3*a^2-3*b^2)+_ + a^2*b*sinh(x)/(a^2-b^2)^2-b*sinh(x)/(a^2-b^2)-b*sinh(x)^3/(3*a^2-3*b^2) +--R +--R +--R (167) +--R 3 a sinh(x) + b cosh(x) +--R - 3a b atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 3 2 3 3 +--R (b - a b)sinh(x) + 3b sinh(x) + (- a b + a )cosh(x) +--R + +--R 2 +--R - 3a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 | 2 2 +--R (3b - 6a b + 3a )\|- b + a +--R Type: Expression Integer +--E 184 + +--S 185 of 531 +a1034:= integrate(t1034,x) +--R +--R +--R (168) +--R [ +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) + 9b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (54b - 90a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (9b - 15a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) + 9b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (54b - 90a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (9b - 15a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 185 + +--S 186 of 531 +m1034a:= a1034.1-r1034 +--R +--R +--R (169) +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 9b - 15a b + 9a b + 15a )cosh(x) - 15b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 36b - 36a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (12b + 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 3 2 2 3 4 +--R (b + 7a b - a b - 7a )cosh(x) + (9b + 9a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 186 + +--S 187 of 531 +d1034a:= D(m1034a,x) +--R +--R +--R (170) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + 5a b +--R + +--R 3 3 4 2 6 +--R 8a b + a b + 3a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (12a b + 36a b + 16a b - 8a b + 20a b + 20a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (14b + 64a b + 62a b - 40a b - 6a b + 88a b + 42a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - 2b + 6a b + 10a b + 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (36b + 92a b - 24a b - 112a b + 68a b + 132a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 16a b + 44a b + 8a b + 20a b + 8a b + 12a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (24b - 24a b - 164a b - 40a b + 144a b + 64a b - 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 14b + 80a b + 98a b + 16a b + 6a b + 32a b + 22a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 +--R - 2a b - 8a b + 12a b - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b - 172a b - 164a b + 80a b + 104a b - 20a b - 20a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (24b + 144a b + 96a b - 8a b + 48a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 8b + 4a b - 4a b - 16a b + 32a b - 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 62b - 160a b - 62a b + 72a b + 22a b - 24a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (66b + 112a b + 50a b - 16a b - 10a b + 32a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (- 26b + 16a b + 2a b - 8a b + 26a b - 8a b - 2a )cosh(x) + 2b +--R + +--R 2 4 4 2 6 +--R - 7a b + 8a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 36b - 60a b - 8a b + 16a b - 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (52b + 32a b + 20a b - 8a b - 12a b + 8a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 3 +--R (- 28b + 20a b + 8a b + 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b - 2a b - 12a b + 4a b + 12a b - 2a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 6 5 2 4 4 2 6 8 +--R (b - 2a b + a b )cosh(x) + (- 7b - 8a b - a b - a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (14b + 6a b - 6a b + 2a )cosh(x) +--R + +--R 6 5 2 4 4 2 4 +--R (- 10b + 8a b + 4a b - 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (b - 4a b + 5a b - 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression Integer +--E 187 + +--S 188 of 531 +m1034b:= a1034.2-r1034 +--R +--R +--R (171) +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 9b - 15a b + 9a b + 15a )cosh(x) - 15b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 36b - 36a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (12b + 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 3 2 2 3 4 +--R (b + 7a b - a b - 7a )cosh(x) + (9b + 9a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 188 + +--S 189 of 531 +d1034b:= D(m1034b,x) +--R +--R +--R (172) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + 5a b +--R + +--R 3 3 4 2 6 +--R 8a b + a b + 3a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (12a b + 36a b + 16a b - 8a b + 20a b + 20a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (14b + 64a b + 62a b - 40a b - 6a b + 88a b + 42a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - 2b + 6a b + 10a b + 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (36b + 92a b - 24a b - 112a b + 68a b + 132a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 16a b + 44a b + 8a b + 20a b + 8a b + 12a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (24b - 24a b - 164a b - 40a b + 144a b + 64a b - 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 14b + 80a b + 98a b + 16a b + 6a b + 32a b + 22a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 +--R - 2a b - 8a b + 12a b - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b - 172a b - 164a b + 80a b + 104a b - 20a b - 20a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (24b + 144a b + 96a b - 8a b + 48a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 8b + 4a b - 4a b - 16a b + 32a b - 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 62b - 160a b - 62a b + 72a b + 22a b - 24a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (66b + 112a b + 50a b - 16a b - 10a b + 32a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (- 26b + 16a b + 2a b - 8a b + 26a b - 8a b - 2a )cosh(x) + 2b +--R + +--R 2 4 4 2 6 +--R - 7a b + 8a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 36b - 60a b - 8a b + 16a b - 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (52b + 32a b + 20a b - 8a b - 12a b + 8a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 3 +--R (- 28b + 20a b + 8a b + 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b - 2a b - 12a b + 4a b + 12a b - 2a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 6 5 2 4 4 2 6 8 +--R (b - 2a b + a b )cosh(x) + (- 7b - 8a b - a b - a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (14b + 6a b - 6a b + 2a )cosh(x) +--R + +--R 6 5 2 4 4 2 4 +--R (- 10b + 8a b + 4a b - 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (b - 4a b + 5a b - 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression Integer +--E 189 + +--S 190 of 531 +t1035:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R C sinh(x) + A +--R (173) ------------------------- +--R c sinh(x) + b cosh(x) + a +--R Type: Expression Integer +--E 190 + +--S 191 of 531 +r1035:= -c*C*x/(b^2-c^2)-2*(A+a*c*C/(b^2-c^2))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(1/2)+b*C*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) +--R +--R +--R (174) +--R +------------+ +--R | 2 2 2 +--R - C b\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c + 2C a c + 2A b )atanh(------------------) + C c x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression Integer +--E 191 + +--S 192 of 531 +a1035:= integrate(t1035,x) +--R +--R +--R (175) +--R [ +--R 2 2 +--R (- A c + C a c + A b ) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R (C c + C b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 2A c + 2C a c + 2A b ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (C c + C b)x\|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 192 + +--S 193 of 531 +m1035a:= a1035.1-r1035 +--R +--R +--R (176) +--R 2 2 +--R (- A c + C a c + A b ) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 +--R C b\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (2A c - 2C a c - 2A b )atanh(------------------) + C b x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression Integer +--E 193 + +--S 194 of 531 +d1035a:= D(m1035a,x) +--R +--R +--R (177) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )sinh(x) +--R + +--R 3 2 2 3 +--R (2A c + (2A b - 2C a)c + (- 2A b - 2C a b)c - 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 +--R (A b - C a b)c - A b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R ((4A c - 4C a c - 4A b c)sinh(x) + (4A c - 4C a c - 4A b c)cosh(x)) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )sinh(x) +--R + +--R 3 2 2 3 +--R (- 2A c + (- 2A b + 2C a)c + (2A b + 2C a b)c + 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 +--R (- A b + C a b)c + A b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression Integer +--E 194 + +--S 195 of 531 +m1035b:= a1035.2-r1035 +--R +--R +--R (178) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R C b\|- c + b - a \|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|- c + b - a \|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R +--------------+ (b - a)tanh(-) + c +--R 2 2 | 2 2 2 2 +--R (2A c - 2C a c - 2A b )\|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R (- 2A c + 2C a c + 2A b )\|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R C b x\|- c + b - a \|c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b - a \|c - b + a +--R Type: Expression Integer +--E 195 + +--S 196 of 531 +d1035b:= D(m1035b,x) +--R +--R +--R (179) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )sinh(x) +--R + +--R 3 2 2 3 +--R (2A c + (2A b - 2C a)c + (- 2A b - 2C a b)c - 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 +--R (A b - C a b)c - A b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R ((4A c - 4C a c - 4A b c)sinh(x) + (4A c - 4C a c - 4A b c)cosh(x)) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )sinh(x) +--R + +--R 3 2 2 3 +--R (- 2A c + (- 2A b + 2C a)c + (2A b + 2C a b)c + 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 +--R (- A b + C a b)c + A b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression Integer +--E 196 + +--S 197 of 531 +t1036:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (180) +--R C sinh(x) + A +--R -------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sinh(x) + (2b c cosh(x) + 2a c)sinh(x) + b cosh(x) + 2a b cosh(x) + a +--R Type: Expression Integer +--E 197 + +--S 198 of 531 +r1036:= -2*(a*A+c*C)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(3/2)+(b*C-(A*c-a*C)*cosh(x)-A*b*sinh(x))/_ + (a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (181) +--R 2 +--R (- 2C c - 2A a c)sinh(x) + (- 2C b c - 2A a b)cosh(x) - 2C a c +--R + +--R 2 +--R - 2A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R (- A b sinh(x) + (- A c + C a)cosh(x) + C b)\|c - b + a +--R / +--R 3 2 2 2 3 2 2 2 +--R (c + (- b + a )c)sinh(x) + (b c - b + a b)cosh(x) + a c - a b +--R + +--R 3 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 198 + +--S 199 of 531 +a1036:= integrate(t1036,x) +--R +--R +--R (182) +--R [ +--R 3 2 2 2 2 +--R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b )sinh(x) +--R + +--R 3 2 2 2 +--R (2C c + (4C b + 2A a)c + (2C b + 4A a b)c + 2A a b )cosh(x) +--R + +--R 2 2 2 +--R 2C a c + (2C a b + 2A a )c + 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 2 2 +--R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b )cosh(x) +--R + +--R 2 2 2 3 2 +--R (2C a c + (2C a b + 2A a )c + 2A a b)cosh(x) - C c - A a c +--R + +--R 2 2 +--R C b c + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )sinh(x) +--R + +--R 2 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )cosh(x) - 2A c + 2C a c +--R + +--R 2 +--R 2A b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 3 2 2 2 +--R (- 2C c + (- 4C b - 2A a)c + (- 2C b - 4A a b)c - 2A a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 2 +--R (- 4C c + (- 8C b - 4A a)c + (- 4C b - 8A a b)c - 4A a b ) +--R * +--R cosh(x) +--R + +--R 2 2 2 +--R - 4C a c + (- 4C a b - 4A a )c - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 2 +--R (- 2C c + (- 4C b - 2A a)c + (- 2C b - 4A a b)c - 2A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 2 +--R (- 4C a c + (- 4C a b - 4A a )c - 4A a b)cosh(x) + 2C c + 2A a c +--R + +--R 2 2 +--R - 2C b c - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )sinh(x) +--R + +--R 2 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )cosh(x) - 2A c + 2C a c +--R + +--R 2 +--R 2A b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 199 + +--S 200 of 531 +m1036a:= a1036.1-r1036 +--R +--R +--R (183) +--R 4 3 2 2 2 3 +--R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b c)sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + (5C b + 2A a)c + (4C b + 5A a b)c +--R + +--R 3 2 3 +--R (C b + 4A a b )c + A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R 3C a c + (4C a b + 3A a )c + (C a b + 4A a b)c + A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R C c + (4C b + A a)c + (5C b + 4A a b)c +--R + +--R 3 2 3 +--R (2C b + 5A a b )c + 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R (4C a c + (8C a b + 4A a )c + (4C a b + 8A a b)c + 4A a b ) +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 2 2 3 +--R - C c - A a c + (C b + 2C a )c + (A a b + 2C a b + 2A a )c +--R + +--R 3 +--R 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 3 +--R (C b c + (2C b + A a b)c + (C b + 2A a b )c + A a b )cosh(x) +--R + +--R 3 2 2 2 2 2 2 2 +--R (C a c + (4C a b + A a )c + (3C a b + 4A a b)c + 3A a b )cosh(x) +--R + +--R 3 2 2 3 2 3 +--R - C b c + (- A a b + 2C a )c + (C b + 2C a b + 2A a )c +--R + +--R 3 3 +--R A a b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - C a c - A a c + C a b c + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 4 3 2 2 2 3 +--R (2C c + (4C b + 2A a)c + (2C b + 4A a b)c + 2A a b c)sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + (10C b + 4A a)c + (8C b + 10A a b)c +--R + +--R 3 2 3 +--R (2C b + 8A a b )c + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R 6C a c + (8C a b + 6A a )c + (2C a b + 8A a b)c + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + (8C b + 2A a)c + (10C b + 8A a b)c +--R + +--R 3 2 3 +--R (4C b + 10A a b )c + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 8C a c + (16C a b + 8A a )c + (8C a b + 16A a b)c +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c - 2A a c + (2C b + 4C a )c +--R + +--R 2 2 3 3 +--R (2A a b + 4C a b + 4A a )c + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 3 +--R (2C b c + (4C b + 2A a b)c + (2C b + 4A a b )c + 2A a b )cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R (2C a c + (8C a b + 2A a )c + (6C a b + 8A a b)c + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 +--R - 2C b c + (- 2A a b + 4C a )c + (2C b + 4C a b + 4A a )c +--R + +--R 3 3 +--R 2A a b + 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - 2C a c - 2A a c + 2C a b c + 2A a b +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 3 3 +--R (A b c + 2A b c + A b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - C a)c + (5A b - 2C a b)c + 2A b - C a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b + 2A a)c + (4A a b - 2C a )c - C b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - 2C a)c + (4A b - 4C a b)c + A b - 2C a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4C a )c + 4A a b - 4C a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 3 +--R (- A b + 2C a)c + (2A b + 2A a )c + A b + 2A a b - 2C a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 2 2 3 2 2 +--R ((- C b + 2A a)c + (4A a b - 2C a )c + C b + 2A a b - 4C a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R - C a b + 2A a b - 2C a +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b - 2A a)c + 2C a c - C b + 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 200 + +--S 201 of 531 +--d1036a:= D(m1036a,x) +--E 201 + +--S 202 of 531 +m1036b:= a1036.2-r1036 +--R +--R +--R (184) +--R 4 3 2 2 2 3 +--R (2C c + (4C b + 2A a)c + (2C b + 4A a b)c + 2A a b c)sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + (10C b + 4A a)c + (8C b + 10A a b)c +--R + +--R 3 2 3 +--R (2C b + 8A a b )c + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R 6C a c + (8C a b + 6A a )c + (2C a b + 8A a b)c + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + (8C b + 2A a)c + (10C b + 8A a b)c +--R + +--R 3 2 3 +--R (4C b + 10A a b )c + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 8C a c + (16C a b + 8A a )c + (8C a b + 16A a b)c +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c - 2A a c + (2C b + 4C a )c +--R + +--R 2 2 3 3 +--R (2A a b + 4C a b + 4A a )c + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 3 +--R (2C b c + (4C b + 2A a b)c + (2C b + 4A a b )c + 2A a b )cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R (2C a c + (8C a b + 2A a )c + (6C a b + 8A a b)c + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 +--R - 2C b c + (- 2A a b + 4C a )c + (2C b + 4C a b + 4A a )c +--R + +--R 3 3 +--R 2A a b + 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - 2C a c - 2A a c + 2C a b c + 2A a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 4 3 2 2 2 +--R (- 2C c + (- 4C b - 2A a)c + (- 2C b - 4A a b)c - 2A a b c) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 4C c + (- 10C b - 4A a)c + (- 8C b - 10A a b)c +--R + +--R 3 2 3 +--R (- 2C b - 8A a b )c - 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R - 6C a c + (- 8C a b - 6A a )c + (- 2C a b - 8A a b)c - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 2C c + (- 8C b - 2A a)c + (- 10C b - 8A a b)c +--R + +--R 3 2 3 +--R (- 4C b - 10A a b )c - 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - 8C a c + (- 16C a b - 8A a )c + (- 8C a b - 16A a b)c +--R + +--R 2 2 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R 2C c + 2A a c + (- 2C b - 4C a )c +--R + +--R 2 2 3 3 +--R (- 2A a b - 4C a b - 4A a )c - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 2C b c + (- 4C b - 2A a b)c + (- 2C b - 4A a b )c - 2A a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - 2C a c + (- 8C a b - 2A a )c + (- 6C a b - 8A a b)c +--R + +--R 2 2 +--R - 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 +--R 2C b c + (2A a b - 4C a )c + (- 2C b - 4C a b - 4A a )c +--R + +--R 3 3 +--R - 2A a b - 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R 2C a c + 2A a c - 2C a b c - 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 3 3 +--R (A b c + 2A b c + A b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - C a)c + (5A b - 2C a b)c + 2A b - C a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b + 2A a)c + (4A a b - 2C a )c - C b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - 2C a)c + (4A b - 4C a b)c + A b - 2C a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4C a )c + 4A a b - 4C a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 3 +--R (- A b + 2C a)c + (2A b + 2A a )c + A b + 2A a b - 2C a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 2 2 3 2 2 +--R ((- C b + 2A a)c + (4A a b - 2C a )c + C b + 2A a b - 4C a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R - C a b + 2A a b - 2C a +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b - 2A a)c + 2C a c - C b + 2A a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression Integer +--E 202 + +--S 203 of 531 +--d1036b:= D(m1036b,x) +--E 203 + +--S 204 of 531 +t1037:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (185) +--R C sinh(x) + A +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3b c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 3 3 +--R (3b c cosh(x) + 6a b c cosh(x) + 3a c)sinh(x) + b cosh(x) +--R + +--R 2 2 2 3 +--R 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression Integer +--E 204 + +--S 205 of 531 +r1037:= -(2*a^2*A+A*b^2-c*(A*c-3*a*C))*atanh((c-(a-b)*tanh(1/2*x))/_ + (a^2-b^2+c^2)^(1/2))/(a^2-b^2+c^2)^(5/2)+1/2*(b*C-(A*c-a*C)*_ + cosh(x)-A*b*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x))^2+_ + 1/2*(a*b*C-(2*c^2*C+a*(3*A*c-a*C))*cosh(x)-b*(3*a*A+2*c*C)*_ + sinh(x))/(a^2-b^2+c^2)^2/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (186) +--R 4 3 2 2 2 2 +--R (2A c - 6C a c + (- 2A b - 4A a )c )sinh(x) +--R + +--R 3 2 3 2 3 +--R (4A b c - 12C a b c + (- 4A b - 8A a b)c)cosh(x) + 4A a c +--R + +--R 2 2 2 3 +--R - 12C a c + (- 4A a b - 8A a )c +--R * +--R sinh(x) +--R + +--R 2 2 2 4 2 2 2 +--R (2A b c - 6C a b c - 2A b - 4A a b )cosh(x) +--R + +--R 2 2 3 3 2 2 3 +--R (4A a b c - 12C a b c - 4A a b - 8A a b)cosh(x) + 2A a c - 6C a c +--R + +--R 2 2 4 +--R - 2A a b - 4A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 +--R (- 2C b c - 3A a b c)sinh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 2C c - 3A a c + (- 2C b + C a )c - 3A a b )cosh(x) - A b c +--R + +--R 3 2 +--R - C a b c + A b - 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 2 +--R (- 2C b c - 3A a b c + C a b)cosh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- A c - C a c + (A b - 4A a )c + 2C a )cosh(x) + C b c - C b +--R + +--R 2 +--R 2C a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (- 4b + 4a )c + (2b - 4a b + 2a )c )sinh(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (- 8b + 8a b)c + (4b - 8a b + 4a b)c)cosh(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (- 8a b + 8a )c + (4a b - 8a b + 4a )c +--R * +--R sinh(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (- 4b + 4a b )c + 2b - 4a b + 2a b )cosh(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (- 8a b + 8a b)c + 4a b - 8a b + 4a b)cosh(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (- 4a b + 4a )c + 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 205 + +--S 206 of 531 +a1037:= integrate(t1037,x) +--R +--R +--R (187) +--R [ +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b - 9C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b - 9C a b - 6A a b)c + (- 3A b - 3C a b - 6A a b )c +--R + +--R 5 2 3 +--R - A b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + (12A b - 12C a)c + (8A b - 36C a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b - 36C a b - 24A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 12A b - 12C a b - 24A a b )c - 4A b - 8A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + (- 24C a b - 8A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 8A a b - 12C a b - 16A a b)c - 4A a b - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 6A c + (18A b - 18C a)c + (12A b - 54C a b - 12A a )c +--R + +--R 3 2 2 2 +--R (- 12A b - 54C a b - 36A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 18A b - 18C a b - 36A a b )c - 6A b - 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 12A a c + (24A a b - 36C a )c + (- 72C a b - 24A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 24A a b - 36C a b - 48A a b)c - 12A a b - 24A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c + (- 2A b + 6C a)c + (4A b + 6C a b + 8A a )c +--R + +--R 3 2 2 3 2 +--R (4A b - 6C a b + 8A a b - 12C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b - 6C a b - 8A a b - 12C a b - 8A a )c - 2A b +--R + +--R 2 3 4 +--R - 8A a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + (12A b - 12C a)c + (8A b - 36C a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b - 36C a b - 24A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 12A b - 12C a b - 24A a b )c - 4A b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 12A a c + (24A a b - 36C a )c + (- 72C a b - 24A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 24A a b - 36C a b - 48A a b)c - 12A a b - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 4A c + (- 4A b + 12C a)c + (8A b + 12C a b + 16A a )c +--R + +--R 3 2 2 3 2 +--R (8A b - 12C a b + 16A a b - 24C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 4A b - 12C a b - 16A a b - 24C a b - 16A a )c - 4A b +--R + +--R 2 3 4 +--R - 16A a b - 16A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 2 2 +--R - 4A a c + 12C a c + (8A a b + 8A a )c - 12C a b c +--R + +--R 4 3 2 +--R - 4A a b - 8A a b +--R * +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b - 9C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b - 9C a b - 6A a b)c + (- 3A b - 3C a b - 6A a b )c +--R + +--R 5 2 3 +--R - A b - 2A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + (- 24C a b - 8A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 8A a b - 12C a b - 16A a b)c - 4A a b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c + (- 2A b + 6C a)c + (4A b + 6C a b + 8A a )c +--R + +--R 3 2 2 3 2 +--R (4A b - 6C a b + 8A a b - 12C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b - 6C a b - 8A a b - 12C a b - 8A a )c - 2A b +--R + +--R 2 3 4 +--R - 8A a b - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 2 2 +--R - 4A a c + 12C a c + (8A a b + 8A a )c - 12C a b c +--R + +--R 4 3 2 +--R - 4A a b - 8A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R A c + (- A b - 3C a)c + (- 2A b + 3C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 5 +--R (2A b + 3C a b + 2A a b)c + (A b - 3C a b + 2A a b )c - A b +--R + +--R 2 3 +--R - 2A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - 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2C c - 3A a c + (4C b - 3A a b + 5C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (3A a b + 9C a b + 6A a )c - 2C b + 3A a b + 4C a b +--R + +--R 3 4 +--R 6A a b - 2C a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 3A c + (- 6A b + 9C a)c + (18C a b + 6A a )c +--R + +--R 3 2 2 4 2 2 +--R (6A b + 9C a b + 12A a b)c + 3A b + 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4C c - 6A a c + (8C b - 6A a b + 10C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b + 18C a b + 12A a )c - 4C b + 6A a b + 8C a b +--R + +--R 3 4 +--R 12A a b - 4C a +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 2 3 +--R - A c - 5C a c + (2A b - 10A a )c + (5C a b + 4C a )c +--R + +--R 4 2 2 +--R - A b + 10A a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 +--R - A c + (- 2A b + 3C a)c + (6C a b + 2A a )c +--R + +--R 3 2 2 4 2 2 +--R (2A b + 3C a b + 4A a b)c + A b + 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c - 3A a c + (4C b - 3A a b + 5C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (3A a b + 9C a b + 6A a )c - 2C b + 3A a b + 4C a b +--R + +--R 3 4 +--R 6A a b - 2C a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 2 3 +--R - A c - 5C a c + (2A b - 10A a )c + (5C a b + 4C a )c +--R + +--R 4 2 2 +--R - A b + 10A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R 2C c + (- 2C b + 3A a)c + (- 2C b - 3A a b - C a )c +--R + +--R 3 2 2 3 +--R (2C b - 3A a b + C a b)c + 3A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 7 6 2 2 5 3 2 4 +--R c + 3b c + (b + 2a )c + (- 5b + 6a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 5b + 4a b + a )c + (b - 4a b + 3a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (3b - 6a b + 3a b )c + b - 2a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 4c + 12b c + (4b + 8a )c + (- 20b + 24a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 20b + 16a b + 4a )c + (4b - 16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 6c + 18b c + (6b + 12a )c + (- 30b + 36a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 30b + 24a b + 6a )c + (6b - 24a b + 18a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (18b - 36a b + 18a b )c + 6b - 12a b + 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 4c + 12b c + (4b + 8a )c + (- 20b + 24a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 20b + 16a b + 4a )c + (4b - 16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b +--R + +--R 6 +--R 8a b +--R * +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R c + 3b c + (b + 2a )c + (- 5b + 6a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 5b + 4a b + a )c + (b - 4a b + 3a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (3b - 6a b + 3a b )c + b - 2a b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 3 2 4 4 2 2 4 3 +--R c - b c + (- 3b + 2a )c + (3b - 2a b)c + (3b - 4a b + a )c +--R + +--R 5 2 3 4 2 6 2 4 4 2 7 2 5 4 3 +--R (- 3b + 4a b - a b)c + (- b + 2a b - a b )c + b - 2a b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 206 + +--S 207 of 531 +--m1037a:= a1037.1-r1037 +--E 207 + +--S 208 of 531 +--d1037a:= D(m1037a,x) +--E 208 + +--S 209 of 531 +--m1037b:= a1037.2-r1037 +--E 209 + +--S 210 of 531 +--d1037b:= D(m1037b,x) +--E 210 + +--S 211 of 531 +t1038:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R B cosh(x) + A +--R (188) ------------------------- +--R c sinh(x) + b cosh(x) + a +--R Type: Expression Integer +--E 211 + +--S 212 of 531 +r1038:= b*B*x/(b^2-c^2)-2*(A-a*b*B/(b^2-c^2))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(1/2)-B*c*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) +--R +--R +--R (189) +--R +------------+ +--R | 2 2 2 +--R B c\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c + 2A b - 2B a b)atanh(------------------) - B b x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression Integer +--E 212 + +--S 213 of 531 +a1038:= integrate(t1038,x) +--R +--R +--R (190) +--R [ +--R 2 2 +--R (A c - A b + B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R (- B c - B b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 2A c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (- B c - B b)x\|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 213 + +--S 214 of 531 +m1038a:= a1038.1-r1038 +--R +--R +--R (191) +--R 2 2 +--R (A c - A b + B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 +--R - B c\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (2A c - 2A b + 2B a b)atanh(------------------) - B c x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression Integer +--E 214 + +--S 215 of 531 +d1038a:= D(m1038a,x) +--R +--R +--R (192) +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + 2A b c + (- 2A b + 2B a b)c - 2A b + 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) - A c + A b c + (A b - B a b)c +--R + +--R 3 2 +--R - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c - 2A b c + (2A b - 2B a b)c + 2A b - 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) + A c - A b c + (- A b + B a b)c +--R + +--R 3 2 +--R A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression Integer +--E 215 + +--S 216 of 531 +m1038b:= a1038.2-r1038 +--R +--R +--R (193) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - B c\|- c + b - a \|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|- c + b - a \|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R +--------------+ (b - a)tanh(-) + c +--R 2 2 | 2 2 2 2 +--R (2A c - 2A b + 2B a b)\|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R (- 2A c + 2A b - 2B a b)\|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - B c x\|- c + b - a \|c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b - a \|c - b + a +--R Type: Expression Integer +--E 216 + +--S 217 of 531 +d1038b:= D(m1038b,x) +--R +--R +--R (194) +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + 2A b c + (- 2A b + 2B a b)c - 2A b + 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) - A c + A b c + (A b - B a b)c +--R + +--R 3 2 +--R - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c - 2A b c + (2A b - 2B a b)c + 2A b - 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) + A c - A b c + (- A b + B a b)c +--R + +--R 3 2 +--R A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression Integer +--E 217 + +--S 218 of 531 +t1039:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (195) +--R B cosh(x) + A +--R -------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sinh(x) + (2b c cosh(x) + 2a c)sinh(x) + b cosh(x) + 2a b cosh(x) + a +--R Type: Expression Integer +--E 218 + +--S 219 of 531 +r1039:= -2*(a*A-b*B)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(3/2)-(B*c+A*c*cosh(x)+(A*b-a*B)*sinh(x))/_ + (a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (196) +--R 2 2 +--R ((2B b - 2A a)c sinh(x) + (2B b - 2A a b)cosh(x) + 2B a b - 2A a ) +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R ((- A b + B a)sinh(x) - A c cosh(x) - B c)\|c - b + a +--R / +--R 3 2 2 2 3 2 2 2 +--R (c + (- b + a )c)sinh(x) + (b c - b + a b)cosh(x) + a c - a b +--R + +--R 3 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 219 + +--S 220 of 531 +a1039:= integrate(t1039,x) +--R +--R +--R (197) +--R [ +--R 2 2 3 2 2 +--R ((B b - A a)c + (2B b - 2A a b)c + B b - A a b )sinh(x) +--R + +--R 2 2 3 2 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + 2B b - 2A a b )cosh(x) +--R + +--R 2 2 2 +--R (2B a b - 2A a )c + 2B a b - 2A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 2 +--R ((B b - A a)c + (2B b - 2A a b)c + B b - A a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((2B a b - 2A a )c + 2B a b - 2A a b)cosh(x) + (- B b + A a)c +--R + +--R 3 2 +--R B b - A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )cosh(x) - 2A c +--R + +--R 2 +--R 2A b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 2 2 3 2 2 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + 2B b - 2A a b )sinh(x) +--R + +--R 2 2 3 2 +--R ((4B b - 4A a)c + (8B b - 8A a b)c + 4B b - 4A a b )cosh(x) +--R + +--R 2 2 2 +--R (4B a b - 4A a )c + 4B a b - 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 2 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + 2B b - 2A a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((4B a b - 4A a )c + 4B a b - 4A a b)cosh(x) + (- 2B b + 2A a)c +--R + +--R 3 2 +--R 2B b - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )cosh(x) - 2A c +--R + +--R 2 +--R 2A b - 2B a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 220 + +--S 221 of 531 +m1039a:= a1039.1-r1039 +--R +--R +--R (198) +--R 3 2 2 3 2 3 +--R ((B b - A a)c + (2B b - 2A a b)c + (B b - A a b )c)sinh(x) +--R + +--R 3 2 2 3 2 +--R (2B b - 2A a)c + (5B b - 5A a b)c + (4B b - 4A a b )c +--R + +--R 4 3 +--R B b - A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (3B a b - 3A a )c + (4B a b - 4A a b)c + B a b - A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (B b - A a)c + (4B b - 4A a b)c + (5B b - 5A a b )c +--R + +--R 4 3 +--R 2B b - 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((4B a b - 4A a )c + (8B a b - 8A a b)c + 4B a b - 4A a b ) +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (- B b + A a)c + (B b - A a b + 2B a b - 2A a )c + 2B a b +--R + +--R 3 +--R - 2A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 3 +--R ((B b - A a b)c + (2B b - 2A a b )c + B b - A a b )cosh(x) +--R + +--R 2 2 2 2 3 2 2 2 +--R ((B a b - A a )c + (4B a b - 4A a b)c + 3B a b - 3A a b )cosh(x) +--R + +--R 2 2 2 3 4 3 2 2 +--R (- B b + A a b)c + (2B a b - 2A a )c + B b - A a b + 2B a b +--R + +--R 3 +--R - 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (- B a b + A a )c + B a b - A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 3 2 2 3 2 +--R ((- 2B b + 2A a)c + (- 4B b + 4A a b)c + (- 2B b + 2A a b )c) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 4B b + 4A a)c + (- 10B b + 10A a b)c +--R + +--R 3 2 4 3 +--R (- 8B b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 6B a b + 6A a )c + (- 8B a b + 8A a b)c - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 2B b + 2A a)c + (- 8B b + 8A a b)c +--R + +--R 3 2 4 3 +--R (- 10B b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (- 8B a b + 8A a )c + (- 16B a b + 16A a b)c - 8B a b +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (2B b - 2A a)c + (- 2B b + 2A a b - 4B a b + 4A a )c - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 +--R ((- 2B b + 2A a b)c + (- 4B b + 4A a b )c - 2B b + 2A a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((- 2B a b + 2A a )c + (- 8B a b + 8A a b)c - 6B a b + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 4 3 +--R (2B b - 2A a b)c + (- 4B a b + 4A a )c - 2B b + 2A a b +--R + +--R 2 2 3 +--R - 4B a b + 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2B a b - 2A a )c - 2B a b + 2A a b +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - 2B a)c + (5A b - 4B a b)c + 2A b - 2B a b ) +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - B c + 2A a c + (B b + 4A a b - 4B a )c + 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - B a)c + (4A b - 2B a b)c + A b - B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4B a )c + 4A a b - 4B a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 +--R (- A b + B a)c + (2A b - 2B a b + 2A a )c + A b - B a b +--R + +--R 2 3 +--R 2A a b - 2B a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 +--R (A c + 2A b c + A b c)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (B c + 2A a c + (- B b + 4A a b)c + 2A a b - 2B a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - A c - 2A b c + (A b + 2A a )c + 2A b - 2B a b + 2A a b +--R + +--R 3 +--R - 2B a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - B c - 2A a c + B b c + 2A a b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 221 + +--S 222 of 531 +--d1039a:= D(m1039a,x) +--E 222 + +--S 223 of 531 +m1039b:= a1039.2-r1039 +--R +--R +--R (199) +--R 3 2 2 3 2 +--R ((- 2B b + 2A a)c + (- 4B b + 4A a b)c + (- 2B b + 2A a b )c) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 4B b + 4A a)c + (- 10B b + 10A a b)c +--R + +--R 3 2 4 3 +--R (- 8B b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 6B a b + 6A a )c + (- 8B a b + 8A a b)c - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 2B b + 2A a)c + (- 8B b + 8A a b)c +--R + +--R 3 2 4 3 +--R (- 10B b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (- 8B a b + 8A a )c + (- 16B a b + 16A a b)c - 8B a b +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (2B b - 2A a)c + (- 2B b + 2A a b - 4B a b + 4A a )c - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 +--R ((- 2B b + 2A a b)c + (- 4B b + 4A a b )c - 2B b + 2A a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((- 2B a b + 2A a )c + (- 8B a b + 8A a b)c - 6B a b + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 4 3 +--R (2B b - 2A a b)c + (- 4B a b + 4A a )c - 2B b + 2A a b +--R + +--R 2 2 3 +--R - 4B a b + 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2B a b - 2A a )c - 2B a b + 2A a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 3 2 3 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + (2B b - 2A a b )c)sinh(x) +--R + +--R 3 2 2 3 2 +--R (4B b - 4A a)c + (10B b - 10A a b)c + (8B b - 8A a b )c +--R + +--R 4 3 +--R 2B b - 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (6B a b - 6A a )c + (8B a b - 8A a b)c + 2B a b - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2B b - 2A a)c + (8B b - 8A a b)c + (10B b - 10A a b )c +--R + +--R 4 3 +--R 4B b - 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (8B a b - 8A a )c + (16B a b - 16A a b)c + 8B a b +--R + +--R 2 2 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (- 2B b + 2A a)c + (2B b - 2A a b + 4B a b - 4A a )c + 4B a b +--R + +--R 3 +--R - 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 3 +--R ((2B b - 2A a b)c + (4B b - 4A a b )c + 2B b - 2A a b )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((2B a b - 2A a )c + (8B a b - 8A a b)c + 6B a b - 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 4 3 +--R (- 2B b + 2A a b)c + (4B a b - 4A a )c + 2B b - 2A a b +--R + +--R 2 2 3 +--R 4B a b - 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 2B a b + 2A a )c + 2B a b - 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - 2B a)c + (5A b - 4B a b)c + 2A b - 2B a b ) +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - B c + 2A a c + (B b + 4A a b - 4B a )c + 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - B a)c + (4A b - 2B a b)c + A b - B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4B a )c + 4A a b - 4B a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 +--R (- A b + B a)c + (2A b - 2B a b + 2A a )c + A b - B a b +--R + +--R 2 3 +--R 2A a b - 2B a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 +--R (A c + 2A b c + A b c)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (B c + 2A a c + (- B b + 4A a b)c + 2A a b - 2B a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - A c - 2A b c + (A b + 2A a )c + 2A b - 2B a b + 2A a b +--R + +--R 3 +--R - 2B a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - B c - 2A a c + B b c + 2A a b - 2B a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression Integer +--E 223 + +--S 224 of 531 +--d1039b:= D(m1039b,x) +--E 224 + +--S 225 of 531 +t1040:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (200) +--R B cosh(x) + A +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3b c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 3 3 +--R (3b c cosh(x) + 6a b c cosh(x) + 3a c)sinh(x) + b cosh(x) +--R + +--R 2 2 2 3 +--R 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression Integer +--E 225 + +--S 226 of 531 +r1040:= -(2*a^2*A+b*(A*b-3*a*B)-A*c^2)*atanh((c-(a-b)*tanh(1/2*x))/_ + (a^2-b^2+c^2)^(1/2))/(a^2-b^2+c^2)^(5/2)-1/2*(B*c+A*c*cosh(x)+_ + (A*b-a*B)*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x))^2-_ + 1/2*(a*B*c+(3*a*A-2*b*B)*c*cosh(x)-(2*b^2*B-a*(3*A*b-a*B))*_ + sinh(x))/(a^2-b^2+c^2)^2/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (201) +--R 4 2 2 2 2 +--R (2A c + (- 2A b + 6B a b - 4A a )c )sinh(x) +--R + +--R 3 3 2 2 3 +--R (4A b c + (- 4A b + 12B a b - 8A a b)c)cosh(x) + 4A a c +--R + +--R 2 2 3 +--R (- 4A a b + 12B a b - 8A a )c +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (2A b c - 2A b + 6B a b - 4A a b )cosh(x) +--R + +--R 2 3 2 2 3 2 2 2 2 +--R (4A a b c - 4A a b + 12B a b - 8A a b)cosh(x) + 2A a c - 2A a b +--R + +--R 3 4 +--R 6B a b - 4A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 2 +--R (2B b - 3A a b + B a )c sinh(x) +--R + +--R 2 3 2 2 2 +--R ((2B b - 3A a)c + 2B b - 3A a b + B a b)cosh(x) - A b c +--R + +--R 3 2 2 3 +--R A b + B a b - 4A a b + 2B a +--R * +--R sinh(x) +--R + +--R 2 2 +--R (2B b - 3A a b)c cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (A b + B a b - 4A a )c)cosh(x) - B c + (B b - 2B a )c +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (- 4b + 4a )c + (2b - 4a b + 2a )c )sinh(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (- 8b + 8a b)c + (4b - 8a b + 4a b)c)cosh(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (- 8a b + 8a )c + (4a b - 8a b + 4a )c +--R * +--R sinh(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (- 4b + 4a b )c + 2b - 4a b + 2a b )cosh(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (- 8a b + 8a b)c + 4a b - 8a b + 4a b)cosh(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (- 4a b + 4a )c + 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 226 + +--S 227 of 531 +a1040:= integrate(t1040,x) +--R +--R +--R (202) +--R [ +--R 5 4 2 2 3 +--R A c + 3A b c + (2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b + 9B a b - 6A a b)c + (- 3A b + 9B a b - 6A a b )c +--R + +--R 5 4 2 3 +--R - A b + 3B a b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + 12A b c + (8A b + 12B a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + 36B a b - 24A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 12A b + 36B a b - 24A a b )c - 4A b + 12B a b +--R + +--R 2 3 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 4A a c + 8A a b c + (12B a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 3 2 +--R (- 8A a b + 24B a b - 16A a b)c - 4A a b + 12B a b - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 6A c + 18A b c + (12A b + 18B a b - 12A a )c +--R + +--R 3 2 2 2 +--R (- 12A b + 54B a b - 36A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 18A b + 54B a b - 36A a b )c - 6A b + 18B a b +--R + +--R 2 3 +--R - 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 12A a c + 24A a b c + (36B a b - 24A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 24A a b + 72B a b - 48A a b)c - 12A a b + 36B a b +--R + +--R 3 2 +--R - 24A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c - 2A b c + (4A b - 6B a b + 8A a )c +--R + +--R 3 2 2 2 +--R (4A b - 6B a b + 8A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b + 6B a b - 8A a b + 12B a b - 8A a )c - 2A b +--R + +--R 4 2 3 3 2 4 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + 12A b c + (8A b + 12B a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + 36B a b - 24A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 12A b + 36B a b - 24A a b )c - 4A b + 12B a b +--R + +--R 2 3 +--R - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 12A a c + 24A a b c + (36B a b - 24A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 24A a b + 72B a b - 48A a b)c - 12A a b + 36B a b +--R + +--R 3 2 +--R - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 4A c - 4A b c + (8A b - 12B a b + 16A a )c +--R + +--R 3 2 2 2 +--R (8A b - 12B a b + 16A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 4A b + 12B a b - 16A a b + 24B a b - 16A a )c - 4A b +--R + +--R 4 2 3 3 2 4 +--R 12B a b - 16A a b + 24B a b - 16A a b +--R * +--R cosh(x) +--R + +--R 4 2 2 3 2 4 2 3 +--R - 4A a c + (8A a b - 12B a b + 8A a )c - 4A a b + 12B a b +--R + +--R 3 2 +--R - 8A a b +--R * +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R A c + 3A b c + (2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b + 9B a b - 6A a b)c + (- 3A b + 9B a b - 6A a b )c +--R + +--R 5 4 2 3 +--R - A b + 3B a b - 2A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 4A a c + 8A a b c + (12B a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 3 2 +--R (- 8A a b + 24B a b - 16A a b)c - 4A a b + 12B a b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c - 2A b c + (4A b - 6B a b + 8A a )c +--R + +--R 3 2 2 2 +--R (4A b - 6B a b + 8A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b + 6B a b - 8A a b + 12B a b - 8A a )c - 2A b +--R + +--R 4 2 3 3 2 4 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 3 2 4 2 3 +--R - 4A a c + (8A a b - 12B a b + 8A a )c - 4A a b + 12B a b +--R + +--R 3 2 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R A c - A b c + (- 2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 5 +--R (2A b - 3B a b + 2A a b)c + (A b - 3B a b + 2A a b )c - A b +--R + +--R 4 2 3 +--R 3B a b - 2A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 4 3 2 2 +--R - 2A c - 4A b c + (- 6B a b + 4A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (4A b - 12B a b + 8A a b)c + 2A b - 6B a b + 4A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 6A c - 12A b c + (- 18B a b + 12A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (12A b - 36B a b + 24A a b)c + 6A b - 18B a b + 12A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4B c - 6A a c + (8B b - 6A a b - 8B a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b - 18B a b + 12A a )c - 4B b + 6A a b - 10B a b +--R + +--R 3 4 +--R 12A a b - 4B a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 6A c - 12A b c + (- 18B a b + 12A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (12A b - 36B a b + 24A a b)c + 6A b - 18B a b + 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 8B c - 12A a c + (16B b - 12A a b - 16B a )c +--R + +--R 2 2 3 4 3 +--R (12A a b - 36B a b + 24A a )c - 8B b + 12A a b +--R + +--R 2 2 3 4 +--R - 20B a b + 24A a b - 8B a +--R * +--R cosh(x) +--R + +--R 4 2 2 2 4 3 +--R - 2A c + (4A b + 10B a b - 20A a )c - 2A b - 10B a b +--R + +--R 2 2 3 +--R 20A a b - 8B a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 2A c - 4A b c + (- 6B a b + 4A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (4A b - 12B a b + 8A a b)c + 2A b - 6B a b + 4A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4B c - 6A a c + (8B b - 6A a b - 8B a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b - 18B a b + 12A a )c - 4B b + 6A a b - 10B a b +--R + +--R 3 4 +--R 12A a b - 4B a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 2 4 3 +--R - 2A c + (4A b + 10B a b - 20A a )c - 2A b - 10B a b +--R + +--R 2 2 3 +--R 20A a b - 8B a b +--R * +--R cosh(x) +--R + +--R 3 2 2 +--R (- 4B b + 6A a)c + (4B b - 6A a b)c +--R + +--R 3 2 2 4 3 2 2 +--R (4B b - 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16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 6c + 18b c + (6b + 12a )c + (- 30b + 36a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 30b + 24a b + 6a )c + (6b - 24a b + 18a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (18b - 36a b + 18a b )c + 6b - 12a b + 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 4c + 12b c + (4b + 8a )c + (- 20b + 24a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 20b + 16a b + 4a )c + (4b - 16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b +--R + +--R 6 +--R 8a b +--R * +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R c + 3b c + (b + 2a )c + (- 5b + 6a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 5b + 4a b + a )c + (b - 4a b + 3a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (3b - 6a b + 3a b )c + b - 2a b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 3 2 4 4 2 2 4 3 +--R c - b c + (- 3b + 2a )c + (3b - 2a b)c + (3b - 4a b + a )c +--R + +--R 5 2 3 4 2 6 2 4 4 2 7 2 5 4 3 +--R (- 3b + 4a b - a b)c + (- b + 2a b - a b )c + b - 2a b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 227 + +--S 228 of 531 +--m1040a:= a1040.1-r1040 +--E 228 + +--S 229 of 531 +--d1040a:= D(m1040a,x) +--E 229 + +--S 230 of 531 +--m1040b:= a1040.2-r1040 +--E 230 + +--S 231 of 531 +--d1040b:= D(m1040b,x) +--E 231 + +--S 232 of 531 +t1041:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R C sinh(x) + B cosh(x) + A +--R (203) ------------------------- +--R c sinh(x) + b cosh(x) + a +--R Type: Expression Integer +--E 232 + +--S 233 of 531 +r1041:= (b*B-c*C)*x/(b^2-c^2)-2*(A-a*(b*B-c*C)/(b^2-c^2))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(1/2)-(B*c-b*C)*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) +--R +--R +--R (204) +--R +------------+ +--R | 2 2 2 +--R (B c - C b)\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R x +--R (b - a)tanh(-) + c +--R 2 2 2 +--R (- 2A c + 2C a c + 2A b - 2B a b)atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R (C c - B b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression Integer +--E 233 + +--S 234 of 531 +a1041:= integrate(t1041,x) +--R +--R +--R (205) +--R [ +--R 2 2 +--R (- A c + C a c + A b - B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R (B c - C b)\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R ((C - B)c + (C - B)b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R (B c - C b)\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 2A c + 2C a c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((C - B)c + (C - B)b)x\|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 234 + +--S 235 of 531 +m1041a:= a1041.1-r1041 +--R +--R +--R (206) +--R 2 2 +--R (- A c + C a c + A b - B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 +--R (- B c + C b)\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R (B c - C b)\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R (b - a)tanh(-) + c +--R 2 2 2 +--R (2A c - 2C a c - 2A b + 2B a b)atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R (- B c + C b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression Integer +--E 235 + +--S 236 of 531 +d1041a:= D(m1041a,x) +--R +--R +--R (207) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R 2A c + (2A b - 2C a)c + (- 2A b + (- 2C + 2B)a b)c - 2A b +--R + +--R 2 +--R 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 2 +--R (A b + (- C - B)a b)c - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 +--R - 2A c + (- 2A b + 2C a)c + (2A b + (2C - 2B)a b)c + 2A b +--R + +--R 2 +--R - 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 2 +--R (- A b + (C + B)a b)c + A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression Integer +--E 236 + +--S 237 of 531 +m1041b:= a1041.2-r1041 +--R +--R +--R (208) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B c + C b)\|- c + b - a \|c - b + a +--R * +--R log(c sinh(x) + b cosh(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (B c - C b)\|- c + b - a \|c - b + a +--R * +--R - 2c sinh(x) - 2b cosh(x) - 2a +--R log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +--------------+ +--R 2 2 | 2 2 2 +--R (2A c - 2C a c - 2A b + 2B a b)\|- c + b - a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R (- 2A c + 2C a c + 2A b - 2B a b)\|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B c + C b)x\|- c + b - a \|c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b - a \|c - b + a +--R Type: Expression Integer +--E 237 + +--S 238 of 531 +d1041b:= D(m1041b,x) +--R +--R +--R (209) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R 2A c + (2A b - 2C a)c + (- 2A b + (- 2C + 2B)a b)c - 2A b +--R + +--R 2 +--R 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 2 +--R (A b + (- C - B)a b)c - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 +--R - 2A c + (- 2A b + 2C a)c + (2A b + (2C - 2B)a b)c + 2A b +--R + +--R 2 +--R - 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 2 +--R (- A b + (C + B)a b)c + A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression Integer +--E 238 + +--S 239 of 531 +t1042:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (210) +--R C sinh(x) + B cosh(x) + A +--R -------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sinh(x) + (2b c cosh(x) + 2a c)sinh(x) + b cosh(x) + 2a b cosh(x) + a +--R Type: Expression Integer +--E 239 + +--S 240 of 531 +r1042:= -2*(a*A-b*B+c*C)*atanh((c-(a-b)*tanh(1/2*x))/_ + (a^2-b^2+c^2)^(1/2))/(a^2-b^2+c^2)^(3/2)-(B*c-b*C+(A*c-a*C)*_ + cosh(x)+(A*b-a*B)*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (211) +--R 2 +--R (- 2C c + (2B b - 2A a)c)sinh(x) +--R + +--R 2 2 +--R (- 2C b c + 2B b - 2A a b)cosh(x) - 2C a c + 2B a b - 2A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R ((- A b + B a)sinh(x) + (- A c + C a)cosh(x) - B c + C b)\|c - b + a +--R / +--R 3 2 2 2 3 2 2 2 +--R (c + (- b + a )c)sinh(x) + (b c - b + a b)cosh(x) + a c - a b +--R + +--R 3 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 240 + +--S 241 of 531 +a1042:= integrate(t1042,x) +--R +--R +--R (212) +--R [ +--R 3 2 2 3 +--R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c - B b +--R + +--R 2 +--R A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R 2C c + ((4C - 2B)b + 2A a)c + ((2C - 4B)b + 4A a b)c +--R + +--R 3 2 +--R - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 +--R 2C a c + ((2C - 2B)a b + 2A a )c - 2B a b + 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 +--R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c - B b +--R + +--R 2 +--R A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 +--R (2C a c + ((2C - 2B)a b + 2A a )c - 2B a b + 2A a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R - C c + (B b - A a)c + C b c - B b + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R cosh(x) +--R + +--R 2 2 +--R - 2A c + 2C a c + 2A b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 3 2 2 +--R - 2C c + ((- 4C + 2B)b - 2A a)c + ((- 2C + 4B)b - 4A a b)c +--R + +--R 3 2 +--R 2B b - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 +--R - 4C c + ((- 8C + 4B)b - 4A a)c +--R + +--R 2 3 2 +--R ((- 4C + 8B)b - 8A a b)c + 4B b - 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 +--R - 4C a c + ((- 4C + 4B)a b - 4A a )c + 4B a b - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 +--R - 2C c + ((- 4C + 2B)b - 2A a)c + ((- 2C + 4B)b - 4A a b)c +--R + +--R 3 2 +--R 2B b - 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 +--R (- 4C a c + ((- 4C + 4B)a b - 4A a )c + 4B a b - 4A a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R 2C c + (- 2B b + 2A a)c - 2C b c + 2B b - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R cosh(x) +--R + +--R 2 2 +--R - 2A c + 2C a c + 2A b - 2B a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 241 + +--S 242 of 531 +m1042a:= a1042.1-r1042 +--R +--R +--R (213) +--R 4 3 2 2 +--R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c +--R + +--R 3 2 +--R (- B b + A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + ((5C - 2B)b + 2A a)c + ((4C - 5B)b + 5A a b)c +--R + +--R 3 2 4 3 +--R ((C - 4B)b + 4A a b )c - B b + A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 3C a c + ((4C - 3B)a b + 3A a )c + ((C - 4B)a b + 4A a b)c +--R + +--R 3 2 2 +--R - B a b + A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R C c + ((4C - B)b + A a)c + ((5C - 4B)b + 4A a b)c +--R + +--R 3 2 4 3 +--R ((2C - 5B)b + 5A a b )c - 2B b + 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R 4C a c + ((8C - 4B)a b + 4A a )c +--R + +--R 2 2 3 2 2 +--R ((4C - 8B)a b + 8A a b)c - 4B a b + 4A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - C c + (B b - A a)c + (C b + 2C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (- B b + A a b + (2C - 2B)a b + 2A a )c - 2B a b + 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 +--R C b c + ((2C - B)b + A a b)c + ((C - 2B)b + 2A a b )c - B b +--R + +--R 3 +--R A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R C a c + ((4C - B)a b + A a )c + ((3C - 4B)a b + 4A a b)c +--R + +--R 3 2 2 +--R - 3B a b + 3A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R - C b c + (B b - A a b + 2C a )c +--R + +--R 3 2 3 4 3 2 2 3 +--R (C b + (2C - 2B)a b + 2A a )c - B b + A a b - 2B a b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - C a c + (B a b - A a )c + C a b c - B a b + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 4 3 2 2 +--R 2C c + ((4C - 2B)b + 2A a)c + ((2C - 4B)b + 4A a b)c +--R + +--R 3 2 +--R (- 2B b + 2A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + ((10C - 4B)b + 4A a)c + ((8C - 10B)b + 10A a b)c +--R + +--R 3 2 4 3 +--R ((2C - 8B)b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 6C a c + ((8C - 6B)a b + 6A a )c + ((2C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + ((8C - 2B)b + 2A a)c + ((10C - 8B)b + 8A a b)c +--R + +--R 3 2 4 3 +--R ((4C - 10B)b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R 8C a c + ((16C - 8B)a b + 8A a )c +--R + +--R 2 2 3 2 2 +--R ((8C - 16B)a b + 16A a b)c - 8B a b + 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c + (2B b - 2A a)c + (2C b + 4C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (- 2B b + 2A a b + (4C - 4B)a b + 4A a )c - 4B a b + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R 2C b c + ((4C - 2B)b + 2A a b)c + ((2C - 4B)b + 4A a b )c +--R + +--R 4 3 +--R - 2B b + 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 2C a c + ((8C - 2B)a b + 2A a )c + ((6C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 6B a b + 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2C b c + (2B b - 2A a b + 4C a )c +--R + +--R 3 2 3 4 3 2 2 +--R (2C b + (4C - 4B)a b + 4A a )c - 2B b + 2A a b - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - 2C a c + (2B a b - 2A a )c + 2C a b c - 2B a b + 2A a b +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 +--R A c + (4A b + (- C - 2B)a)c + (5A b + (- 2C - 4B)a b)c +--R + +--R 3 2 +--R 2A b + (- C - 2B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - B c + (C b + 2A a)c + (B b + 4A a b + (- 2C - 4B)a )c - C b +--R + +--R 2 2 +--R 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R 2A c + (5A b + (- 2C - B)a)c + (4A b + (- 4C - 2B)a b)c +--R + +--R 3 2 +--R A b + (- 2C - B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 +--R 4A a c + (8A a b + (- 4C - 4B)a )c + 4A a b +--R + +--R 2 +--R (- 4C - 4B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2A c + (- A b + (2C + B)a)c + (2A b - 2B a b + 2A a )c +--R + +--R 3 2 2 3 +--R A b - B a b + 2A a b + (- 2C - 2B)a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 3 2 2 2 3 +--R B c + (- C b + 2A a)c + (- B b + 4A a b - 2C a )c + C b +--R + +--R 2 2 +--R 2A a b + (- 4C - 2B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R (- C - 2B)a b + 2A a b + (- 2C - 2B)a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - B c + (C b - 2A a)c + (B b + 2C a )c - C b + 2A a b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 242 + +--S 243 of 531 +--d1042a:= D(m1042a,x) +--E 243 + +--S 244 of 531 +m1042b:= a1042.2-r1042 +--R +--R +--R (214) +--R 4 3 2 2 +--R 2C c + ((4C - 2B)b + 2A a)c + ((2C - 4B)b + 4A a b)c +--R + +--R 3 2 +--R (- 2B b + 2A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + ((10C - 4B)b + 4A a)c + ((8C - 10B)b + 10A a b)c +--R + +--R 3 2 4 3 +--R ((2C - 8B)b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 6C a c + ((8C - 6B)a b + 6A a )c + ((2C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + ((8C - 2B)b + 2A a)c + ((10C - 8B)b + 8A a b)c +--R + +--R 3 2 4 3 +--R ((4C - 10B)b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R 8C a c + ((16C - 8B)a b + 8A a )c +--R + +--R 2 2 3 2 2 +--R ((8C - 16B)a b + 16A a b)c - 8B a b + 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c + (2B b - 2A a)c + (2C b + 4C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (- 2B b + 2A a b + (4C - 4B)a b + 4A a )c - 4B a b + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R 2C b c + ((4C - 2B)b + 2A a b)c + ((2C - 4B)b + 4A a b )c +--R + +--R 4 3 +--R - 2B b + 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 2C a c + ((8C - 2B)a b + 2A a )c + ((6C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 6B a b + 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2C b c + (2B b - 2A a b + 4C a )c +--R + +--R 3 2 3 4 3 2 2 +--R (2C b + (4C - 4B)a b + 4A a )c - 2B b + 2A a b - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - 2C a c + (2B a b - 2A a )c + 2C a b c - 2B a b + 2A a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 4 3 2 2 +--R - 2C c + ((- 4C + 2B)b - 2A a)c + ((- 2C + 4B)b - 4A a b)c +--R + +--R 3 2 +--R (2B b - 2A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 +--R - 4C c + ((- 10C + 4B)b - 4A a)c +--R + +--R 2 2 3 2 +--R ((- 8C + 10B)b - 10A a b)c + ((- 2C + 8B)b - 8A a b )c +--R + +--R 4 3 +--R 2B b - 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 +--R - 6C a c + ((- 8C + 6B)a b - 6A a )c +--R + +--R 2 2 3 2 2 +--R ((- 2C + 8B)a b - 8A a b)c + 2B a b - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 +--R - 2C c + ((- 8C + 2B)b - 2A a)c +--R + +--R 2 2 3 2 +--R ((- 10C + 8B)b - 8A a b)c + ((- 4C + 10B)b - 10A a b )c +--R + +--R 4 3 +--R 4B b - 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R - 8C a c + ((- 16C + 8B)a b - 8A a )c +--R + +--R 2 2 3 2 2 +--R ((- 8C + 16B)a b - 16A a b)c + 8B a b - 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R 2C c + (- 2B b + 2A a)c + (- 2C b - 4C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (2B b - 2A a b + (- 4C + 4B)a b - 4A a )c + 4B a b - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 +--R - 2C b c + ((- 4C + 2B)b - 2A a b)c +--R + +--R 3 2 4 3 +--R ((- 2C + 4B)b - 4A a b )c + 2B b - 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 +--R - 2C a c + ((- 8C + 2B)a b - 2A a )c +--R + +--R 2 2 3 2 2 +--R ((- 6C + 8B)a b - 8A a b)c + 6B a b - 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R 2C b c + (- 2B b + 2A a b - 4C a )c +--R + +--R 3 2 3 4 3 2 2 +--R (- 2C b + (- 4C + 4B)a b - 4A a )c + 2B b - 2A a b + 4B a b +--R + +--R 3 +--R - 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R 2C a c + (- 2B a b + 2A a )c - 2C a b c + 2B a b - 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 +--R A c + (4A b + (- C - 2B)a)c + (5A b + (- 2C - 4B)a b)c +--R + +--R 3 2 +--R 2A b + (- C - 2B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - B c + (C b + 2A a)c + (B b + 4A a b + (- 2C - 4B)a )c - C b +--R + +--R 2 2 +--R 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R 2A c + (5A b + (- 2C - B)a)c + (4A b + (- 4C - 2B)a b)c +--R + +--R 3 2 +--R A b + (- 2C - B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 +--R 4A a c + (8A a b + (- 4C - 4B)a )c + 4A a b +--R + +--R 2 +--R (- 4C - 4B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2A c + (- A b + (2C + B)a)c + (2A b - 2B a b + 2A a )c +--R + +--R 3 2 2 3 +--R A b - B a b + 2A a b + (- 2C - 2B)a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 3 2 2 2 3 +--R B c + (- C b + 2A a)c + (- B b + 4A a b - 2C a )c + C b +--R + +--R 2 2 +--R 2A a b + (- 4C - 2B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R (- C - 2B)a b + 2A a b + (- 2C - 2B)a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - B c + (C b - 2A a)c + (B b + 2C a )c - C b + 2A a b - 2B a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression Integer +--E 244 + +--S 245 of 531 +--d1042b:= D(m1042b,x) +--E 245 + +--S 246 of 531 +t1043:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (215) +--R C sinh(x) + B cosh(x) + A +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3b c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 3 3 +--R (3b c cosh(x) + 6a b c cosh(x) + 3a c)sinh(x) + b cosh(x) +--R + +--R 2 2 2 3 +--R 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression Integer +--E 246 + +--S 247 of 531 +r1043:= -(2*a^2*A+b*(A*b-3*a*B)-c*(A*c-3*a*C))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(5/2)-1/2*(B*c-b*C+(A*c-a*C)*cosh(x)+_ + (A*b-a*B)*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x))^2-_ + 1/2*(a*B*c-a*b*C+(a*(3*A*c-a*C)-2*c*(b*B-c*C))*cosh(x)+_ + (a*(3*A*b-a*B)-2*b*(b*B-c*C))*sinh(x))/(a^2-b^2+c^2)^2/_ + (a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (216) +--R 4 3 2 2 2 2 +--R (2A c - 6C a c + (- 2A b + 6B a b - 4A a )c )sinh(x) +--R + +--R 3 2 3 2 2 +--R (4A b c - 12C a b c + (- 4A b + 12B a b - 8A a b)c)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R 4A a c - 12C a c + (- 4A a b + 12B a b - 8A a )c +--R * +--R sinh(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R (2A b c - 6C a b c - 2A b + 6B a b - 4A a b )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4A a b c - 12C a b c - 4A a b + 12B a b - 8A a b)cosh(x) +--R + +--R 2 2 3 2 2 3 4 +--R 2A a c - 6C a c - 2A a b + 6B a b - 4A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 2 2 +--R (- 2C b c + (2B b - 3A a b + B a )c)sinh(x) +--R + +--R 3 2 2 2 3 +--R - 2C c + (2B b - 3A a)c + (- 2C b + C a )c + 2B b +--R + +--R 2 2 +--R - 3A a b + B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 3 +--R - A b c - C a b c + A b + B a b - 4A a b + 2B a +--R * +--R sinh(x) +--R + +--R 2 2 2 2 +--R (- 2C b c + (2B b - 3A a b)c + C a b)cosh(x) +--R + +--R 3 2 2 2 3 3 +--R (- A c - C a c + (A b + B a b - 4A a )c + 2C a )cosh(x) - B c +--R + +--R 2 2 2 3 2 +--R C b c + (B b - 2B a )c - C b + 2C a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (- 4b + 4a )c + (2b - 4a b + 2a )c )sinh(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (- 8b + 8a b)c + (4b - 8a b + 4a b)c)cosh(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (- 8a b + 8a )c + (4a b - 8a b + 4a )c +--R * +--R sinh(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (- 4b + 4a b )c + 2b - 4a b + 2a b )cosh(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (- 8a b + 8a b)c + 4a b - 8a b + 4a b)cosh(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (- 4a b + 4a )c + 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 247 + +--S 248 of 531 +a1043:= integrate(t1043,x) +--R +--R +--R (217) +--R [ +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b + (- 9C + 3B)a b - 2A a )c +--R + +--R 3 2 2 2 +--R (- 2A b + (- 9C + 9B)a b - 6A a b)c +--R + +--R 4 3 2 2 5 4 2 3 +--R (- 3A b + (- 3C + 9B)a b - 6A a b )c - A b + 3B a b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 +--R 4A c + (12A b - 12C a)c +--R + +--R 2 2 3 +--R (8A b + (- 36C + 12B)a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + (- 36C + 36B)a b - 24A a b)c +--R + +--R 4 3 2 2 5 +--R (- 12A b + (- 12C + 36B)a b - 24A a b )c - 4A b +--R + +--R 4 2 3 +--R 12B a b - 8A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + ((- 24C + 12B)a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 8A a b + (- 12C + 24B)a b - 16A a b)c - 4A a b + 12B a b +--R + +--R 3 2 +--R - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 +--R 6A c + (18A b - 18C a)c +--R + +--R 2 2 3 +--R (12A b + (- 54C + 18B)a b - 12A a )c +--R + +--R 3 2 2 2 +--R (- 12A b + (- 54C + 54B)a b - 36A a b)c +--R + +--R 4 3 2 2 5 +--R (- 18A b + (- 18C + 54B)a b - 36A a b )c - 6A b +--R + +--R 4 2 3 +--R 18B a b - 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 +--R 12A a c + (24A a b - 36C a )c +--R + +--R 2 3 2 +--R ((- 72C + 36B)a b - 24A a )c +--R + +--R 3 2 2 3 4 +--R (- 24A a b + (- 36C + 72B)a b - 48A a b)c - 12A a b +--R + +--R 2 3 3 2 +--R 36B a b - 24A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c + (- 2A b + 6C a)c + (4A b + (6C - 6B)a b + 8A a )c +--R + +--R 3 2 2 3 2 +--R (4A b + (- 6C - 6B)a b + 8A a b - 12C a )c +--R + +--R 4 3 2 2 3 +--R - 2A b + (- 6C + 6B)a b - 8A a b + (- 12C + 12B)a b +--R + +--R 4 +--R - 8A a +--R * +--R c +--R + +--R 5 4 2 3 3 2 4 +--R - 2A b + 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 +--R 4A c + (12A b - 12C a)c +--R + +--R 2 2 3 +--R (8A b + (- 36C + 12B)a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + (- 36C + 36B)a b - 24A a b)c +--R + +--R 4 3 2 2 5 +--R (- 12A b + (- 12C + 36B)a b - 24A a b )c - 4A b +--R + +--R 4 2 3 +--R 12B a b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 +--R 12A a c + (24A a b - 36C a )c +--R + +--R 2 3 2 +--R ((- 72C + 36B)a b - 24A a )c +--R + +--R 3 2 2 3 4 +--R (- 24A a b + (- 36C + 72B)a b - 48A a b)c - 12A a b +--R + +--R 2 3 3 2 +--R 36B a b - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 +--R - 4A c + (- 4A b + 12C a)c +--R + +--R 2 2 3 +--R (8A b + (12C - 12B)a b + 16A a )c +--R + +--R 3 2 2 3 2 +--R (8A b + (- 12C - 12B)a b + 16A a b - 24C a )c +--R + +--R 4 3 2 2 +--R - 4A b + (- 12C + 12B)a b - 16A a b +--R + +--R 3 4 +--R (- 24C + 24B)a b - 16A a +--R * +--R c +--R + +--R 5 4 2 3 3 2 4 +--R - 4A b + 12B a b - 16A a b + 24B a b - 16A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R - 4A a c + 12C a c + (8A a b - 12B a b + 8A a )c +--R + +--R 2 2 4 2 3 3 2 +--R - 12C a b c - 4A a b + 12B a b - 8A a b +--R * +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b + (- 9C + 3B)a b - 2A a )c +--R + +--R 3 2 2 2 +--R (- 2A b + (- 9C + 9B)a b - 6A a b)c +--R + +--R 4 3 2 2 5 4 2 3 +--R (- 3A b + (- 3C + 9B)a b - 6A a b )c - A b + 3B a b - 2A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + ((- 24C + 12B)a b - 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4A a )c +--R + +--R 3 2 2 3 3 +--R (36A a b + (- 174C + 66B)a b - 44A a b)c +--R + +--R 4 2 3 3 2 2 +--R (- 38A a b + (- 174C + 174B)a b - 116A a b )c +--R + +--R 5 2 4 3 3 6 +--R (- 58A a b + (- 60C + 174B)a b - 116A a b )c - 20A a b +--R + +--R 2 5 3 4 +--R 60B a b - 40A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 2 2 5 +--R - 4A b c + (- 8A b + 12C a b + 12A a )c +--R + +--R 3 2 2 3 4 +--R (4A b + (24C - 12B)a b + 68A a b - 36C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (16A b - 24B a b + 88A a b + (- 180C + 36B)a b - 24A a )c +--R + +--R 5 4 2 3 3 2 +--R 4A b - 24C a b - 24A a b + (- 252C + 180B)a b +--R + +--R 4 +--R - 120A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 +--R - 8A b + (- 12C + 24B)a b - 100A a b +--R + +--R 3 3 4 2 +--R (- 108C + 252B)a b - 168A a b +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 4A b + 12B a b - 44A a b + 108B a b - 72A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 5 +--R - 4A a c + (- 20A a b + 12C a )c +--R + +--R 2 2 3 4 +--R (- 4A a b + (60C - 12B)a b + 28A a )c +--R + +--R 3 2 2 3 4 3 +--R (40A a b + (24C - 60B)a b + 88A a b - 60C a )c +--R + +--R 4 2 3 3 2 +--R 20A a b + (- 60C - 24B)a b + 24A a b +--R + +--R 4 5 +--R (- 144C + 60B)a b - 40A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 +--R - 20A a b + (- 36C + 60B)a b - 88A a b +--R + +--R 4 2 5 +--R (- 84C + 144B)a b - 96A a b +--R * +--R c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 12A a b + 36B a b - 52A a b + 84B a b - 56A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 2 5 +--R 2A b c + (- 2A b - 6C a b - 12A a )c +--R + +--R 3 2 2 3 4 +--R (- 4A b + (6C + 6B)a b - 16A a b + 36C a )c +--R + +--R 4 3 2 2 3 +--R 4A b + (6C - 6B)a b + 28A a b + (36C - 36B)a b +--R + +--R 4 +--R 32A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 +--R 2A b + (- 6C - 6B)a b + 28A a b + (- 36C - 36B)a b +--R + +--R 4 5 +--R 32A a b - 24C a +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R - 2A b + 6B a b - 16A a b + (- 36C + 36B)a b +--R + +--R 4 2 5 6 +--R - 32A a b + (- 24C + 24B)a b - 16A a +--R * +--R c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 12A a b + 36B a b - 32A a b + 24B a b - 16A a b +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R 2A a c + (- 2A a b - 6C a )c +--R + +--R 2 2 3 4 +--R (- 4A a b + (6C + 6B)a b - 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (4A a b + (6C - 6B)a b + 4A a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2A a b + (- 6C - 6B)a b + 12A a b - 12B a b + 8A a )c +--R + +--R 5 2 4 3 3 4 2 3 4 4 3 +--R (- 2A a b + 6B a b - 4A a b - 12C a b )c - 4A a b + 12B a b +--R + +--R 5 2 +--R - 8A a b +--R * +--R sinh(x) +--R + +--R 2 5 3 2 4 +--R A b c + (3A b - 3C a b )c +--R + +--R 4 3 2 2 3 +--R (2A b + (- 9C + 3B)a b - 2A a b )c +--R + +--R 5 4 2 3 2 +--R (- 2A b + (- 9C + 9B)a b - 6A a b )c +--R + +--R 6 5 2 4 7 6 2 5 +--R (- 3A b + (- 3C + 9B)a b - 6A a b )c - A b + 3B a b - 2A a b +--R * +--R 6 +--R cosh(x) +--R + +--R 5 2 2 4 +--R 2A a b c + (10A a b - 6C a b)c +--R + +--R 3 2 2 3 3 +--R (12A a b + (- 30C + 6B)a b - 4A a b)c +--R + +--R 4 2 3 3 2 2 +--R (- 4A a b + (- 42C + 30B)a b - 20A a b )c +--R + +--R 5 2 4 3 3 6 2 5 +--R (- 14A a b + (- 18C + 42B)a b - 28A a b )c - 6A a b + 18B a b +--R + +--R 3 4 +--R - 12A a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- 2A b + A a )c + (- 2A b + 6C a b + 11A a b - 3C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (4A b + (6C - 6B)a b + 26A a b + (- 33C + 3B)a b - 2A a )c +--R + +--R 5 4 2 3 3 2 +--R 4A b + (- 6C - 6B)a b + 6A a b + (- 69C + 33B)a b +--R + +--R 4 +--R - 22A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R - 2A b + (- 6C + 6B)a b - 27A a b + (- 39C + 69B)a b +--R + +--R 4 2 +--R - 46A a b +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2A b + 6B a b - 17A a b + 39B a b - 26A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 2 3 4 +--R - 4A a b c + (- 8A a b + 12C a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (8A a b + (24C - 12B)a b + 24A a b - 12C a )c +--R + +--R 4 2 3 3 2 4 +--R 16A a b + (- 12C - 24B)a b + 24A a b + (- 48C + 12B)a b +--R + +--R 5 +--R - 8A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 4 2 +--R - 4A a b + (- 24C + 12B)a b - 24A a b + (- 36C + 48B)a b +--R + +--R 5 +--R - 32A a b +--R * +--R c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 8A a b + 24B a b - 28A a b + 36B a b - 24A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (A b - 2A a )c + (- A b - 3C a b - 10A a b + 6C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- 2A b + (3C + 3B)a b + 2A a b + (30C - 6B)a b + 8A a )c +--R + +--R 5 4 2 3 3 2 4 +--R 2A b + (3C - 3B)a b + 22A a b + (- 6C - 30B)a b + 24A a b +--R + +--R 5 +--R - 12C a +--R * +--R 2 +--R c +--R + +--R 6 5 3 3 4 2 +--R A b + (- 3C - 3B)a b + (- 30C + 6B)a b - 8A a b +--R + +--R 5 6 +--R (- 12C + 12B)a b - 8A a +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - A b + 3B a b - 12A a b + 30B a b - 24A a b + 12B a b +--R + +--R 6 +--R - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 2 3 4 +--R 2A a b c + (- 2A a b - 6C a b - 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4A a b + (6C + 6B)a b - 4A a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (4A a b + (6C - 6B)a b + 12A a b - 12B a b + 8A a )c +--R + +--R 5 2 4 3 3 4 2 6 +--R (2A a b + (- 6C - 6B)a b + 4A a b - 12C a b )c - 2A a b +--R + +--R 2 5 3 4 4 3 5 2 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R cosh(x) +--R + +--R 2 5 2 3 4 2 2 3 4 3 +--R A a c + (- A a b - 3C a )c + (- 2A a b + (3C + 3B)a b - 2A a )c +--R + +--R 2 3 3 2 4 2 +--R (2A a b + (3C - 3B)a b + 2A a b)c +--R + +--R 2 4 3 3 4 2 2 5 3 4 4 3 +--R (A a b + (- 3C - 3B)a b + 2A a b )c - A a b + 3B a b - 2A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 7 6 2 2 5 +--R - 2A c + (- 6A b + 6C a)c + (- 4A b + (18C - 6B)a b + 4A a )c +--R + +--R 3 2 2 4 +--R (4A b + (18C - 18B)a b + 12A a b)c +--R + +--R 4 3 2 2 3 +--R (6A b + (6C - 18B)a b + 12A a b )c +--R + +--R 5 4 2 3 2 +--R (2A b - 6B a b + 4A a b )c +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 +--R - 8A c + (- 28A b + 24C a)c +--R + +--R 2 2 5 +--R (- 28A b + (84C - 24B)a b + 16A a )c +--R + +--R 3 2 2 4 +--R (8A b + (108C - 84B)a b + 56A a b)c +--R + +--R 4 3 2 2 3 +--R (32A b + (60C - 108B)a b + 72A a b )c +--R + +--R 5 4 2 3 2 +--R (20A b + (12C - 60B)a b + 40A a b )c +--R + +--R 6 5 2 4 +--R (4A b - 12B a b + 8A a b )c +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R - 12A a c + (- 28A a b + 36C a )c +--R + +--R 2 2 3 4 +--R (- 8A a b + (84C - 36B)a b + 24A a )c +--R + +--R 3 2 2 3 3 +--R (24A a b + (60C - 84B)a b + 56A a b)c +--R + +--R 4 2 3 3 2 2 +--R (20A a b + (12C - 60B)a b + 40A a b )c +--R + +--R 5 2 4 3 3 +--R (4A a b - 12B a b + 8A a b )c +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 +--R - 12A c + (- 52A b + 36C a)c +--R + +--R 2 2 5 +--R (- 74A b + (156C - 36B)a b + 24A a )c +--R + +--R 3 2 2 4 +--R (- 14A b + (258C - 156B)a b + 104A a b)c +--R + +--R 4 3 2 2 3 +--R (64A b + (198C - 258B)a b + 172A a b )c +--R + +--R 5 4 2 3 2 +--R (64A b + (66C - 198B)a b + 132A a b )c +--R + +--R 6 5 2 4 7 6 +--R (22A b + (6C - 66B)a b + 44A a b )c + 2A b - 6B a b +--R + +--R 2 5 +--R 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 +--R - 40A a c + (- 116A a b + 120C a )c +--R + +--R 2 2 3 4 +--R (- 76A a b + (348C - 120B)a b + 80A a )c +--R + +--R 3 2 2 3 3 +--R (72A a b + (348C - 348B)a b + 232A a b)c +--R + +--R 4 2 3 3 2 2 +--R (112A a b + (132C - 348B)a b + 232A a b )c +--R + +--R 5 2 4 3 3 6 +--R (44A a b + (12C - 132B)a b + 88A a b )c + 4A a b +--R + +--R 2 5 3 4 +--R - 12B a b + 8A a b +--R * +--R cosh(x) +--R + +--R 7 6 +--R 4A c + (4A b - 12C a)c +--R + +--R 2 2 5 +--R (- 8A b + (- 12C + 12B)a b - 34A a )c +--R + +--R 3 2 2 3 4 +--R (- 8A b + (12C + 12B)a b - 54A a b + 78C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (4A b + (12C - 12B)a b + 12A a b + (138C - 78B)a b + 52A a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (4A b - 12B a b + 52A a b + (66C - 138B)a b + 92A a b)c +--R + +--R 2 4 3 3 4 2 2 5 3 4 +--R (22A a b + (6C - 66B)a b + 44A a b )c + 2A a b - 6B a b +--R + +--R 4 3 +--R 4A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 +--R - 8A c + (- 48A b + 24C a)c +--R + +--R 2 2 5 +--R (- 96A b + (144C - 24B)a b + 16A a )c +--R + +--R 3 2 2 4 +--R (- 56A b + (312C - 144B)a b + 96A a b)c +--R + +--R 4 3 2 2 3 +--R (56A b + (312C - 312B)a b + 208A a b )c +--R + +--R 5 4 2 3 2 +--R (96A b + (144C - 312B)a b + 208A a b )c +--R + +--R 6 5 2 4 7 6 +--R (48A b + (24C - 144B)a b + 96A a b )c + 8A b - 24B a b +--R + +--R 2 5 +--R 16A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 5 +--R - 48A a c + (- 184A a b + 144C a )c +--R + +--R 2 2 3 4 +--R (- 200A a b + (552C - 144B)a b + 96A a )c +--R + +--R 3 2 2 3 3 +--R (48A a b + (744C - 552B)a b + 368A a b)c +--R + +--R 4 2 3 3 2 2 +--R (224A a b + (408C - 744B)a b + 496A a b )c +--R + +--R 5 2 4 3 3 6 +--R (136A a b + (72C - 408B)a b + 272A a b )c + 24A a b +--R + +--R 2 5 3 4 +--R - 72B a b + 48A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 +--R 8A c + (16A b - 24C a)c +--R + +--R 2 2 5 +--R (- 8A b + (- 48C + 24B)a b - 88A a )c +--R + +--R 3 2 2 3 4 +--R (- 32A b + 48B a b - 200A a b + 216C a )c +--R + +--R 4 3 2 2 3 +--R - 8A b + 48C a b - 48A a b + (504C - 216B)a b +--R + +--R 4 +--R 144A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 +--R 16A b + (24C - 48B)a b + 176A a b + (360C - 504B)a b +--R + +--R 4 +--R 336A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R 8A b - 24B a b + 136A a b + (72C - 360B)a b +--R + +--R 4 2 +--R 240A a b +--R * +--R c +--R + +--R 2 5 3 4 4 3 +--R 24A a b - 72B a b + 48A a b +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R 16A a c + (8A a b - 48C a )c +--R + +--R 2 2 3 4 +--R (- 32A a b + (- 24C + 48B)a b - 56A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 16A a b + (48C + 24B)a b - 48A a b + 72C a )c +--R + +--R 4 2 3 3 2 4 +--R 16A a b + (24C - 48B)a b + 48A a b + (96C - 72B)a b +--R + +--R 5 +--R 48A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 4 2 5 +--R (8A a b - 24B a b + 48A a b + (24C - 96B)a b + 64A a b)c +--R + +--R 3 4 4 3 5 2 +--R 8A a b - 24B a b + 16A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 +--R - 2A c + (- 22A b + 6C a)c +--R + +--R 2 2 5 +--R (- 64A b + (66C - 6B)a b + 4A a )c +--R + +--R 3 2 2 4 +--R (- 64A b + (198C - 66B)a b + 44A a b)c +--R + +--R 4 3 2 2 3 +--R (14A b + (258C - 198B)a b + 132A a b )c +--R + +--R 5 4 2 3 2 +--R (74A b + (156C - 258B)a b + 172A a b )c +--R + +--R 6 5 2 4 7 6 +--R (52A b + (36C - 156B)a b + 104A a b )c + 12A b - 36B a b +--R + +--R 2 5 +--R 24A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 2 5 +--R - 24A a c + (- 136A a b + 72C a )c +--R + +--R 2 2 3 4 +--R (- 224A a b + (408C - 72B)a b + 48A a )c +--R + +--R 3 2 2 3 3 +--R (- 48A a b + (744C - 408B)a b + 272A a b)c +--R + +--R 4 2 3 3 2 2 +--R (200A a b + (552C - 744B)a b + 496A a b )c +--R + +--R 5 2 4 3 3 6 +--R (184A a b + (144C - 552B)a b + 368A a b )c + 48A a b +--R + +--R 2 5 3 4 +--R - 144B a b + 96A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 +--R 4A c + (20A b - 12C a)c +--R + +--R 2 2 5 +--R (12A b + (- 60C + 12B)a b - 76A a )c +--R + +--R 3 2 2 3 4 +--R (- 36A b + (- 48C + 60B)a b - 260A a b + 204C a )c +--R + +--R 4 3 2 2 3 +--R - 36A b + (48C + 48B)a b - 184A a b + (660C - 204B)a b +--R + +--R 4 +--R 136A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 +--R 12A b + (60C - 48B)a b + 184A a b + (660C - 660B)a b +--R + +--R 4 +--R 440A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R 20A b + (12C - 60B)a b + 260A a b + (204C - 660B)a b +--R + +--R 4 2 +--R 440A a b +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 +--R 4A b - 12B a b + 76A a b - 204B a b + 136A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 +--R 24A a c + (40A a b - 72C a )c +--R + +--R 2 2 3 4 +--R (- 40A a b + (- 120C + 72B)a b - 104A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 80A a b + (48C + 120B)a b - 176A a b + 168C a )c +--R + +--R 4 2 3 3 2 4 +--R 8A a b + (120C - 48B)a b + 48A a b + (288C - 168B)a b +--R + +--R 5 +--R 112A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 +--R 40A a b + (24C - 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32a b)c + (6b - 20a b + 2a b + 12a )c +--R + +--R 7 2 5 4 3 6 2 +--R (- 6b - 52a b + 62a b - 4a b)c +--R + +--R 8 2 6 4 4 6 2 8 9 2 7 4 5 +--R (- 2b + 8a b - 2a b - 12a b + 8a )c + 2b + 16a b - 30a b +--R + +--R 6 3 8 +--R 4a b + 8a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 3 6 3 3 5 +--R 4a b c + (- 4a b - 8a )c + (- 12a b + 8a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (12a b + 16a b - 16a )c + (12a b - 16a b + 4a b)c +--R + +--R 6 3 4 5 2 7 2 7 3 5 5 3 +--R (- 12a b - 8a b + 28a b - 8a )c + (- 4a b + 8a b - 4a b )c +--R + +--R 8 5 4 7 2 +--R 4a b - 12a b + 8a b +--R * +--R cosh(x) +--R + +--R 2 7 2 6 2 2 4 5 2 3 4 4 +--R 2a c - 2a b c + (- 6a b + 4a )c + (6a b - 4a b)c +--R + +--R 2 4 4 2 6 3 2 5 4 3 6 2 +--R (6a b - 8a b + 2a )c + (- 6a b + 8a b - 2a b)c +--R + +--R 2 6 4 4 6 2 2 7 4 5 6 3 +--R (- 2a b + 4a b - 2a b )c + 2a b - 4a b + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression Integer +--E 249 + +--S 250 of 531 +--d1043a:= D(m1043a,x) +--E 250 + +--S 251 of 531 +m1043b:= a1043.2-r1043 +--R +--R +--R (219) +--R 7 6 2 2 5 +--R - 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24B)a b + 48A a b - 72C a )c +--R + +--R 4 2 3 3 2 4 +--R - 16A a b + (- 24C + 48B)a b - 48A a b + (- 96C + 72B)a b +--R + +--R 5 +--R - 48A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 8A a b + 24B a b - 48A a b + (- 24C + 96B)a b - 64A a b)c +--R + +--R 3 4 4 3 5 2 +--R - 8A a b + 24B a b - 16A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 +--R 2A c + (22A b - 6C a)c +--R + +--R 2 2 5 +--R (64A b + (- 66C + 6B)a b - 4A a )c +--R + +--R 3 2 2 4 +--R (64A b + (- 198C + 66B)a b - 44A a b)c +--R + +--R 4 3 2 2 3 +--R (- 14A b + (- 258C + 198B)a b - 132A a b )c +--R + +--R 5 4 2 3 2 +--R (- 74A b + (- 156C + 258B)a b - 172A a b )c +--R + +--R 6 5 2 4 7 +--R (- 52A b + (- 36C + 156B)a b - 104A a b )c - 12A b +--R + +--R 6 2 5 +--R 36B a b - 24A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 2 5 +--R 24A a c + (136A a b - 72C a )c +--R + +--R 2 2 3 4 +--R (224A a b + (- 408C + 72B)a b - 48A a )c +--R + +--R 3 2 2 3 3 +--R (48A a b + (- 744C + 408B)a b - 272A a b)c +--R + +--R 4 2 3 3 2 2 +--R (- 200A a b + (- 552C + 744B)a b - 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8c - 16b c + (16b + 56a )c + (48b + 136a b)c +--R + +--R 2 2 4 5 5 2 3 4 4 +--R (- 8a b + 136a )c + (- 48b - 248a b + 320a b)c +--R + +--R 6 2 4 4 2 6 3 +--R (- 16b - 152a b + 96a b + 72a )c +--R + +--R 7 2 5 4 3 6 2 +--R (16b + 88a b - 272a b + 168a b)c +--R + +--R 8 2 6 4 4 6 2 2 7 4 5 6 3 +--R (8b + 104a b - 232a b + 120a b )c + 24a b - 48a b + 24a b +--R * +--R cosh(x) +--R + +--R 8 7 2 3 6 3 3 5 +--R - 16a c - 8a b c + (48a b - 8a )c + (24a b + 16a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (- 48a b + 24a b + 32a )c + (- 24a b - 32a b + 56a b)c +--R + +--R 6 3 4 5 2 7 2 +--R (16a b - 24a b - 16a b + 24a )c +--R + +--R 7 3 5 5 3 7 3 6 5 4 7 2 +--R (8a b + 16a b - 56a b + 32a b)c + 8a b - 16a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 2 2 7 3 2 6 +--R 2c + 22b c + (62b + 4a )c + (42b + 44a b)c +--R + +--R 4 2 2 4 5 5 2 3 4 4 +--R (- 78b + 128a b + 2a )c + (- 138b + 128a b + 22a b)c +--R + +--R 6 2 4 4 2 3 7 2 5 4 3 2 +--R (- 38b - 28a b + 66a b )c + (62b - 148a b + 86a b )c +--R + +--R 8 2 6 4 4 9 2 7 4 5 +--R (52b - 104a b + 52a b )c + 12b - 24a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 3 6 3 3 5 +--R 24a c + 136a b c + (200a b + 48a )c + (- 88a b + 272a b)c +--R + +--R 4 3 2 5 4 +--R (- 424a b + 448a b + 24a )c +--R + +--R 5 3 3 5 3 +--R (- 232a b + 96a b + 136a b)c +--R + +--R 6 3 4 5 2 2 +--R (152a b - 400a b + 248a b )c +--R + +--R 7 3 5 5 3 8 3 6 5 4 +--R (184a b - 368a b + 184a b )c + 48a b - 96a b + 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 2 7 3 2 6 +--R - 4c - 20b c + (- 8b + 60a )c + (56b + 180a b)c +--R + +--R 4 2 2 4 5 5 2 3 4 4 +--R (48b + 60a b + 132a )c + (- 48b - 300a b + 420a b)c +--R + +--R 6 2 4 4 2 6 3 +--R (- 56b - 300a b + 288a b + 68a )c +--R + +--R 7 2 5 4 3 6 2 +--R (8b + 60a b - 288a b + 220a b)c +--R + +--R 8 2 6 4 4 6 2 9 2 7 4 5 +--R (20b + 180a b - 420a b + 220a b )c + 4b + 60a b - 132a b +--R + +--R 6 3 +--R 68a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 3 6 3 3 5 +--R - 24a c - 40a b c + (64a b + 8a )c + (120a b + 16a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (- 48a b + 8a b + 88a )c + (- 120a b - 32a b + 152a b)c +--R + +--R 3 4 5 2 7 2 +--R (- 40a b - 16a b + 56a )c +--R + +--R 7 3 5 5 3 7 8 3 6 5 4 +--R (40a b + 16a b - 152a b + 96a b)c + 8a b + 24a b - 72a b +--R + +--R 7 2 +--R 40a b +--R * +--R cosh(x) +--R + +--R 9 8 2 2 7 3 2 6 +--R 2c - 2b c + (- 6b - 16a )c + (6b - 8a b)c +--R + +--R 4 2 2 4 5 5 2 3 4 4 +--R (6b + 52a b - 30a )c + (- 6b + 20a b - 2a b)c +--R + +--R 6 2 4 4 2 6 3 +--R (- 2b - 56a b + 62a b - 4a )c +--R + +--R 7 2 5 4 3 6 2 2 6 4 4 6 2 8 +--R (2b - 16a b + 2a b + 12a b)c + (20a b - 32a b + 4a b + 8a )c +--R + +--R 2 7 6 3 8 +--R 4a b - 12a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 2 7 3 2 6 4 2 2 5 +--R 4b c + 20b c + (28b + 8a b)c + (- 12b + 40a b )c +--R + +--R 5 2 3 4 4 6 2 4 4 2 3 +--R (- 60b + 64a b + 4a b)c + (- 36b + 16a b + 20a b )c +--R + +--R 7 2 5 4 3 2 8 2 6 4 4 9 +--R (20b - 56a b + 36a b )c + (28b - 56a b + 28a b )c + 8b +--R + +--R 2 7 4 5 +--R - 16a b + 8a b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 3 6 3 3 5 +--R 4a c + 44a b c + (108a b + 8a )c + (28a b + 88a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (- 188a b + 224a b + 4a )c + (- 188a b + 144a b + 44a b)c +--R + +--R 6 3 4 5 2 2 7 3 5 5 3 +--R (36a b - 152a b + 116a b )c + (116a b - 232a b + 116a b )c +--R + +--R 8 3 6 5 4 +--R 40a b - 80a b + 40a b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 2 7 3 2 6 +--R - 8b c + (- 16b + 24a )c + (16b + 104a b)c +--R + +--R 4 2 2 4 5 2 3 4 4 +--R (48b + 88a b + 48a )c + (- 152a b + 232a b)c +--R + +--R 6 2 4 4 2 6 3 +--R (- 48b - 248a b + 272a b + 24a )c +--R + +--R 7 2 5 4 3 6 2 +--R (- 16b - 8a b - 96a b + 120a b)c +--R + +--R 8 2 6 4 4 6 2 9 2 7 4 5 +--R (16b + 136a b - 320a b + 168a b )c + 8b + 56a b - 136a b +--R + +--R 6 3 +--R 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 3 6 3 3 5 +--R - 8a c - 40a b c + 24a c + (120a b + 16a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (48a b - 40a b + 72a )c + (- 120a b - 32a b + 152a b)c +--R + +--R 6 3 4 5 2 7 2 +--R (- 64a b + 8a b + 16a b + 40a )c +--R + +--R 7 3 5 5 3 7 8 3 6 5 4 +--R (40a b + 16a b - 152a b + 96a b)c + 24a b + 8a b - 88a b +--R + +--R 7 2 +--R 56a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 2 7 3 2 6 +--R 4b c + (- 4b - 24a )c + (- 12b - 16a b)c +--R + +--R 4 2 2 4 5 5 2 3 4 4 +--R (12b + 64a b - 32a )c + (12b + 56a b - 28a b)c +--R + +--R 6 2 4 4 2 6 3 +--R (- 12b - 56a b + 60a b + 8a )c +--R + +--R 7 2 5 4 3 6 2 +--R (- 4b - 64a b + 60a b + 8a b)c +--R + +--R 8 2 6 4 4 6 2 8 2 7 4 5 +--R (4b + 16a b - 28a b - 8a b + 16a )c + 24a b - 32a b +--R + +--R 6 3 8 +--R - 8a b + 16a b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 3 5 +--R 4a c - 4a b c - 12a b c + (12a b - 8a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (12a b + 8a b - 12a )c + (- 12a b + 16a b - 4a b)c +--R + +--R 6 3 4 5 2 7 2 7 3 5 5 3 +--R (- 4a b - 16a b + 28a b - 8a )c + (4a b - 8a b + 4a b )c +--R + +--R 3 6 5 4 7 2 +--R 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 2 7 3 6 4 2 2 5 5 2 3 4 +--R 2b c + 6b c + (2b + 4a b )c + (- 10b + 12a b )c +--R + +--R 6 2 4 4 2 3 7 2 5 4 3 2 +--R (- 10b + 8a b + 2a b )c + (2b - 8a b + 6a b )c +--R + +--R 8 2 6 4 4 9 2 7 4 5 +--R (6b - 12a b + 6a b )c + 2b - 4a b + 2a b +--R * +--R 6 +--R cosh(x) +--R + +--R 7 2 6 3 3 5 4 3 2 4 +--R 4a b c + 20a b c + (20a b + 8a b)c + (- 28a b + 40a b )c +--R + +--R 5 3 3 5 3 6 3 4 5 2 2 +--R (- 52a b + 48a b + 4a b)c + (- 4a b - 16a b + 20a b )c +--R + +--R 7 3 5 5 3 8 3 6 5 4 +--R (28a b - 56a b + 28a b )c + 12a b - 24a b + 12a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 7 3 2 6 4 2 2 4 5 +--R (- 4b + 2a )c + (- 4b + 22a b)c + (12b + 34a b + 4a )c +--R + +--R 5 2 3 4 4 6 2 4 4 2 6 3 +--R (12b - 26a b + 44a b)c + (- 12b - 74a b + 84a b + 2a )c +--R + +--R 7 2 5 4 3 6 2 +--R (- 12b - 14a b + 4a b + 22a b)c +--R + +--R 8 2 6 4 4 6 2 9 2 7 4 5 6 3 +--R (4b + 38a b - 88a b + 46a b )c + 4b + 18a b - 48a b + 26a b +--R * +--R 4 +--R cosh(x) +--R + +--R 7 2 3 6 3 3 5 +--R - 8a b c + (- 16a b + 8a )c + (24a b + 16a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (48a b - 24a b + 16a )c + (- 24a b - 32a b + 56a b)c +--R + +--R 6 3 4 5 2 7 2 +--R (- 48a b + 24a b + 16a b + 8a )c +--R + +--R 7 3 5 5 3 7 8 3 6 5 4 7 2 +--R (8a b + 16a b - 56a b + 32a b)c + 16a b - 8a b - 32a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 7 3 2 6 4 2 2 5 +--R (2b - 4a )c + (- 2b - 20a b)c + (- 6b + 16a b )c +--R + +--R 5 2 3 4 4 6 2 4 4 2 6 3 +--R (6b + 56a b - 32a b)c + (6b - 20a b + 2a b + 12a )c +--R + +--R 7 2 5 4 3 6 2 +--R (- 6b - 52a b + 62a b - 4a b)c +--R + +--R 8 2 6 4 4 6 2 8 9 2 7 4 5 +--R (- 2b + 8a b - 2a b - 12a b + 8a )c + 2b + 16a b - 30a b +--R + +--R 6 3 8 +--R 4a b + 8a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 3 6 3 3 5 +--R 4a b c + (- 4a b - 8a )c + (- 12a b + 8a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (12a b + 16a b - 16a )c + (12a b - 16a b + 4a b)c +--R + +--R 6 3 4 5 2 7 2 7 3 5 5 3 +--R (- 12a b - 8a b + 28a b - 8a )c + (- 4a b + 8a b - 4a b )c +--R + +--R 8 5 4 7 2 +--R 4a b - 12a b + 8a b +--R * +--R cosh(x) +--R + +--R 2 7 2 6 2 2 4 5 2 3 4 4 +--R 2a c - 2a b c + (- 6a b + 4a )c + (6a b - 4a b)c +--R + +--R 2 4 4 2 6 3 2 5 4 3 6 2 +--R (6a b - 8a b + 2a )c + (- 6a b + 8a b - 2a b)c +--R + +--R 2 6 4 4 6 2 2 7 4 5 6 3 +--R (- 2a b + 4a b - 2a b )c + 2a b - 4a b + 2a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression Integer +--E 251 + +--S 252 of 531 +--d1043b:= D(m1043b,x) +--E 252 + +--S 253 of 531 +t1044:= 1/(a+b*sinh(x)+c*sinh(x)^2) +--R +--R +--R 1 +--R (220) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a +--R Type: Expression Integer +--E 253 + +--S 254 of 531 +r1044:= -4*c*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2)+_ + 4*c*atanh((2*c-(b+(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ + (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (221) +--R - +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R - +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression Integer +--E 254 + +--S 255 of 531 +a1044:= integrate(t1044,x) +--R +--R +--R (222) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c + (- 2b - 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + (2b + 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 255 + +--S 256 of 531 +m1044:= a1044-r1044 +--R +--R +--R (223) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c + (- 2b - 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + (2b + 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression Integer +--E 256 + +--S 257 of 531 +d1044:= D(m1044,x) +--R +--R +--R (224) +--R 4 3 +--R - c sinh(x) + (- 4c cosh(x) - 2b)sinh(x) +--R + +--R 2 2 +--R (- 6c cosh(x) - 6b cosh(x) + 2c)sinh(x) +--R + +--R 3 2 4 +--R (- 4c cosh(x) - 6b cosh(x) + 4c cosh(x) + 2b)sinh(x) - c cosh(x) +--R + +--R 3 2 +--R - 2b cosh(x) + 2c cosh(x) + 2b cosh(x) - c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 x 3 +--R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) )tanh(-) +--R 2 +--R + +--R 4 3 +--R 2c sinh(x) + (8c cosh(x) + 4b)sinh(x) +--R + +--R 2 2 +--R (12c cosh(x) + 12b cosh(x) + 12c)sinh(x) +--R + +--R 3 2 4 +--R (8c cosh(x) + 12b cosh(x) + 24c cosh(x) - 4b)sinh(x) + 2c cosh(x) +--R + +--R 3 2 +--R 4b cosh(x) + 12c cosh(x) - 4b cosh(x) + 2c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 x 4 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )tanh(-) - c sinh(x) +--R 2 +--R + +--R 3 2 2 +--R (- 4c cosh(x) - 2b)sinh(x) + (- 6c cosh(x) - 6b cosh(x) + 2c)sinh(x) +--R + +--R 3 2 4 +--R (- 4c cosh(x) - 6b cosh(x) + 4c cosh(x) + 2b)sinh(x) - c cosh(x) +--R + +--R 3 2 +--R - 2b cosh(x) + 2c cosh(x) + 2b cosh(x) - c +--R / +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) +--R + +--R a c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R - 2b c sinh(x) + (- 8b c cosh(x) - 4b )sinh(x) +--R + +--R 2 2 2 +--R (- 12b c cosh(x) - 12b cosh(x) + 4b c - 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (- 8b c cosh(x) - 12b cosh(x) + (8b c - 16a b)cosh(x) + 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R - 2b c cosh(x) - 4b cosh(x) + (4b c - 8a b)cosh(x) + 4b cosh(x) +--R + +--R - 2b c +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (4c - 2a c)sinh(x) + ((16c - 8a c)cosh(x) + 8b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (24c - 12a c)cosh(x) + (24b c - 12a b)cosh(x) - 8c + 20a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (16c - 8a c)cosh(x) + (24b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (- 16c + 40a c - 16a )cosh(x) - 8b c + 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (4c - 2a c)cosh(x) + (8b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 8c + 20a c - 8a )cosh(x) + (- 8b c + 4a b)cosh(x) + 4c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2b c sinh(x) + (8b c cosh(x) + 4b )sinh(x) +--R + +--R 2 2 2 +--R (12b c cosh(x) + 12b cosh(x) - 4b c + 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8b c cosh(x) + 12b cosh(x) + (- 8b c + 16a b)cosh(x) - 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R 2b c cosh(x) + 4b cosh(x) + (- 4b c + 8a b)cosh(x) - 4b cosh(x) +--R + +--R 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) + a c +--R Type: Expression Integer +--E 257 + +--S 258 of 531 +t1045:= sinh(x)/(a+b*sinh(x)+c*sinh(x)^2) +--R +--R +--R sinh(x) +--R (225) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a +--R Type: Expression Integer +--E 258 + +--S 259 of 531 +r1045:= -2*(1-b/(b^2-4*a*c)^(1/2))*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*_ + tanh(1/2*x))/(4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2)-2*(1+b/(b^2-4*a*c)^(1/2))*_ + atanh((2*c-(b+(b^2-4*a*c)^(1/2))*tanh(1/2*x))/(4*c^2+_ + (b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (226) +--R +-----------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2\|- 4a c + b + 2b)\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (2\|- 4a c + b + 2b)\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression Integer +--E 259 + +--S 260 of 531 +a1045:= integrate(t1045,x) +--R +--R +--R (227) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b - 4a b)c + (5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b + 5a b + 4a b)c - a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (- 8a c + (2a b + 16a )c + (- 12a b - 8a )c + 2a b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b - 4a b)c + (5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b + 5a b + 4a b)c - a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b + 4a b)c + (- 5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b - 5a b - 4a b)c + a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R