diff --git a/buglist b/buglist index 66d1112..19c20b8 100644 --- a/buglist +++ b/buglist @@ -1,6 +1,6 @@ ========================================================================= -bug 7246: +bug 7247: todo 335: wish 1011: meh 5: @@ -12,6 +12,14 @@ dup 50006: nonextend 60077: ========================================================================= +bug 7246: kamke tests missing +kamke1 seems to be missing ode97 +kamke2 missing 104, 105 +kamke6 missing 332 +kamke7 missing 357, 359, 360, 362 and many others +kamke7 repeats 776 with different equations + +========================================================================= bug 7245: v81crcp50-2.6.5.2 and v81crcp50-2.6.5.3 graphs differ from CRC (see ps/v81crcp50-2.6.5.1-3.eps) diff --git a/changelog b/changelog index 898a111..e88dbba 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,22 @@ +20130715 tpd src/axiom-website/patches.html 20130715.01.tpd.patch +20130715 tpd buglist add kamke4, kamke6 missing bug +20130715 tpd src/axiom-website/CATS/index.html updated +20130715 tpd src/axiom-website/CATS/charlwood.input added +20130715 tpd src/axiom-website/CATS/charlwood.input.pdf added +20130715 tpd src/axiom-website/CATS/kamke6.input fixed +20130715 tpd src/axiom-website/CATS/kamke4.input fixed +20130715 tpd src/axiom-website/CATS/kamke0.txt added +20130715 tpd src/axiom-website/CATS/kamke1.txt added +20130715 tpd src/axiom-website/CATS/kamke2.txt added +20130715 tpd src/axiom-website/CATS/kamke3.txt added +20130715 tpd src/axiom-website/CATS/kamke5.txt added +20130715 tpd src/axiom-website/CATS/kamke6.txt added +20130715 tpd src/axiom-website/CATS/kamke7.txt added +20130715 tpd src/input/Makefile add charlwood +20130715 tpd src/input/charlwood.input added +20130714 tpd src/axiom-website/patches.html 20130714.02.tpd.patch +20140714 tpd src/input/Makefile charlwood.input added +20140714 tpd src/input/charlwood.input added 20130714 tpd src/axiom-website/patches.html 20130714.01.tpd.patch 20130714 tpd src/axiom-website/CATS/axiom.sty added 20130714 tpd src/axiom-website/CATS/index.html added @@ -79,7 +98,7 @@ 20130714 tpd src/axiom-website/CATS/richtrig700-799.input.pdf added 20130714 tpd src/axiom-website/CATS/richtrig800-899.input added 20130714 tpd src/axiom-website/CATS/richtrig800-899.input.pdf added -20130714 tpd src/axiom-website/CATS/richtrig900-920.input added +20130714 tpd src/axiom-website/CATS/richtrig900-920.input added 20130714 tpd src/axiom-website/CATS/richtrig900-920.input.pdf added 20130702 tpd src/axiom-website/patches.html 20130702.01.tpd.patch 20130702 tpd books/bookvolbib add Griesmer ref, sort items diff --git a/src/axiom-website/CATS/charlwood.input.pamphlet b/src/axiom-website/CATS/charlwood.input.pamphlet new file mode 100644 index 0000000..ddb9f5d --- /dev/null +++ b/src/axiom-website/CATS/charlwood.input.pamphlet @@ -0,0 +1,6914 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input charlwood.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +Integrals taken from sci.math.symbolic posting of Charlwood, Kevin +``Integration on Computer Algebra Systems'' +Electronic Journal of Mathematics and Technology (2008) +\verb|www.freepatentsonline.com/article/| +\verb|Electronic-journal-Mathematics-Technology/188213666.html| +by Albert Rich at +\verb|www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf| +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f charlwood.output +)spool charlwood.output +)set message auto off +)clear all + +\end{chunk} +\subsection{Problem 1} +\begin{chunk}{*} + +--S 1 of 250 +t0001:= asin(x)*log(x) +--R +--R +--R (1) asin(x)log(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 250 +r0001:= -2*sqrt(1-x^2)+atanh(sqrt(1-x^2))-x*asin(x)*(1-log(x))+_ + sqrt(1-x^2)*log(x) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | 2 | 2 +--R atanh(\|- x + 1 ) + (log(x) - 2)\|- x + 1 + x asin(x)log(x) - x asin(x) +--R Type: Expression(Integer) +--E 2 + +--S 3 of 250 +a0001:= integrate(t0001,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | 2 | 2 +--R log(\|- x + 1 + 1) - log(\|- x + 1 - 1) +--R + +--R +--------+ +--R | 2 +--------+ +--R 2x\|- x + 1 | 2 +--R (- x log(x) + x)atan(-------------) + (2log(x) - 4)\|- x + 1 +--R 2 +--R 2x - 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 250 +m0001:= a0001-r0001 +--R +--R +--R (4) +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R log(\|- x + 1 + 1) - log(\|- x + 1 - 1) - 2atanh(\|- x + 1 ) +--R + +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R (- x log(x) + x)atan(-------------) - 2x asin(x)log(x) + 2x asin(x) +--R 2 +--R 2x - 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 250 +d0001:= D(m0001,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - log(x)atan(-------------) - 2asin(x)log(x) +--R 2 +--R 2x - 1 +--R (5) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 5 + + +\end{chunk} +\subsection{Problem 2} +\begin{chunk}{*} + +--S 6 of 250 +t0002:= x*asin(x)/sqrt(1-x^2) +--R +--R +--R x asin(x) +--R (6) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 250 +r0002:= x-sqrt(1-x^2)*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (7) - asin(x)\|- x + 1 + x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 250 +a0002:= integrate(t0002,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R \|- x + 1 atan(-------------) + 2x +--R 2 +--R 2x - 1 +--R (8) ----------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 250 +m0002:= a0002-r0002 +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2x\|- x + 1 | 2 +--R \|- x + 1 atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R (9) ---------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 250 +d0002:= D(m0002,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - x atan(-------------) - 2x asin(x) +--R 2 +--R 2x - 1 +--R (10) ------------------------------------ +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 10 + + +\end{chunk} +\subsection{Problem 3} +\begin{chunk}{*} + +--S 11 of 250 +t0003:= asin(sqrt(x+1)-sqrt(x)) +--R +--R +--R +-----+ +-+ +--R (11) asin(\|x + 1 - \|x ) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 250 +r0003:= ((sqrt(x)+3*sqrt(1+x))*sqrt(-x+sqrt(x)*sqrt(1+x)))/(4*sqrt(2))-_ + (3/8+x)*asin(sqrt(x)-sqrt(1+x)) +--R +--R +--R (12) +--R +----------------+ +--R +-----+ +-+ | +-+ +-----+ +-+ +-----+ +-+ +--R (6\|x + 1 + 2\|x )\|\|x \|x + 1 - x + (8x + 3)\|2 asin(\|x + 1 - \|x ) +--R -------------------------------------------------------------------------- +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 250 +a0003:= integrate(t0003,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 13 + +--S 14 of 250 +--m0003:= a0003-r0003 +--E 14 + +--S 15 of 250 +--d0003:= D(m0003,x) +--E 15 + + +\end{chunk} +\subsection{Problem 4} +\begin{chunk}{*} + +--S 16 of 250 +t0004:= log(1+x*sqrt(1+x^2)) +--R +--R +--R +------+ +--R | 2 +--R (13) log(x\|x + 1 + 1) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 250 +r0004:= -2*x+sqrt(2*(1+sqrt(5)))*atan(sqrt(-2+sqrt(5))*(x+sqrt(1+x^2)))-_ + sqrt(2*(-1+sqrt(5)))*atanh(sqrt(2+sqrt(5))*(x+sqrt(1+x^2)))+_ + x*log(1+x*sqrt(1+x^2)) +--R +--R +--R (14) +--R +------+ +---------+ +------+ +--------+ +--R | 2 | +-+ | 2 | +-+ +--R x log(x\|x + 1 + 1) - \|2\|5 - 2 atanh((\|x + 1 + x)\|\|5 + 2 ) +--R + +--R +---------+ +------+ +--------+ +--R | +-+ | 2 | +-+ +--R \|2\|5 + 2 atan((\|x + 1 + x)\|\|5 - 2 ) - 2x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 250 +a0004:= integrate(t0004,x) +--R +--R +--R (15) +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((\|5 + 1)\|x + 1 - x\|5 - x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +--------+ +--------+ +------+ +--R | +-+ | +-+ +-+ +-+ | 2 +--R \|\|5 - 1 log(\|\|5 - 1 + x\|2 ) + 2x\|2 log(x\|x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R - \|\|5 - 1 log(- \|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((- \|5 - 1)\|x + 1 + x\|5 + x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +------+ +--------+ +--R +--------+ +-+ | 2 +-+ | +-+ +--R | +-+ ((\|5 - 1)\|x + 1 - x\|5 + x)\|\|5 + 1 +--R 2\|\|5 + 1 atan(--------------------------------------------) +--R +------+ +--R +-+ | 2 2 +-+ +--R 2x\|2 \|x + 1 + (- 2x - 2)\|2 +--R + +--R +--------+ +--R +--------+ | +-+ +--R | +-+ \|\|5 + 1 +-+ +--R - 2\|\|5 + 1 atan(-----------) - 4x\|2 +--R +-+ +--R x\|2 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 250 +m0004:= a0004-r0004 +--R +--R +--R (16) +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((\|5 + 1)\|x + 1 - x\|5 - x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R \|\|5 - 1 log(\|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ +-+ +--R - \|\|5 - 1 log(- \|\|5 - 1 + x\|2 ) +--R + +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R log +--R +------+ +--------+ +------+ +--R +-+ | 2 +-+ | +-+ +-+ | 2 +--R ((- \|5 - 1)\|x + 1 + x\|5 + x)\|\|5 - 1 - 2x\|2 \|x + 1 +--R + +--R 2 +-+ +--R (2x + 2)\|2 +--R + +--R +---------+ +------+ +--------+ +--R +-+ | +-+ | 2 | +-+ +--R 2\|2 \|2\|5 - 2 atanh((\|x + 1 + x)\|\|5 + 2 ) +--R + +--R +------+ +--------+ +--R +--------+ +-+ | 2 +-+ | +-+ +--R | +-+ ((\|5 - 1)\|x + 1 - x\|5 + x)\|\|5 + 1 +--R 2\|\|5 + 1 atan(--------------------------------------------) +--R +------+ +--R +-+ | 2 2 +-+ +--R 2x\|2 \|x + 1 + (- 2x - 2)\|2 +--R + +--R +--------+ +--R +--------+ | +-+ +--R | +-+ \|\|5 + 1 +--R - 2\|\|5 + 1 atan(-----------) +--R +-+ +--R x\|2 +--R + +--R +---------+ +------+ +--------+ +--R +-+ | +-+ | 2 | +-+ +--R - 2\|2 \|2\|5 + 2 atan((\|x + 1 + x)\|\|5 - 2 ) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 250 +d0004:= D(m0004,x) +--R +--R +--R (17) +--R +------+ +--------+ +---------+ +--R +-+ | 2 +-+ | +-+ | +-+ +--R ((- \|5 - 1)\|x + 1 - x\|5 - 3x)\|\|5 - 2 \|2\|5 + 2 +--R + +--R +------+ +--------+ +---------+ +------+ +--R +-+ | 2 +-+ | +-+ | +-+ | 2 +--R ((- \|5 + 1)\|x + 1 - x\|5 + 3x)\|\|5 + 2 \|2\|5 - 2 + 8\|x + 1 +--R + +--R 4x +--R / +--R +------+ +--R | 2 3 +--R 4\|x + 1 + 4x + 4x +--R Type: Expression(Integer) +--E 20 + + +\end{chunk} +\subsection{Problem 5} +\begin{chunk}{*} + +--S 21 of 250 +t0005:= cos(x)^2/sqrt(cos(x)^4+cos(x)^2+1) +--R +--R +--R 2 +--R cos(x) +--R (18) ------------------------ +--R +---------------------+ +--R | 4 2 +--R \|cos(x) + cos(x) + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 250 +r0005:= x/3+1/3*atan((cos(x)*(1+cos(x)^2)*sin(x))/_ + (1+cos(x)^2*sqrt(1+cos(x)^2+cos(x)^4))) +--R +--R +--R 3 +--R (cos(x) + cos(x))sin(x) +--R atan(-----------------------------------) + x +--R +---------------------+ +--R 2 | 4 2 +--R cos(x) \|cos(x) + cos(x) + 1 + 1 +--R (19) --------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 250 +a0005:= integrate(t0005,x) +--R +--R +--R (20) +--R atan +--R 5 4 3 +--R (cos(x) + 2cos(x) + cos(x) )sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 6 +--R 4cos(x) - 2 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 250 +m0005:= a0005-r0005 +--R +--R +--R (21) +--R atan +--R 5 4 3 +--R (cos(x) + 2cos(x) + cos(x) )sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 6 +--R 4cos(x) - 2 +--R + +--R 3 +--R (cos(x) + cos(x))sin(x) +--R - 2atan(-----------------------------------) - 2x +--R +---------------------+ +--R 2 | 4 2 +--R cos(x) \|cos(x) + cos(x) + 1 + 1 +--R / +--R 6 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 250 +d0005:= D(m0005,x) +--R +--R +--R (22) +--R 26 25 24 23 +--R - 4cos(x) - 8cos(x) - 20cos(x) - 32cos(x) +--R + +--R 22 21 20 19 +--R - 44cos(x) - 56cos(x) - 72cos(x) - 88cos(x) +--R + +--R 18 17 16 15 +--R - 76cos(x) - 64cos(x) - 64cos(x) - 64cos(x) +--R + +--R 14 13 12 10 9 +--R - 36cos(x) - 8cos(x) - 4cos(x) + 12cos(x) + 24cos(x) +--R + +--R 8 7 6 +--R 16cos(x) + 8cos(x) + 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 25 +--R - 8cos(x) - 16cos(x) - 32cos(x) - 48cos(x) +--R + +--R 24 23 22 21 +--R - 72cos(x) - 96cos(x) - 128cos(x) - 160cos(x) +--R + +--R 20 19 18 17 +--R - 176cos(x) - 192cos(x) - 216cos(x) - 240cos(x) +--R + +--R 16 15 14 13 +--R - 209cos(x) - 178cos(x) - 156cos(x) - 134cos(x) +--R + +--R 12 11 10 9 +--R - 94cos(x) - 54cos(x) - 48cos(x) - 42cos(x) +--R + +--R 8 7 6 5 4 +--R - 29cos(x) - 16cos(x) - 11cos(x) - 6cos(x) - cos(x) +--R + +--R 3 2 +--R 4cos(x) + 3cos(x) + 2cos(x) + 1 +--R * +--R 2 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R - 4cos(x) - 8cos(x) - 12cos(x) - 16cos(x) - 32cos(x) +--R + +--R 25 24 23 22 21 +--R - 48cos(x) - 52cos(x) - 56cos(x) - 72cos(x) - 88cos(x) +--R + +--R 20 19 18 17 16 +--R - 56cos(x) - 24cos(x) - 9cos(x) + 6cos(x) + 49cos(x) +--R + +--R 15 14 13 12 11 +--R 92cos(x) + 72cos(x) + 52cos(x) + 46cos(x) + 40cos(x) +--R + +--R 10 9 8 7 6 +--R 11cos(x) - 18cos(x) - 14cos(x) - 10cos(x) - 12cos(x) +--R + +--R 5 4 3 2 +--R - 14cos(x) - 8cos(x) - 2cos(x) - 2cos(x) - 2cos(x) - 1 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 26 24 22 20 18 +--R 8cos(x) + 40cos(x) + 104cos(x) + 180cos(x) + 236cos(x) +--R + +--R 16 14 12 10 8 +--R 260cos(x) + 248cos(x) + 200cos(x) + 132cos(x) + 76cos(x) +--R + +--R 6 4 +--R 40cos(x) + 12cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 22 20 +--R 16cos(x) + 64cos(x) + 144cos(x) + 208cos(x) + 272cos(x) +--R + +--R 18 16 14 12 +--R 336cos(x) + 424cos(x) + 436cos(x) + 388cos(x) +--R + +--R 10 8 6 4 2 +--R 296cos(x) + 180cos(x) + 88cos(x) + 16cos(x) + 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 30 28 26 24 22 +--R 8cos(x) + 24cos(x) + 48cos(x) + 52cos(x) + 84cos(x) +--R + +--R 20 18 16 14 12 +--R 96cos(x) + 124cos(x) + 48cos(x) - 4cos(x) - 68cos(x) +--R + +--R 10 8 6 4 +--R - 40cos(x) - 28cos(x) - 4cos(x) - 4cos(x) +--R * +--R +---------------------+ +--R | 4 2 +--R \|cos(x) + cos(x) + 1 +--R + +--R 28 27 26 25 24 +--R - 4cos(x) - 8cos(x) - 24cos(x) - 40cos(x) - 68cos(x) +--R + +--R 23 22 21 20 +--R - 96cos(x) - 136cos(x) - 176cos(x) - 180cos(x) +--R + +--R 19 18 17 16 +--R - 184cos(x) - 164cos(x) - 144cos(x) - 80cos(x) +--R + +--R 15 14 13 12 11 +--R - 16cos(x) + 8cos(x) + 32cos(x) + 40cos(x) + 48cos(x) +--R + +--R 10 9 8 +--R 28cos(x) + 8cos(x) + 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R - 8cos(x) - 16cos(x) - 40cos(x) - 64cos(x) - 112cos(x) +--R + +--R 25 24 23 22 +--R - 160cos(x) - 220cos(x) - 280cos(x) - 304cos(x) +--R + +--R 21 20 19 18 +--R - 328cos(x) - 328cos(x) - 328cos(x) - 289cos(x) +--R + +--R 17 16 15 14 +--R - 250cos(x) - 249cos(x) - 248cos(x) - 223cos(x) +--R + +--R 13 12 11 10 +--R - 198cos(x) - 174cos(x) - 150cos(x) - 100cos(x) +--R + +--R 9 8 7 6 5 +--R - 50cos(x) - 27cos(x) - 4cos(x) + 3cos(x) + 10cos(x) +--R + +--R 4 3 2 +--R 6cos(x) + 2cos(x) + cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 29 28 +--R - 4cos(x) - 8cos(x) - 16cos(x) - 24cos(x) - 48cos(x) +--R + +--R 27 26 25 24 23 +--R - 72cos(x) - 84cos(x) - 96cos(x) - 108cos(x) - 120cos(x) +--R + +--R 22 21 20 19 18 +--R - 84cos(x) - 48cos(x) - 29cos(x) - 10cos(x) + 36cos(x) +--R + +--R 17 16 15 14 13 +--R 82cos(x) + 76cos(x) + 70cos(x) + 78cos(x) + 86cos(x) +--R + +--R 12 11 10 9 8 +--R 53cos(x) + 20cos(x) + 11cos(x) + 2cos(x) - 13cos(x) +--R + +--R 7 6 5 4 3 2 +--R - 28cos(x) - 21cos(x) - 14cos(x) - 11cos(x) - 8cos(x) - 4cos(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 24 22 20 18 16 +--R 16cos(x) + 80cos(x) + 208cos(x) + 360cos(x) + 456cos(x) +--R + +--R 14 12 10 8 6 +--R 456cos(x) + 368cos(x) + 232cos(x) + 104cos(x) + 24cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 26 24 22 20 18 +--R 48cos(x) + 192cos(x) + 448cos(x) + 680cos(x) + 800cos(x) +--R + +--R 16 14 12 10 8 +--R 768cos(x) + 672cos(x) + 528cos(x) + 368cos(x) + 232cos(x) +--R + +--R 6 4 +--R 112cos(x) + 48cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 28 26 24 22 20 +--R 32cos(x) + 96cos(x) + 192cos(x) + 208cos(x) + 176cos(x) +--R + +--R 18 16 14 12 10 +--R 64cos(x) + 16cos(x) - 48cos(x) - 48cos(x) - 64cos(x) +--R + +--R 8 6 +--R - 32cos(x) - 16cos(x) +--R / +--R 26 25 24 23 22 +--R 12cos(x) + 24cos(x) + 60cos(x) + 96cos(x) + 144cos(x) +--R + +--R 21 20 19 18 +--R 192cos(x) + 216cos(x) + 240cos(x) + 228cos(x) +--R + +--R 17 16 15 14 +--R 216cos(x) + 192cos(x) + 168cos(x) + 144cos(x) +--R + +--R 13 12 11 10 9 +--R 120cos(x) + 96cos(x) + 72cos(x) + 48cos(x) + 24cos(x) +--R + +--R 8 +--R 12cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 25 24 +--R 24cos(x) + 48cos(x) + 96cos(x) + 144cos(x) + 192cos(x) +--R + +--R 23 22 21 20 +--R 240cos(x) + 228cos(x) + 216cos(x) + 240cos(x) +--R + +--R 19 18 17 16 +--R 264cos(x) + 288cos(x) + 312cos(x) + 363cos(x) +--R + +--R 15 14 13 12 +--R 414cos(x) + 336cos(x) + 258cos(x) + 201cos(x) +--R + +--R 11 10 9 8 7 +--R 144cos(x) + 81cos(x) + 18cos(x) + 27cos(x) + 36cos(x) +--R + +--R 6 5 4 3 2 +--R 24cos(x) + 12cos(x) + 9cos(x) + 6cos(x) + 3cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 30 29 28 27 26 +--R 12cos(x) + 24cos(x) + 36cos(x) + 48cos(x) + 60cos(x) +--R + +--R 25 24 23 22 21 +--R 72cos(x) + 48cos(x) + 24cos(x) + 72cos(x) + 120cos(x) +--R + +--R 20 19 18 17 16 +--R 96cos(x) + 72cos(x) + 87cos(x) + 102cos(x) - 27cos(x) +--R + +--R 15 14 13 12 11 +--R - 156cos(x) - 129cos(x) - 102cos(x) - 117cos(x) - 132cos(x) +--R + +--R 10 9 8 7 6 +--R - 45cos(x) + 42cos(x) + 27cos(x) + 12cos(x) + 24cos(x) +--R + +--R 5 4 2 +--R 36cos(x) + 18cos(x) + 3cos(x) + 6cos(x) + 3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +---------------------+ +--R | 16cos(x) + 16cos(x) + 16 | 4 2 +--R |------------------------------------------- \|cos(x) + cos(x) + 1 +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 24 23 22 21 20 +--R 24cos(x) + 48cos(x) + 120cos(x) + 192cos(x) + 288cos(x) +--R + +--R 19 18 17 16 +--R 384cos(x) + 432cos(x) + 480cos(x) + 432cos(x) +--R + +--R 15 14 13 12 +--R 384cos(x) + 288cos(x) + 192cos(x) + 120cos(x) +--R + +--R 11 10 +--R 48cos(x) + 24cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 26 25 24 23 +--R 72cos(x) + 144cos(x) + 288cos(x) + 432cos(x) +--R + +--R 22 21 20 19 +--R 600cos(x) + 768cos(x) + 768cos(x) + 768cos(x) +--R + +--R 18 17 16 15 +--R 672cos(x) + 576cos(x) + 432cos(x) + 288cos(x) +--R + +--R 14 13 12 11 +--R 270cos(x) + 252cos(x) + 216cos(x) + 180cos(x) +--R + +--R 10 9 8 7 6 +--R 162cos(x) + 144cos(x) + 90cos(x) + 36cos(x) + 24cos(x) +--R + +--R 5 4 +--R 12cos(x) + 6cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 28 27 26 25 24 +--R 48cos(x) + 96cos(x) + 144cos(x) + 192cos(x) + 240cos(x) +--R + +--R 23 22 21 20 18 +--R 288cos(x) + 192cos(x) + 96cos(x) + 48cos(x) - 96cos(x) +--R + +--R 17 16 15 14 13 +--R - 192cos(x) - 132cos(x) - 72cos(x) - 108cos(x) - 144cos(x) +--R + +--R 12 11 10 9 7 +--R - 84cos(x) - 24cos(x) - 36cos(x) - 48cos(x) + 48cos(x) +--R + +--R 6 5 4 3 2 +--R 36cos(x) + 24cos(x) + 24cos(x) + 24cos(x) + 12cos(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) + 16cos(x) + 16 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Expression(Integer) +--E 25 + + +\end{chunk} +\subsection{Problem 6} +\begin{chunk}{*} + +--S 26 of 250 +t0006:= tan(x)*sqrt(1+tan(x)^4) +--R +--R +--R +-----------+ +--R | 4 +--R (23) tan(x)\|tan(x) + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 250 +r0006:= -1/2*asinh(tan(x)^2)-atanh((1-tan(x)^2)/(sqrt(2)*sqrt(1+tan(x)^4)))/_ + sqrt(2)+1/2*sqrt(1+tan(x)^4) +--R +--R +--R 2 +-----------+ +--R tan(x) - 1 +-+ | 4 +-+ 2 +--R 2atanh(------------------) + \|2 \|tan(x) + 1 - \|2 asinh(tan(x) ) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R (24) -------------------------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 250 +a0006:= integrate(t0006,x) +--R +--R +--R (25) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R +-+ 4 +-+ 2 |2cos(x) - 2cos(x) + 1 +--R (4\|2 cos(x) - 2\|2 cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 4 2 +--R 8cos(x) - 8cos(x) + 3 +--R + +--R log +--R +-----------------------+ +--R | 4 2 +--R 4 2 |2cos(x) - 2cos(x) + 1 4 +--R (2cos(x) - 2cos(x) ) |----------------------- + 3cos(x) +--R | 4 +--R \| cos(x) +--R + +--R 2 +--R - 4cos(x) + 2 +--R / +--R 4 +--R cos(x) +--R + +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R 2 |----------------------- +--R | 4 +--R \| cos(x) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 250 +m0006:= a0006-r0006 +--R +--R +--R (26) +--R - +--R 2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R +-+ 4 +-+ 2 |2cos(x) - 2cos(x) + 1 +--R (4\|2 cos(x) - 2\|2 cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 4 2 +--R 8cos(x) - 8cos(x) + 3 +--R + +--R +-+ +--R \|2 +--R * +--R log +--R +-----------------------+ +--R | 4 2 +--R 4 2 |2cos(x) - 2cos(x) + 1 4 +--R (2cos(x) - 2cos(x) ) |----------------------- + 3cos(x) +--R | 4 +--R \| cos(x) +--R + +--R 2 +--R - 4cos(x) + 2 +--R / +--R 4 +--R cos(x) +--R + +--R 2 +-----------+ +--R tan(x) - 1 +-+ | 4 +--R - 4atanh(------------------) - 2\|2 \|tan(x) + 1 +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R + +--R +-----------------------+ +--R | 4 2 +--R +-+ |2cos(x) - 2cos(x) + 1 +-+ 2 +--R 2\|2 |----------------------- + 2\|2 asinh(tan(x) ) +--R | 4 +--R \| cos(x) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 250 +d0006:= D(m0006,x) +--R +--R +--R (27) +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (8\|2 cos(x) - 12\|2 cos(x) + 8\|2 cos(x) - 2\|2 cos(x) )sin(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R (16cos(x) - 32cos(x) + 30cos(x) - 14cos(x) + 3)sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R + +--R 9 7 5 5 +--R (- 8cos(x) + 8cos(x) - 3cos(x) )tan(x) +--R + +--R 9 7 5 +--R (- 8cos(x) + 8cos(x) - 3cos(x) )tan(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 5 +--R (- 8\|2 cos(x) + 12\|2 cos(x) - 8\|2 cos(x) + 2\|2 cos(x) )tan(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 8\|2 cos(x) + 12\|2 cos(x) - 8\|2 cos(x) + 2\|2 cos(x) )tan(x) +--R / +--R +-----------------------+ +--R | 4 2 +--R 9 7 5 |2cos(x) - 2cos(x) + 1 +--R (8cos(x) - 8cos(x) + 3cos(x) ) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R 8\|2 cos(x) - 12\|2 cos(x) + 8\|2 cos(x) - 2\|2 cos(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 30 + + +\end{chunk} +\subsection{Problem 7} +\begin{chunk}{*} + +--S 31 of 250 +t0007:= tan(x)/sqrt(1+sec(x)^3) +--R +--R +--R tan(x) +--R (28) -------------- +--R +-----------+ +--R | 3 +--R \|sec(x) + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 250 +r0007:= -2/3*atanh(sqrt(1+sec(x)^3)) +--R +--R +--R +-----------+ +--R | 3 +--R 2atanh(\|sec(x) + 1 ) +--R (29) - ---------------------- +--R 3 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 250 +a0007:= integrate(t0007,x) +--R +--R +--R (30) +--R - +--R log +--R 6 5 3 2 +--R (- 4cos(x) - 4cos(x) - 2cos(x) - 2cos(x) ) +--R * +--R +----------------------+ +--R | 2 +--R |4cos(x) - 4cos(x) + 4 +--R |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R + +--R 6 3 +--R 8cos(x) + 8cos(x) + 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 250 +m0007:= a0007-r0007 +--R +--R +--R (31) +--R - +--R log +--R 6 5 3 2 +--R (- 4cos(x) - 4cos(x) - 2cos(x) - 2cos(x) ) +--R * +--R +----------------------+ +--R | 2 +--R |4cos(x) - 4cos(x) + 4 +--R |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R + +--R 6 3 +--R 8cos(x) + 8cos(x) + 1 +--R + +--R +-----------+ +--R | 3 +--R 4atanh(\|sec(x) + 1 ) +--R / +--R 6 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 250 +d0007:= D(m0007,x) +--R +--R +--R (32) +--R +----------------------+ +--R +-----------+ | 2 +--R | 3 |4cos(x) - 4cos(x) + 4 +--R - 2sin(x)\|sec(x) + 1 + (- cos(x) - 1)tan(x) |---------------------- +--R | 2 +--R \| cos(x) + cos(x) +--R ----------------------------------------------------------------------- +--R +----------------------+ +--R | 2 +-----------+ +--R |4cos(x) - 4cos(x) + 4 | 3 +--R (cos(x) + 1) |---------------------- \|sec(x) + 1 +--R | 2 +--R \| cos(x) + cos(x) +--R Type: Expression(Integer) +--E 35 + + +\end{chunk} +\subsection{Problem 8} +\begin{chunk}{*} + +--S 36 of 250 +t0008:= sqrt(tan(x)^2+2*tan(x)+2) +--R +--R +--R +---------------------+ +--R | 2 +--R (33) \|tan(x) + 2tan(x) + 2 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 250 +r0008:= asinh(1+tan(x))+sqrt(1/2*(1+sqrt(5)))*_ + atan(((-sqrt(-1+sqrt(5)))+sqrt(1+sqrt(5))*tan(x))/_ + (sqrt(2)*sqrt(2+tan(x)*(2+tan(x)))))-_ + sqrt(1/2*(-1+sqrt(5)))*_ + atanh((sqrt(1+sqrt(5))+sqrt(-1+sqrt(5))*tan(x))/_ + (sqrt(2)*sqrt(2+tan(x)*(2+tan(x))))) +--R +--R +--R (34) +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ \|\|5 + 1 + tan(x)\|\|5 - 1 +--R - \|\|5 - 1 atanh(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ tan(x)\|\|5 + 1 - \|\|5 - 1 +-+ +--R \|\|5 + 1 atan(-------------------------------) + \|2 asinh(tan(x) + 1) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 250 +a0008:= integrate(t0008,x) +--R +--R +--R (35) +--R [ +--R 4+-+ atan(2) +--R \|5 cos(-------) +--R 2 +--R * +--R log +--R 4+-+3 9 4+-+3 7 +--R - 38400\|5 cos(x) + 451328\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 169072\|5 cos(x) - 134856\|5 cos(x) +--R + +--R 4+-+3 +--R - 3760\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (- 39040\|5 + 640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (184768\|5 + 266560\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (6952\|5 - 204600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 61356\|5 - 157740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 3074\|5 - 5820\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 211200\|5 cos(x) + 203904\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R 322352\|5 cos(x) - 233648\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 35408\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 94720\|5 - 116480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (19584\|5 + 184320\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (182464\|5 + 208720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 63684\|5 - 247100\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 21759\|5 - 46975\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 9 4+-+3 7 +--R 211200\|5 cos(x) + 11904\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 568096\|5 cos(x) - 103208\|5 cos(x) +--R + +--R 4+-+3 +--R - 80\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (83200\|5 + 505600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (580352\|5 + 604160\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 500976\|5 - 1653200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 239244\|5 - 497740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 7102\|5 - 10480\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 38400\|5 cos(x) + 572672\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R - 276464\|5 cos(x) - 331064\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 13344\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 342400\|5 - 419200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (627136\|5 + 1772480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (244464\|5 - 266640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 459800\|5 - 1168280\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 62635\|5 - 110195\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 9 +--R (79104\|5 + 1228800)cos(x) +--R + +--R 4+-+2 7 +--R (- 1115328\|5 - 1857600)cos(x) +--R + +--R 4+-+2 5 +--R (335640\|5 - 1628200)cos(x) +--R + +--R 4+-+2 3 +--R (639072\|5 + 947080)cos(x) +--R + +--R 4+-+2 +--R (64992\|5 + 147580)cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 10 +--R (483072\|5 + 358400)cos(x) +--R + +--R 4+-+2 8 +--R (- 411840\|5 + 2104000)cos(x) +--R + +--R 4+-+2 6 +--R (- 1076712\|5 - 3359000)cos(x) +--R + +--R 4+-+2 4 +--R (679732\|5 + 91940)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (271292\|5 + 534070)cos(x) + 6656\|5 + 16540 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 246528\|5 - 358400)cos(x) +--R + +--R 4+-+2 7 +--R (- 1667904\|5 - 3089600)cos(x) +--R + +--R 4+-+2 5 +--R (1801320\|5 + 3027400)cos(x) +--R + +--R 4+-+2 3 +--R (1139496\|5 + 2216640)cos(x) +--R + +--R 4+-+2 +--R (61656\|5 + 133640)cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 55936\|5 + 292480)cos(x) +--R + +--R 4+-+2 7 +--R (- 549568\|5 - 1127360)cos(x) +--R + +--R 4+-+2 5 +--R (424480\|5 + 168880)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (409732\|5 + 790380)cos(x) + (41322\|5 + 94610)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 10 +--R (708096\|5 + 1228800)cos(x) +--R + +--R 4+-+2 8 +--R (- 1675520\|5 - 2707200)cos(x) +--R + +--R 4+-+2 6 +--R (- 1078016\|5 - 2334000)cos(x) +--R + +--R 4+-+2 4 +--R (1846276\|5 + 3353220)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (360756\|5 + 738960)cos(x) + 4208\|5 + 9720 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 10 4+-+2 8 +--R (260352\|5 + 368640)cos(x) + (- 468800\|5 - 4800)cos(x) +--R + +--R 4+-+2 6 +--R (- 428592\|5 - 1392000)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (503512\|5 + 699440)cos(x) + (169147\|5 + 364435)cos(x) +--R + +--R 4+-+2 +--R 4451\|5 + 10610 +--R / +--R 4+-+3 4+-+ 7 +--R (25984\|5 + 55680\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 63008\|5 - 136480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 32640\|5 - 73760\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 952\|5 - 2240\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 8 +--R (30912\|5 + 66240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (20000\|5 + 46240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 60112\|5 - 132640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 8600\|5 - 19840\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 7 +--R (44352\|5 + 95040\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 101984\|5 - 220640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 54000\|5 - 122080\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 1496\|5 - 3520\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 8 +--R (47936\|5 + 102720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (37120\|5 + 85120\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 99536\|5 - 219520\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 14000\|5 - 32320\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 7 4+-+2 5 +--R - 143488\|5 cos(x) + 156480\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 246752\|5 cos(x) + 24736\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R - 45184\|5 cos(x) - 256768\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 258464\|5 cos(x) + 105024\|5 cos(x) + 2464\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 7 4+-+2 5 +--R - 73984\|5 cos(x) + 71040\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 129536\|5 cos(x) + 12448\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 7 +--R (- 124288\|5 - 180480)cos(x) +--R + +--R 4+-+2 5 +--R (136000\|5 + 192000)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (213952\|5 + 311520)cos(x) + (21456\|5 + 30960)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 8 4+-+2 6 +--R - 14912\|5 cos(x) - 141824\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 131952\|5 cos(x) + 54832\|5 cos(x) + 1152\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 8 +--R (- 39584\|5 - 52640)cos(x) +--R + +--R 4+-+2 6 +--R (- 222208\|5 - 327680)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (224184\|5 + 324440)cos(x) + (91064\|5 + 132440)cos(x) +--R + +--R 4+-+2 +--R 2144\|5 + 3045 +--R + +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 sin(-------) +--R 2 +--R * +--R atan +--R 4+-+3 4+-+ 5 +--R (72\|5 - 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 62\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 36\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 + 76\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 107\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (- 96\|5 - 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 40\|5 + 144\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (8\|5 + 27\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 146\|5 - 362\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (17\|5 + 144\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 +--R - 240\|5 cos(x) + 540\|5 cos(x) +--R + +--R 4+-+2 +--R 202\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R - 320\|5 cos(x) - 120\|5 cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R 476\|5 cos(x) + 30\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (320\|5 cos(x) + 280\|5 cos(x) - 184\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (56\|5 + 440)cos(x) + (78\|5 - 170)cos(x) +--R + +--R 4+-+2 +--R (79\|5 - 110)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 240\|5 cos(x) + 660\|5 cos(x) - 122\|5 cos(x) +--R + +--R 4+-+2 +--R - 50\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 192\|5 - 80)cos(x) + (100\|5 + 480)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (69\|5 - 290)cos(x) + 26\|5 - 10 +--R / +--R 4+-+3 4+-+ 5 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (40\|5 - 204\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 8\|5 - 59\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (- 72\|5 + 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (146\|5 + 34\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 17\|5 - 192\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 822\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 92\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 - 368\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 451\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 +--R - 320\|5 cos(x) - 280\|5 cos(x) +--R + +--R 4+-+2 +--R 184\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R 240\|5 cos(x) - 660\|5 cos(x) + 122\|5 cos(x) +--R + +--R 4+-+2 +--R 50\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R - 240\|5 cos(x) + 540\|5 cos(x) +--R + +--R 4+-+2 +--R 202\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (- 192\|5 - 80)cos(x) + (228\|5 + 920)cos(x) +--R + +--R 4+-+2 +--R (151\|5 + 320)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 56\|5 - 440)cos(x) + (- 218\|5 + 30)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (283\|5 + 760)cos(x) + 32\|5 + 50 +--R / +--R 4 +--R , +--R +--R - +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+3 4+-+ 3 4+-+3 +--R ((6\|5 - 10\|5 )cos(x) - 2\|5 cos(x))sin(x) +--R + +--R 4+-+3 4+-+ 4 4+-+ 2 +--R (8\|5 + 20\|5 )cos(x) - 10\|5 cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R ((8\|5 - 20\|5 )cos(x) + (4\|5 + 10\|5 )cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 4 +--R (- 6\|5 - 10\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (10\|5 + 10\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 3 4+-+2 atan(2) +--R (- 12\|5 cos(x) + 12\|5 cos(x))cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 atan(2) +--R (- 16\|5 cos(x) + 4\|5 cos(x) + 4\|5 )cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 atan(2) 2 +--R (24\|5 cos(x) - 24\|5 cos(x))cos(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 +--R - 12\|5 cos(x) + (2\|5 - 30)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 atan(2) 2 +--R (32\|5 cos(x) - 8\|5 cos(x) - 8\|5 )cos(-------) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R - 16\|5 cos(x) + (- \|5 - 15)cos(x) - \|5 - 10 +--R / +--R 4+-+3 4+-+ 3 4+-+3 +--R ((24\|5 + 40\|5 )cos(x) + 8\|5 cos(x))sin(x) +--R + +--R 4+-+3 4+-+ 4 +--R (32\|5 - 80\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 12\|5 + 100\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R ((32\|5 + 80\|5 )cos(x) + (4\|5 + 20\|5 )cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 4 +--R (- 24\|5 + 40\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (44\|5 + 20\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (- 64\|5 cos(x) + (- 16\|5 - 80)cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 48\|5 cos(x) + (- 72\|5 - 40)cos(x) + 8\|5 +--R + +--R - 40 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 atan(2) 2 +--R (- 32\|5 cos(x) + (- 8\|5 - 40)cos(x))cos(-------) +--R 2 +--R + +--R 4+-+2 3 4+-+2 +--R (16\|5 - 240)cos(x) + (- 56\|5 - 40)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R (24\|5 cos(x) + (- 36\|5 - 20)cos(x) + 4\|5 - 20) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 4 4+-+2 2 +--R (- 12\|5 + 180)cos(x) + (- 12\|5 - 260)cos(x) +--R + +--R 4+-+2 +--R - 17\|5 + 5 +--R + +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R 2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R 4+-+ atan(2) +--R \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R 4+-+ atan(2) +--R 2\|5 cos(-------) +--R 2 +--R * +--R atan +--R 4+-+2 2 atan(2) +--R \|5 cos(x) sin(-------) +--R 2 +--R + +--R 4+-+2 atan(2) +--R - \|5 cos(x)cos(-------)sin(x) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 4+-+ +--R \|5 cos(x)sin(x) - 2\|5 cos(x) + \|5 +--R / +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) )sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) - cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 4+-+ +--R 2\|5 cos(x)sin(x) + \|5 cos(x) + \|5 +--R / +--R 4 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 38 + +--S 39 of 250 +m0008:= a0008.1-r0008 +--R +--R +--R (36) +--R +-+4+-+ atan(2) +--R \|2 \|5 cos(-------) +--R 2 +--R * +--R log +--R 4+-+3 9 4+-+3 7 +--R - 38400\|5 cos(x) + 451328\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 169072\|5 cos(x) - 134856\|5 cos(x) +--R + +--R 4+-+3 +--R - 3760\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (- 39040\|5 + 640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (184768\|5 + 266560\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (6952\|5 - 204600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 61356\|5 - 157740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 3074\|5 - 5820\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 211200\|5 cos(x) + 203904\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R 322352\|5 cos(x) - 233648\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 35408\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 94720\|5 - 116480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (19584\|5 + 184320\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (182464\|5 + 208720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 63684\|5 - 247100\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 21759\|5 - 46975\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 9 4+-+3 7 +--R 211200\|5 cos(x) + 11904\|5 cos(x) +--R + +--R 4+-+3 5 4+-+3 3 +--R - 568096\|5 cos(x) - 103208\|5 cos(x) +--R + +--R 4+-+3 +--R - 80\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 9 +--R (83200\|5 + 505600\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 7 +--R (580352\|5 + 604160\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 500976\|5 - 1653200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 239244\|5 - 497740\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 7102\|5 - 10480\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+3 10 4+-+3 8 +--R - 38400\|5 cos(x) + 572672\|5 cos(x) +--R + +--R 4+-+3 6 4+-+3 4 +--R - 276464\|5 cos(x) - 331064\|5 cos(x) +--R + +--R 4+-+3 2 +--R - 13344\|5 cos(x) +--R * +--R atan(2) 3 +--R cos(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 10 +--R (- 342400\|5 - 419200\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 8 +--R (627136\|5 + 1772480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (244464\|5 - 266640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 459800\|5 - 1168280\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 62635\|5 - 110195\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 9 +--R (79104\|5 + 1228800)cos(x) +--R + +--R 4+-+2 7 +--R (- 1115328\|5 - 1857600)cos(x) +--R + +--R 4+-+2 5 +--R (335640\|5 - 1628200)cos(x) +--R + +--R 4+-+2 3 +--R (639072\|5 + 947080)cos(x) +--R + +--R 4+-+2 +--R (64992\|5 + 147580)cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 10 +--R (483072\|5 + 358400)cos(x) +--R + +--R 4+-+2 8 +--R (- 411840\|5 + 2104000)cos(x) +--R + +--R 4+-+2 6 +--R (- 1076712\|5 - 3359000)cos(x) +--R + +--R 4+-+2 4 +--R (679732\|5 + 91940)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (271292\|5 + 534070)cos(x) + 6656\|5 + 16540 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 246528\|5 - 358400)cos(x) +--R + +--R 4+-+2 7 +--R (- 1667904\|5 - 3089600)cos(x) +--R + +--R 4+-+2 5 +--R (1801320\|5 + 3027400)cos(x) +--R + +--R 4+-+2 3 +--R (1139496\|5 + 2216640)cos(x) +--R + +--R 4+-+2 +--R (61656\|5 + 133640)cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 9 +--R (- 55936\|5 + 292480)cos(x) +--R + +--R 4+-+2 7 +--R (- 549568\|5 - 1127360)cos(x) +--R + +--R 4+-+2 5 +--R (424480\|5 + 168880)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (409732\|5 + 790380)cos(x) + (41322\|5 + 94610)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 10 +--R (708096\|5 + 1228800)cos(x) +--R + +--R 4+-+2 8 +--R (- 1675520\|5 - 2707200)cos(x) +--R + +--R 4+-+2 6 +--R (- 1078016\|5 - 2334000)cos(x) +--R + +--R 4+-+2 4 +--R (1846276\|5 + 3353220)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (360756\|5 + 738960)cos(x) + 4208\|5 + 9720 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 10 4+-+2 8 +--R (260352\|5 + 368640)cos(x) + (- 468800\|5 - 4800)cos(x) +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 428592\|5 - 1392000)cos(x) + (503512\|5 + 699440)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (169147\|5 + 364435)cos(x) + 4451\|5 + 10610 +--R / +--R 4+-+3 4+-+ 7 +--R (25984\|5 + 55680\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 63008\|5 - 136480\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 32640\|5 - 73760\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 952\|5 - 2240\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 8 +--R (30912\|5 + 66240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (20000\|5 + 46240\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 60112\|5 - 132640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 8600\|5 - 19840\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 7 +--R (44352\|5 + 95040\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 5 +--R (- 101984\|5 - 220640\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 54000\|5 - 122080\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 1496\|5 - 3520\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 8 +--R (47936\|5 + 102720\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 6 +--R (37120\|5 + 85120\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 99536\|5 - 219520\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 14000\|5 - 32320\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 7 4+-+2 5 +--R - 143488\|5 cos(x) + 156480\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 246752\|5 cos(x) + 24736\|5 cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R - 45184\|5 cos(x) - 256768\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 258464\|5 cos(x) + 105024\|5 cos(x) + 2464\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 7 4+-+2 5 +--R - 73984\|5 cos(x) + 71040\|5 cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R 129536\|5 cos(x) + 12448\|5 cos(x) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 7 +--R (- 124288\|5 - 180480)cos(x) +--R + +--R 4+-+2 5 +--R (136000\|5 + 192000)cos(x) +--R + +--R 4+-+2 3 4+-+2 +--R (213952\|5 + 311520)cos(x) + (21456\|5 + 30960)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 8 4+-+2 6 +--R - 14912\|5 cos(x) - 141824\|5 cos(x) +--R + +--R 4+-+2 4 4+-+2 2 4+-+2 +--R 131952\|5 cos(x) + 54832\|5 cos(x) + 1152\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 8 4+-+2 6 +--R (- 39584\|5 - 52640)cos(x) + (- 222208\|5 - 327680)cos(x) +--R + +--R 4+-+2 4 4+-+2 2 +--R (224184\|5 + 324440)cos(x) + (91064\|5 + 132440)cos(x) +--R + +--R 4+-+2 +--R 2144\|5 + 3045 +--R + +--R +-+ +--R 2\|2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) + 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (- 4\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (- 2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R - +--R +-+ +--R 2\|2 +--R * +--R log +--R 4+-+ 2 atan(2) 4+-+2 +--R - 4\|5 cos(x) sin(-------) - 2\|5 cos(x)sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) +--R - 2\|5 cos(x) cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+ 4+-+ 2 atan(2) +--R (4\|5 cos(x)sin(x) + 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+2 +--R (2\|5 cos(x)cos(-------) + 2\|5 cos(x))sin(x) +--R 2 +--R + +--R 4+-+ 2 atan(2) 4+-+2 2 4+-+2 +--R - 4\|5 cos(x) cos(-------) + (\|5 + 5)cos(x) + 2\|5 +--R 2 +--R + +--R +-+4+-+ atan(2) +--R \|2 \|5 sin(-------) +--R 2 +--R * +--R log +--R 4+-+ 4+-+ 2 atan(2) +--R (- 2\|5 cos(x)sin(x) - 2\|5 cos(x) )sin(-------) +--R 2 +--R + +--R 4+-+ atan(2) 4+-+ 2 atan(2) +--R - 2\|5 cos(x)cos(-------)sin(x) - 4\|5 cos(x) cos(-------) +--R 2 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 4+-+2 2 4+-+2 +--R (2\|5 + 6)cos(x)sin(x) + (\|5 + 3)cos(x) + \|5 + 2 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ \|\|5 + 1 + tan(x)\|\|5 - 1 +--R 4\|\|5 - 1 atanh(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R - +--R +-+4+-+ atan(2) +--R 2\|2 \|5 cos(-------) +--R 2 +--R * +--R atan +--R +---------------------------+ +--R | 2 +--R 4+-+ |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x)sin(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (- 2cos(x)sin(x) - cos(x) - 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - cos(x)cos(-------)sin(x) + (2cos(x) - 1)cos(-------) +--R 2 2 +--R / +--R +---------------------------+ +--R | 2 +--R 4+-+ 2 |2cos(x)sin(x) + cos(x) + 1 +--R \|5 cos(x) |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 atan(2) +--R (cos(x)sin(x) - 2cos(x) + 1)sin(-------) +--R 2 +--R + +--R atan(2) 2 atan(2) +--R - 2cos(x)cos(-------)sin(x) + (- cos(x) - 1)cos(-------) +--R 2 2 +--R + +--R - +--R +-+4+-+ atan(2) +--R 2\|2 \|5 sin(-------) +--R 2 +--R * +--R atan +--R 4+-+3 4+-+ 5 +--R (72\|5 - 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 62\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 36\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 + 76\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 107\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (- 96\|5 - 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 4+-+3 4+-+ +--R (- 40\|5 + 144\|5 )cos(x) + (8\|5 + 27\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 146\|5 - 362\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (17\|5 + 144\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 240\|5 cos(x) + 540\|5 cos(x) + 202\|5 cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (320\|5 cos(x) + 280\|5 cos(x) - 184\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (56\|5 + 440)cos(x) + (78\|5 - 170)cos(x) +--R + +--R 4+-+2 +--R (79\|5 - 110)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 240\|5 cos(x) + 660\|5 cos(x) - 122\|5 cos(x) +--R + +--R 4+-+2 +--R - 50\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 192\|5 - 80)cos(x) + (100\|5 + 480)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (69\|5 - 290)cos(x) + 26\|5 - 10 +--R / +--R 4+-+3 4+-+ 5 +--R (96\|5 + 16\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (40\|5 - 204\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 8\|5 - 59\|5 )cos(x) +--R * +--R sin(x) +--R + +--R 4+-+3 4+-+ 6 +--R (- 72\|5 + 88\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (146\|5 + 34\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 17\|5 - 192\|5 )cos(x) +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+3 4+-+ 5 +--R (72\|5 + 8\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 3 +--R (- 110\|5 - 822\|5 )cos(x) +--R + +--R 4+-+3 4+-+ +--R (- 15\|5 - 92\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+3 4+-+ 6 +--R (96\|5 + 544\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 4 +--R (- 8\|5 - 368\|5 )cos(x) +--R + +--R 4+-+3 4+-+ 2 +--R (- 68\|5 - 451\|5 )cos(x) +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R +---------------------------+ +--R | 2 +--R |2cos(x)sin(x) + cos(x) + 1 +--R |--------------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 320\|5 cos(x) - 280\|5 cos(x) + 184\|5 cos(x)) +--R * +--R atan(2) +--R cos(-------)sin(x) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R 240\|5 cos(x) - 660\|5 cos(x) + 122\|5 cos(x) +--R + +--R 4+-+2 +--R 50\|5 +--R * +--R atan(2) +--R cos(-------) +--R 2 +--R * +--R atan(2) +--R sin(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 4+-+2 +--R (- 240\|5 cos(x) + 540\|5 cos(x) + 202\|5 cos(x)) +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 5 4+-+2 3 +--R (- 192\|5 - 80)cos(x) + (228\|5 + 920)cos(x) +--R + +--R 4+-+2 +--R (151\|5 + 320)cos(x) +--R * +--R sin(x) +--R + +--R 4+-+2 6 4+-+2 4 4+-+2 2 +--R - 320\|5 cos(x) - 120\|5 cos(x) + 476\|5 cos(x) +--R + +--R 4+-+2 +--R 30\|5 +--R * +--R atan(2) 2 +--R cos(-------) +--R 2 +--R + +--R 4+-+2 6 4+-+2 4 +--R (- 56\|5 - 440)cos(x) + (- 218\|5 + 30)cos(x) +--R + +--R 4+-+2 2 4+-+2 +--R (283\|5 + 760)cos(x) + 32\|5 + 50 +--R + +--R +--------+ +--------+ +--R +--------+ | +-+ | +-+ +--R | +-+ tan(x)\|\|5 + 1 - \|\|5 - 1 +--R - 4\|\|5 + 1 atan(-------------------------------) +--R +---------------------+ +--R +-+ | 2 +--R \|2 \|tan(x) + 2tan(x) + 2 +--R + +--R +-+ +--R - 4\|2 asinh(tan(x) + 1) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 250 +--d0008:= D(m0008,x) +--E 40 + + +\end{chunk} +\subsection{Problem 9} +\begin{chunk}{*} + +--S 41 of 250 +t0009:= sin(x)*atan(sqrt(sec(x)-1)) +--R +--R +--R +----------+ +--R (37) sin(x)atan(\|sec(x) - 1 ) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 250 +r0009:= 1/2*atan(sqrt(-1+sec(x)))-atan(sqrt(-1+sec(x)))*cos(x)+_ + 1/2*cos(x)*sqrt(-1+sec(x)) +--R +--R +--R +----------+ +----------+ +--R (- 2cos(x) + 1)atan(\|sec(x) - 1 ) + cos(x)\|sec(x) - 1 +--R (38) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 250 +a0009:= integrate(t0009,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 250 +--m0009:= a0009-r0009 +--E 44 + +--S 45 of 250 +--d0009:= D(m0009,x) +--E 45 + + +\end{chunk} +\subsection{Problem 10} +\begin{chunk}{*} + +--S 46 of 250 +t0010:= x^3*%e^asin(x)/sqrt(1-x^2) +--R +--R +--R 3 asin(x) +--R x %e +--R (39) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 250 +r0010:= 1/10*%e^asin(x)*(3*x+x^3-3*sqrt(1-x^2)-3*x^2*sqrt(1-x^2)) +--R +--R +--R +--------+ +--R 2 | 2 3 asin(x) +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R (40) ------------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 250 +a0010:= integrate(t0010,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R +--------+ - ------------------- +--R 2 | 2 3 2 +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R (41) --------------------------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 250 +m0010:= a0010-r0010 +--R +--R +--R (42) +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R +--------+ - ------------------- +--R 2 | 2 3 2 +--R ((- 3x - 3)\|- x + 1 + x + 3x)%e +--R + +--R +--------+ +--R 2 | 2 3 asin(x) +--R ((3x + 3)\|- x + 1 - x - 3x)%e +--R / +--R 10 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 250 +d0010:= D(m0010,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R atan(-------------) +--R 2 +--R 2x - 1 +--R - ------------------- +--R 3 2 3 asin(x) +--R x %e - x %e +--R (43) --------------------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 50 + + +\end{chunk} +\subsection{Problem 11} +\begin{chunk}{*} + +--S 51 of 250 +t0011:= x*log(1+x^2)*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R 2 | 2 +--R x log(x + 1)log(\|x + 1 + x) +--R (44) ------------------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 250 +r0011:= 4*x-2*atan(x)-2*sqrt(1+x^2)*log(x+sqrt(1+x^2))+_ + log(1+x^2)*(-x+sqrt(1+x^2)*log(x+sqrt(1+x^2))) +--R +--R +--R (45) +--R +------+ +------+ +--R 2 | 2 | 2 2 +--R (log(x + 1) - 2)\|x + 1 log(\|x + 1 + x) - x log(x + 1) - 2atan(x) + 4x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 250 +a0011:= integrate(t0011,x) +--R +--R +--R (46) +--R +------+ +--R 2 | 2 2 2 2 +--R ((- x log(x + 1) + 2x)\|x + 1 + (x + 1)log(x + 1) - 2x - 2) +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R + +--R +------+ +--R 2 | 2 2 2 +--R (- x log(x + 1) - 2atan(x) + 4x)\|x + 1 + x log(x + 1) + 2x atan(x) +--R + +--R 2 +--R - 4x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 250 +m0011:= a0011-r0011 +--R +--R +--R (47) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 250 +d0011:= D(m0011,x) +--R +--R +--R (48) 0 +--R Type: Expression(Integer) +--E 55 + + +\end{chunk} +\subsection{Problem 12} +\begin{chunk}{*} + +--S 56 of 250 +t0012:= atan(x+sqrt(1-x^2)) +--R +--R +--R +--------+ +--R | 2 +--R (49) atan(\|- x + 1 + x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 250 +r0012:= -asin(x)/2+1/4*sqrt(3)*atan((-1+sqrt(3)*x)/sqrt(1-x^2))+_ + 1/4*sqrt(3)*atan((1+sqrt(3)*x)/sqrt(1-x^2))-_ + 1/4*sqrt(3)*atan((-1+2*x^2)/sqrt(3))+x*atan(x+sqrt(1-x^2))-_ + 1/4*atanh(x*sqrt(1-x^2))-1/8*log(1-x^2+x^4) +--R +--R +--R (50) +--R +--------+ +--------+ +--R | 2 | 2 +--R - 2atanh(x\|- x + 1 ) + 8x atan(\|- x + 1 + x) +--R + +--R +-+ +-+ +--R +-+ x\|3 + 1 +-+ x\|3 - 1 4 2 +--R 2\|3 atan(-----------) + 2\|3 atan(-----------) - log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R - 2\|3 atan(-------------) - 4asin(x) +--R 3 +--R / +--R 8 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 250 +a0012:= integrate(t0012,x) +--R +--R +--R (51) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R - log(2x\|- x + 1 - x + x + 1) + log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--R | 2 2 +-+ +--R \|- x + 1 + x +-+ (2x - 1)\|3 +--R - 8x atan(---------------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x 4 2 +--R 2\|3 atan(-----------------) - 8atan(-----------) - 2log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R 2\|3 atan(-------------) +--R 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 250 +m0012:= a0012-r0012 +--R +--R +--R (52) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R - log(2x\|- x + 1 - x + x + 1) + log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R 4atanh(x\|- x + 1 ) - 16x atan(\|- x + 1 + x) +--R + +--R +--------+ +--R | 2 +-+ +--R \|- x + 1 + x +-+ x\|3 + 1 +--R - 8x atan(---------------) - 4\|3 atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 \|- x + 1 +--R + +--R +-+ 2 +-+ +--R +-+ x\|3 - 1 +-+ (2x - 1)\|3 +--R - 4\|3 atan(-----------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x +--R 2\|3 atan(-----------------) - 8atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ 2 +-+ +--R +-+ (2x - 1)\|3 +-+ (2x - 1)\|3 +--R 4\|3 atan(-------------) + 2\|3 atan(-------------) + 8asin(x) +--R 3 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 250 +d0012:= D(m0012,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 + x +--R - 2atan(\|- x + 1 + x) - atan(---------------) +--R +--------+ +--R | 2 +--R x\|- x + 1 +--R (53) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 60 + + +\end{chunk} +\subsection{Problem 13} +\begin{chunk}{*} + +--S 61 of 250 +t0013:= x*atan(x+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x atan(\|- x + 1 + x) +--R (54) ----------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 250 +r0013:= -asin(x)/2+1/4*sqrt(3)*atan((-1+sqrt(3)*x)/sqrt(1-x^2))+_ + 1/4*sqrt(3)*atan((1+sqrt(3)*x)/sqrt(1-x^2))-_ + 1/4*sqrt(3)*atan((-1+2*x^2)/sqrt(3))-sqrt(1-x^2)*atan(x+sqrt(1-x^2))+_ + 1/4*atanh(x*sqrt(1-x^2))+1/8*log(1-x^2+x^4) +--R +--R +--R (55) +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R 2atanh(x\|- x + 1 ) - 8\|- x + 1 atan(\|- x + 1 + x) +--R + +--R +-+ +-+ +--R +-+ x\|3 + 1 +-+ x\|3 - 1 4 2 +--R 2\|3 atan(-----------) + 2\|3 atan(-----------) + log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R - 2\|3 atan(-------------) - 4asin(x) +--R 3 +--R / +--R 8 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 250 +a0013:= integrate(t0013,x) +--R +--R +--R (56) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R log(2x\|- x + 1 - x + x + 1) - log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--R +--------+ | 2 2 +-+ +--R | 2 \|- x + 1 + x +-+ (2x - 1)\|3 +--R 8\|- x + 1 atan(---------------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x 4 2 +--R 2\|3 atan(-----------------) - 8atan(-----------) + 2log(x - x + 1) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 +--R 2\|3 atan(-------------) +--R 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 250 +m0013:= a0013-r0013 +--R +--R +--R (57) +--R +--------+ +--------+ +--R | 2 4 2 | 2 4 2 +--R log(2x\|- x + 1 - x + x + 1) - log(- 2x\|- x + 1 - x + x + 1) +--R + +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R - 4atanh(x\|- x + 1 ) + 16\|- x + 1 atan(\|- x + 1 + x) +--R + +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 \|- x + 1 + x +-+ x\|3 + 1 +--R 8\|- x + 1 atan(---------------) - 4\|3 atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R x\|- x + 1 \|- x + 1 +--R + +--R +-+ 2 +-+ +--R +-+ x\|3 - 1 +-+ (2x - 1)\|3 +--R - 4\|3 atan(-----------) + 2\|3 atan(-----------------) +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 4x\|- x + 1 - 1 +--R + +--R 2 +-+ +--R +-+ (2x - 1)\|3 x +--R 2\|3 atan(-----------------) - 8atan(-----------) +--R +--------+ +--------+ +--R | 2 | 2 +--R 4x\|- x + 1 + 1 \|- x + 1 +--R + +--R 2 +-+ 2 +-+ +--R +-+ (2x - 1)\|3 +-+ (2x - 1)\|3 +--R 4\|3 atan(-------------) + 2\|3 atan(-------------) + 8asin(x) +--R 3 4 2 +--R 2x - 2x - 1 +--R / +--R 16 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 250 +d0013:= D(m0013,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 + x +--R - 2x atan(\|- x + 1 + x) - x atan(---------------) +--R +--------+ +--R | 2 +--R x\|- x + 1 +--R (58) ---------------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 65 + + +\end{chunk} +\subsection{Problem 14} +\begin{chunk}{*} + +--S 66 of 250 +t0014:= asin(x)/(1+sqrt(1-x^2)) +--R +--R +--R asin(x) +--R (59) --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 250 +r0014:= ((-1+sqrt(1-x^2))*asin(x))/x+asin(x)^2/2-log(1+sqrt(1-x^2)) +--R +--R +--R (60) +--R +--------+ +--------+ +--R | 2 | 2 2 +--R - 2x log(\|- x + 1 + 1) + 2asin(x)\|- x + 1 + x asin(x) - 2asin(x) +--R ----------------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 250 +a0014:= integrate(t0014,x) +--R +--R +--R (61) +--R +--------+ +--------+ +--R | 2 | 2 +--R (- 4\|- x + 1 - 4)log(\|- x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 - 1) +--R + +--R +--------+ 2 +--------+ +--R +--------+ | 2 | 2 +--R | 2 2x\|- x + 1 2x\|- x + 1 +--R (\|- x + 1 + 1)atan(-------------) + 4x atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R | 2 +--R - 8log(x)\|- x + 1 - 8log(x) +--R / +--R +--------+ +--R | 2 +--R 8\|- x + 1 + 8 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 250 +m0014:= a0014-r0014 +--R +--R +--R (62) +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 + 1) +--R + +--R +--------+ +--------+ +--R | 2 | 2 +--R (4\|- x + 1 + 4)log(\|- x + 1 - 1) +--R + +--R +--------+ 2 +--------+ +--R +--------+ | 2 | 2 +--R | 2 2x\|- x + 1 2x\|- x + 1 +--R (\|- x + 1 + 1)atan(-------------) + 4x atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R 2 | 2 2 +--R (- 8log(x) - 4asin(x) )\|- x + 1 - 8log(x) - 4asin(x) + 8x asin(x) +--R / +--R +--------+ +--R | 2 +--R 8\|- x + 1 + 8 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 250 +d0014:= D(m0014,x) +--R +--R +--R (63) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2 2x\|- x + 1 | 2 +--R (\|- x + 1 - x + 1)atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R + +--R 2 +--R (- 2x + 2)asin(x) +--R / +--R +--------+ +--R 2 | 2 2 +--R (2x - 4)\|- x + 1 + 4x - 4 +--R Type: Expression(Integer) +--E 70 + + +\end{chunk} +\subsection{Problem 15} +\begin{chunk}{*} + +--S 71 of 250 +t0015:= log(x+sqrt(1+x^2))/(1-x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R (64) - ------------------- +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 250 +r0015:= -1/2*asin(x^2)+x*x*log(x+sqrt(1+x^2))/sqrt(1-x^2) +--R +--R +--R +------+ +--------+ +--R 2 | 2 2 | 2 +--R 2x log(\|x + 1 + x) - asin(x )\|- x + 1 +--R (65) ------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 250 +a0015:= integrate(t0015,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 73 + +--S 74 of 250 +--m0015:= a0015-r0015 +--E 74 + +--S 75 of 250 +--d0015:= D(m0015,x) +--E 75 + + +\end{chunk} +\subsection{Problem 16} +\begin{chunk}{*} + +--S 76 of 250 +t0016:= asin(x)/(1+x^2)^(3/2) +--R +--R +--R asin(x) +--R (66) ----------------- +--R +------+ +--R 2 | 2 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 250 +r0016:= x*asin(x)/sqrt(1+x^2)-asin(x^2)/2 +--R +--R +--R +------+ +--R 2 | 2 +--R - asin(x )\|x + 1 + 2x asin(x) +--R (67) -------------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 250 +a0016:= integrate(t0016,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 78 + +--S 79 of 250 +--m0016:= a0016-r0016 +--E 79 + +--S 80 of 250 +--d0016:= D(m0016,x) +--E 80 + + +\end{chunk} +\subsection{Problem 17} +\begin{chunk}{*} + +--S 81 of 250 +t0017:= log(x+sqrt(x^2-1))/(1+x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R log(\|x - 1 + x) +--R (68) ------------------ +--R +------+ +--R 2 | 2 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 250 +r0017:= -1/2*acosh(x^2)+x*log(x+sqrt(-1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +------+ +--R | 2 2 | 2 +--R 2x log(\|x - 1 + x) - acosh(x )\|x + 1 +--R (69) ------------------------------------------ +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 250 +a0017:= integrate(t0017,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 83 + +--S 84 of 250 +--m0017:= a0017-r0017 +--E 84 + +--S 85 of 250 +--d0017:= D(m0017,x) +--E 85 + + +\end{chunk} +\subsection{Problem 18} +\begin{chunk}{*} + +--S 86 of 250 +t0018:= log(x)/(x^2*sqrt(x^2-1)) +--R +--R +--R log(x) +--R (70) ----------- +--R +------+ +--R 2 | 2 +--R x \|x - 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 250 +r0018:= sqrt(-1+x^2)/x-atanh(x/sqrt(-1+x^2))+(sqrt(-1+x^2)*log(x))/x +--R +--R +--R +------+ +--R x | 2 +--R - x atanh(---------) + (log(x) + 1)\|x - 1 +--R +------+ +--R | 2 +--R \|x - 1 +--R (71) -------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 250 +a0018:= integrate(t0018,x) +--R +--R +--R (72) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (x\|x - 1 - x )log(\|x - 1 - x) - x log(x)\|x - 1 + (x - 1)log(x) - 1 +--R ---------------------------------------------------------------------------- +--R +------+ +--R | 2 2 +--R x\|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 250 +m0018:= a0018-r0018 +--R +--R +--R +------+ +--R | 2 x +--R (73) log(\|x - 1 - x) + atanh(---------) + 1 +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 250 +d0018:= D(m0018,x) +--R +--R +--R (74) 0 +--R Type: Expression(Integer) +--E 90 + + +\end{chunk} +\subsection{Problem 19} +\begin{chunk}{*} + +--S 91 of 250 +t0019:= sqrt(1+x^3)/x +--R +--R +--R +------+ +--R | 3 +--R \|x + 1 +--R (75) --------- +--R x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 250 +r0019:= 2*sqrt(1+x^3)/3 - 2/3*atanh(sqrt(1+x^3)) +--R +--R +--R +------+ +------+ +--R | 3 | 3 +--R - 2atanh(\|x + 1 ) + 2\|x + 1 +--R (76) -------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 250 +a0019:= integrate(t0019,x) +--R +--R +--R +------+ +------+ +------+ +--R | 3 | 3 | 3 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2\|x + 1 +--R (77) ------------------------------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 250 +m0019:= a0019-r0019 +--R +--R +--R +------+ +------+ +------+ +--R | 3 | 3 | 3 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (78) ------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 250 +d0019:= D(m0019,x) +--R +--R +--R (79) 0 +--R Type: Expression(Integer) +--E 95 + + +\end{chunk} +\subsection{Problem 20} +\begin{chunk}{*} + +--S 96 of 250 +t0020:= x*log(x+sqrt(x^2-1))/sqrt(x^2-1) +--R +--R +--R +------+ +--R | 2 +--R x log(\|x - 1 + x) +--R (80) -------------------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 250 +r0020:= -x+sqrt(-1+x^2)*log(x+sqrt(-1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (81) \|x - 1 log(\|x - 1 + x) - x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 250 +a0020:= integrate(t0020,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x - 1 + x - 1)log(\|x - 1 + x) - x\|x - 1 + x +--R (82) ----------------------------------------------------------- +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 250 +m0020:= a0020-r0020 +--R +--R +--R (83) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 250 +d0020:= D(m0020,x) +--R +--R +--R (84) 0 +--R Type: Expression(Integer) +--E 100 + + +\end{chunk} +\subsection{Problem 21} +\begin{chunk}{*} + +--S 101 of 250 +t0021:= x^3*asin(x)/sqrt(1-x^4) +--R +--R +--R 3 +--R x asin(x) +--R (85) ----------- +--R +--------+ +--R | 4 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 250 +r0021:= 1/4*x*sqrt(1+x^2)-1/2*sqrt(1-x^4)*asin(x)+asinh(x)/4 +--R +--R +--R +------+ +--------+ +--R | 2 | 4 +--R x\|x + 1 - 2asin(x)\|- x + 1 + asinh(x) +--R (86) ------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 250 +a0021:= integrate(t0021,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 103 + +--S 104 of 250 +--m0021:= a0021-r0021 +--E 104 + +--S 105 of 250 +--d0021:= D(m0021,x) +--E 105 + + +\end{chunk} +\subsection{Problem 22} +\begin{chunk}{*} + +--S 106 of 250 +t0022:= x^3*asec(x)/sqrt(x^4-1) +--R +--R +--R 3 +--R x asec(x) +--R (87) --------- +--R +------+ +--R | 4 +--R \|x - 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 250 +r0022:= -sqrt(-1+x^4)/(2*sqrt(1-1/x^2)*x)+1/2*sqrt(-1+x^4)*asec(x)+_ + 1/2*atanh((sqrt(1-1/x^2)*x)/sqrt(-1+x^4)) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R +------+ x |------ +------+ +--R | 2 | 2 | 2 +------+ +--R |x - 1 \| x |x - 1 | 4 +--R x |------ atanh(----------) + (x asec(x) |------ - 1)\|x - 1 +--R | 2 +------+ | 2 +--R \| x | 4 \| x +--R \|x - 1 +--R (88) --------------------------------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R 2x |------ +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 250 +a0022:= integrate(t0022,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 108 + +--S 109 of 250 +--m0022:= a0022-r0022 +--E 109 + +--S 110 of 250 +--d0022:= D(m0022,x) +--E 110 + + +\end{chunk} +\subsection{Problem 23} +\begin{chunk}{*} + +--S 111 of 250 +t0023:= x*atan(x)*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R | 2 +--R x atan(x)log(\|x + 1 + x) +--R (89) --------------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 250 +r0023:= -x*atan(x)+1/2*log(1+x^2)+_ + sqrt(1+x^2)*atan(x)*log(x+sqrt(1+x^2))-1/2*log(x+sqrt(1+x^2))^2 +--R +--R +--R (90) +--R +------+ 2 +------+ +------+ +--R | 2 | 2 | 2 2 +--R - log(\|x + 1 + x) + 2atan(x)\|x + 1 log(\|x + 1 + x) + log(x + 1) +--R + +--R - 2x atan(x) +--R / +--R 2 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 250 +a0023:= integrate(t0023,x) +--R +--R +--R (91) +--R +------+ +------+ 2 +--R | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R 2x | 2 2 2x | 2 +--R (x atan(------)\|x + 1 + (- x - 1)atan(------))log(\|x + 1 + x) +--R 2 2 +--R x - 1 x - 1 +--R + +--R +------+ +--R 2 2x | 2 2 2 2x +--R (log(x + 1) + x atan(------))\|x + 1 - x log(x + 1) - x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 250 +m0023:= a0023-r0023 +--R +--R +--R (92) +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) + x atan(------))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) +--R 2 +--R x - 1 +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 + x) +--R + +--R +------+ +--R 2x | 2 2 2 2x +--R (2x atan(x) + x atan(------))\|x + 1 - 2x atan(x) - x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 250 +d0023:= D(m0023,x) +--R +--R +--R +------+ +--R 2x | 2 +--R (- 2x atan(x) - x atan(------))log(\|x + 1 + x) +--R 2 +--R x - 1 +--R (93) ------------------------------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 115 + + +\end{chunk} +\subsection{Problem 24} +\begin{chunk}{*} + +--S 116 of 250 +t0024:= x*log(1+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x log(\|- x + 1 + 1) +--R (94) ---------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 250 +r0024:= sqrt(1-x^2)-log(1+sqrt(1-x^2))-sqrt(1-x^2)*log(1+sqrt(1-x^2)) +--R +--R +--R +--------+ +--------+ +--------+ +--R | 2 | 2 | 2 +--R (95) (- \|- x + 1 - 1)log(\|- x + 1 + 1) + \|- x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 250 +a0024:= integrate(t0024,x) +--R +--R +--R +--------+ +--R 2 | 2 2 +--R x log(\|- x + 1 + 1) - x +--R (96) --------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 250 +m0024:= a0024-r0024 +--R +--R +--R (97) 1 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 250 +d0024:= D(m0024,x) +--R +--R +--R (98) 0 +--R Type: Expression(Integer) +--E 120 + + +\end{chunk} +\subsection{Problem 25} +\begin{chunk}{*} + +--S 121 of 250 +t0025:= x*log(x+sqrt(1+x^2))/sqrt(1+x^2) +--R +--R +--R +------+ +--R | 2 +--R x log(\|x + 1 + x) +--R (99) -------------------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 250 +r0025:= -x+sqrt(1+x^2)*log(x+sqrt(1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (100) \|x + 1 log(\|x + 1 + x) - x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 250 +a0025:= integrate(t0025,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x + 1 + x + 1)log(\|x + 1 + x) - x\|x + 1 + x +--R (101) ----------------------------------------------------------- +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 250 +m0025:= a0025-r0025 +--R +--R +--R (102) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 250 +d0025:= D(m0025,x) +--R +--R +--R (103) 0 +--R Type: Expression(Integer) +--E 125 + + +\end{chunk} +\subsection{Problem 26} +\begin{chunk}{*} + +--S 126 of 250 +t0026:= x*log(x+sqrt(1-x^2))/sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x log(\|- x + 1 + x) +--R (104) ---------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 250 +r0026:= sqrt(1-x^2)+atanh(sqrt(2)*x)/sqrt(2)-_ + atanh(sqrt(2)*sqrt(1-x^2))/sqrt(2)-sqrt(1-x^2)*log(x+sqrt(1-x^2)) +--R +--R +--R (105) +--R +--------+ +--------+ +--------+ +--R +-+ | 2 | 2 +-+ | 2 +--R - \|2 \|- x + 1 log(\|- x + 1 + x) - atanh(\|2 \|- x + 1 ) +--R + +--R +--------+ +--R +-+ | 2 +-+ +--R \|2 \|- x + 1 + atanh(x\|2 ) +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 250 +a0026:= integrate(t0026,x) +--R +--R +--R (106) +--R +--------+ +--R 2 +-+ | 2 +--R 2x \|2 log(\|- x + 1 + x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (x - 1)\|- x + 1 - x - x + 1 +--R (\|2 \|- x + 1 - \|2 )log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x + 1)\|2 - 2x)\|- x + 1 + (- x - x - 1)\|2 + 2x + 2x +--R log(-------------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x + 1)\|- x + 1 + x - x - 1 +--R + +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 1)\|2 - 2x)\|- x + 1 + (x - x + 1)\|2 - 2x + 2x +--R log(-----------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R + +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (- x - 1)\|- x + 1 - x + x + 1 +--R (- \|2 \|- x + 1 + \|2 )log(---------------------------------) +--R 2 +--R x +--R + +--R 2 +-+ +--------+ +--R (2x + 1)\|2 + 4x +-+ 2 | 2 +--R (log(------------------) + \|2 log(2x - 1))\|- x + 1 +--R 2 +--R 2x - 1 +--R + +--R 2 +-+ +--R (2x + 1)\|2 + 4x +-+ 2 2 +-+ +--R - log(------------------) - \|2 log(2x - 1) - 2x \|2 +--R 2 +--R 2x - 1 +--R / +--R +--------+ +--R +-+ | 2 +-+ +--R 2\|2 \|- x + 1 - 2\|2 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 250 +m0026:= a0026-r0026 +--R +--R +--R (107) +--R +--------+ +--R +--------+ | 2 2 +--R +-+ | 2 +-+ (x - 1)\|- x + 1 - x - x + 1 +--R - 2\|2 log(\|- x + 1 + x) + \|2 log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x + 1)\|2 - 2x)\|- x + 1 + (- x - x - 1)\|2 + 2x + 2x +--R log(-------------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x + 1)\|- x + 1 + x - x - 1 +--R + +--R +--------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 1)\|2 - 2x)\|- x + 1 + (x - x + 1)\|2 - 2x + 2x +--R log(-----------------------------------------------------------) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R + +--R +--------+ +--R | 2 2 +--------+ +--R +-+ (- x - 1)\|- x + 1 - x + x + 1 +-+ | 2 +--R - \|2 log(---------------------------------) + 2atanh(\|2 \|- x + 1 ) +--R 2 +--R x +--R + +--R 2 +-+ +--R (2x + 1)\|2 + 4x +-+ 2 +-+ +-+ +--R log(------------------) + \|2 log(2x - 1) - 2atanh(x\|2 ) + 2\|2 +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 250 +d0026:= D(m0026,x) +--R +--R +--R (108) 0 +--R Type: Expression(Integer) +--E 130 + + +\end{chunk} +\subsection{Problem 27} +\begin{chunk}{*} + +--S 131 of 250 +t0027:= log(x)/(x^2*sqrt(1-x^2)) +--R +--R +--R log(x) +--R (109) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 250 +r0027:= -sqrt(1-x^2)/x-asin(x)-sqrt(1-x^2)*log(x)/x +--R +--R +--R +--------+ +--R | 2 +--R (- log(x) - 1)\|- x + 1 - x asin(x) +--R (110) ------------------------------------- +--R x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 250 +a0027:= integrate(t0027,x) +--R +--R +--R (111) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 \|- x + 1 - 1 | 2 +--R (2x\|- x + 1 - 2x)atan(---------------) + (log(x) + 1)\|- x + 1 +--R x +--R + +--R 2 2 +--R (x - 1)log(x) + x - 1 +--R / +--R +--------+ +--R | 2 +--R x\|- x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 250 +m0027:= a0027-r0027 +--R +--R +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R (112) 2atan(---------------) + asin(x) +--R x +--R Type: Expression(Integer) +--E 134 + +--S 135 of 250 +d0027:= D(m0027,x) +--R +--R +--R (113) 0 +--R Type: Expression(Integer) +--E 135 + + +\end{chunk} +\subsection{Problem 28} +\begin{chunk}{*} + +--S 136 of 250 +t0028:= x*atan(x)/sqrt(1+x^2) +--R +--R +--R x atan(x) +--R (114) --------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 250 +r0028:= -asinh(x)+sqrt(1+x^2)*atan(x) +--R +--R +--R +------+ +--R | 2 +--R (115) atan(x)\|x + 1 - asinh(x) +--R Type: Expression(Integer) +--E 137 + +--S 138 of 250 +a0028:= integrate(t0028,x) +--R +--R +--R (116) +--R +------+ +------+ +------+ +--R | 2 | 2 2x | 2 +--R (2\|x + 1 - 2x)log(\|x + 1 - x) + x atan(------)\|x + 1 +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 250 +m0028:= a0028-r0028 +--R +--R +--R (117) +--R +------+ +------+ +--R | 2 | 2 +--R (2\|x + 1 - 2x)log(\|x + 1 - x) +--R + +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) + x atan(------) + 2asinh(x))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (- x - 1)atan(------) - 2x asinh(x) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 +--R 2\|x + 1 - 2x +--R Type: Expression(Integer) +--E 139 + +--S 140 of 250 +d0028:= D(m0028,x) +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (118) ----------------------------- +--R +------+ +--R | 2 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 140 + + +\end{chunk} +\subsection{Problem 29} +\begin{chunk}{*} + +--S 141 of 250 +t0029:= atan(x)/(x^2*sqrt(1-x^2)) +--R +--R +--R atan(x) +--R (119) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 250 +r0029:= -sqrt(1-x^2)*atan(x)/x-atanh(sqrt(1-x^2))+_ + sqrt(2)*atanh(sqrt(1-x^2)/sqrt(2)) +--R +--R +--R (120) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 +-+ \|- x + 1 | 2 +--R - x atanh(\|- x + 1 ) + x\|2 atanh(-----------) - atan(x)\|- x + 1 +--R +-+ +--R \|2 +--R --------------------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 250 +a0029:= integrate(t0029,x) +--R +--R +--R (121) +--R +--------+ +--------+ +--R | 2 | 2 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +--------+ +--R +-+ | 2 2 +--------+ +--R +-+ - 2\|2 \|- x + 1 + x - 3 2x | 2 +--R x\|2 log(---------------------------) + atan(------)\|- x + 1 +--R 2 2 +--R x + 1 x - 1 +--R / +--R 2x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 250 +m0029:= a0029-r0029 +--R +--R +--R (122) +--R +--------+ +--------+ +--R | 2 | 2 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +--------+ +--R +-+ | 2 2 +--------+ +--R +-+ - 2\|2 \|- x + 1 + x - 3 | 2 +--R x\|2 log(---------------------------) + 2x atanh(\|- x + 1 ) +--R 2 +--R x + 1 +--R + +--R +--------+ +--R | 2 +--------+ +--R +-+ \|- x + 1 2x | 2 +--R - 2x\|2 atanh(-----------) + (2atan(x) + atan(------))\|- x + 1 +--R +-+ 2 +--R \|2 x - 1 +--R / +--R 2x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 250 +d0029:= D(m0029,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (123) ------------------------- +--R +--------+ +--R 2 | 2 +--R 2x \|- x + 1 +--R Type: Expression(Integer) +--E 145 + + +\end{chunk} +\subsection{Problem 30} +\begin{chunk}{*} + +--S 146 of 250 +t0030:= x*atan(x)/sqrt(1-x^2) +--R +--R +--R x atan(x) +--R (124) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 250 +r0030:= -asin(x)-sqrt(1-x^2)*atan(x)+sqrt(2)*atan(sqrt(2)*x/sqrt(1-x^2)) +--R +--R +--R +-+ +--------+ +--R +-+ x\|2 | 2 +--R (125) \|2 atan(-----------) - atan(x)\|- x + 1 - asin(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 250 +a0030:= integrate(t0030,x) +--R +--R +--R (126) +--R +--------+ +--R +-+ | 2 +--------+ +--R +-+ 2x\|2 \|- x + 1 x 2x | 2 +--R - \|2 atan(-----------------) - 2atan(-----------) + atan(------)\|- x + 1 +--R 2 +--------+ 2 +--R 3x - 1 | 2 x - 1 +--R \|- x + 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 250 +m0030:= a0030-r0030 +--R +--R +--R (127) +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ 2x\|2 \|- x + 1 +-+ x\|2 +--R - \|2 atan(-----------------) - 2\|2 atan(-----------) +--R 2 +--------+ +--R 3x - 1 | 2 +--R \|- x + 1 +--R + +--R +--------+ +--R x 2x | 2 +--R - 2atan(-----------) + (2atan(x) + atan(------))\|- x + 1 + 2asin(x) +--R +--------+ 2 +--R | 2 x - 1 +--R \|- x + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 250 +d0030:= D(m0030,x) +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (128) ----------------------------- +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 150 + + +\end{chunk} +\subsection{Problem 31} +\begin{chunk}{*} + +--S 151 of 250 +t0031:= atan(x)/(x^2*sqrt(1+x^2)) +--R +--R +--R atan(x) +--R (129) ----------- +--R +------+ +--R 2 | 2 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 250 +r0031:= sqrt(1+x^2)*atan(x)/x-atanh(sqrt(1+x^2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R - x atanh(\|x + 1 ) + atan(x)\|x + 1 +--R (130) --------------------------------------- +--R x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 250 +a0031:= integrate(t0031,x) +--R +--R +--R (131) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 2x | 2 +--R (2x\|x + 1 - 2x )log(\|x + 1 - x - 1) - x atan(------)\|x + 1 +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (x + 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 2 +--R 2x\|x + 1 - 2x +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 250 +m0031:= a0031-r0031 +--R +--R +--R (132) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x )log(\|x + 1 - x - 1) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x )atanh(\|x + 1 ) +--R + +--R +------+ +--R 2x | 2 2 +--R (2x atan(x) - x atan(------))\|x + 1 + (- 2x - 2)atan(x) +--R 2 +--R x - 1 +--R + +--R 2 2x +--R (x + 1)atan(------) +--R 2 +--R x - 1 +--R / +--R +------+ +--R | 2 2 +--R 2x\|x + 1 - 2x +--R Type: Expression(Integer) +--E 154 + +--S 155 of 250 +d0031:= D(m0031,x) +--R +--R +--R 2x +--R 2atan(x) - atan(------) - 4x +--R 2 +--R x - 1 +--R (133) ---------------------------- +--R +------+ +--R 2 | 2 +--R 2x \|x + 1 +--R Type: Expression(Integer) +--E 155 + + +\end{chunk} +\subsection{Problem 32} +\begin{chunk}{*} + +--S 156 of 250 +t0032:= asin(x)/((x^2)*sqrt(1-x^2)) +--R +--R +--R asin(x) +--R (134) ------------- +--R +--------+ +--R 2 | 2 +--R x \|- x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 250 +r0032:= -sqrt(1-x^2)*asin(x)/x+log(x) +--R +--R +--R +--------+ +--R | 2 +--R - asin(x)\|- x + 1 + x log(x) +--R (135) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 250 +a0032:= integrate(t0032,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R \|- x + 1 atan(-------------) + 2x log(x) +--R 2 +--R 2x - 1 +--R (136) ------------------------------------------ +--R 2x +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 250 +m0032:= a0032-r0032 +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2x\|- x + 1 | 2 +--R \|- x + 1 atan(-------------) + 2asin(x)\|- x + 1 +--R 2 +--R 2x - 1 +--R (137) ---------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 250 +d0032:= D(m0032,x) +--R +--R +--R +--------+ +--R | 2 +--R 2x\|- x + 1 +--R - atan(-------------) - 2asin(x) +--R 2 +--R 2x - 1 +--R (138) -------------------------------- +--R +--------+ +--R 2 | 2 +--R 2x \|- x + 1 +--R Type: Expression(Integer) +--E 160 + + +\end{chunk} +\subsection{Problem 33} +\begin{chunk}{*} + +--S 161 of 250 +t0033:= x*log(x)/sqrt(x^2-1) +--R +--R +--R x log(x) +--R (139) --------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 250 +r0033:= -sqrt(x^2-1)+atan(sqrt(x^2-1))+sqrt(x^2-1)*log(x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (140) atan(\|x - 1 ) + (log(x) - 1)\|x - 1 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 250 +a0033:= integrate(t0033,x) +--R +--R +--R (141) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (2\|x - 1 - 2x)atan(\|x - 1 - x) + (- x log(x) + x)\|x - 1 +--R + +--R 2 2 +--R (x - 1)log(x) - x + 1 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 250 +m0033:= a0033-r0033 +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (142) - atan(\|x - 1 ) + 2atan(\|x - 1 - x) +--R Type: Expression(Integer) +--E 164 + +--S 165 of 250 +d0033:= D(m0033,x) +--R +--R +--R (143) 0 +--R Type: Expression(Integer) +--E 165 + + +\end{chunk} +\subsection{Problem 34} +\begin{chunk}{*} + +--S 166 of 250 +t0034:= log(x)/(x^2*sqrt(1+x^2)) +--R +--R +--R log(x) +--R (144) ----------- +--R +------+ +--R 2 | 2 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 250 +r0034:= -sqrt(1+x^2)/x+asinh(x)-sqrt(1+x^2)*log(x)/x +--R +--R +--R +------+ +--R | 2 +--R (- log(x) - 1)\|x + 1 + x asinh(x) +--R (145) ------------------------------------ +--R x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 250 +a0034:= integrate(t0034,x) +--R +--R +--R (146) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 +--R (- x\|x + 1 + x )log(\|x + 1 - x) + x log(x)\|x + 1 +--R + +--R 2 +--R (- x - 1)log(x) - 1 +--R / +--R +------+ +--R | 2 2 +--R x\|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 250 +m0034:= a0034-r0034 +--R +--R +--R +------+ +--R | 2 +--R (147) - log(\|x + 1 - x) - asinh(x) - 1 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 250 +d0034:= D(m0034,x) +--R +--R +--R (148) 0 +--R Type: Expression(Integer) +--E 170 + + +\end{chunk} +\subsection{Problem 35} +\begin{chunk}{*} + +--S 171 of 250 +t0035:= x*asec(x)/sqrt(x^2-1) +--R +--R +--R x asec(x) +--R (149) --------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 250 +r0035:= sqrt(x^2-1)*asec(x)-sqrt(1-1/x^2)*x*log(x)/sqrt(x^2-1) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 2 +--R - x log(x) |------ + (x - 1)asec(x) +--R | 2 +--R \| x +--R (150) ------------------------------------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 250 +a0035:= integrate(t0035,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 173 + +--S 174 of 250 +--m0035:= a0035-r0035 +--E 174 + +--S 175 of 250 +--d0035:= D(m0035,x) +--E 175 + + +\end{chunk} +\subsection{Problem 36} +\begin{chunk}{*} + +--S 176 of 250 +t0036:= x*log(x)/sqrt(1+x^2) +--R +--R +--R x log(x) +--R (151) --------- +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 250 +r0036:= -sqrt(1+x^2)+atanh(sqrt(1+x^2))+sqrt(1+x^2)*log(x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (152) atanh(\|x + 1 ) + (log(x) - 1)\|x + 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 250 +a0036:= integrate(t0036,x) +--R +--R +--R (153) +--R +------+ +------+ +--R | 2 | 2 +--R (\|x + 1 - x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 - x - 1) + (- x log(x) + x)\|x + 1 +--R + +--R 2 2 +--R (x + 1)log(x) - x - 1 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 250 +m0036:= a0036-r0036 +--R +--R +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (154) log(\|x + 1 - x + 1) - log(\|x + 1 - x - 1) - atanh(\|x + 1 ) +--R Type: Expression(Integer) +--E 179 + +--S 180 of 250 +d0036:= D(m0036,x) +--R +--R +--R (155) 0 +--R Type: Expression(Integer) +--E 180 + + +\end{chunk} +\subsection{Problem 37} +\begin{chunk}{*} + +--S 181 of 250 +t0037:= sin(x)/(1+sin(x)^2) +--R +--R +--R sin(x) +--R (156) ----------- +--R 2 +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 250 +r0037:= atanh(cos(x)/sqrt(2))/sqrt(2) +--R +--R +--R cos(x) +--R atanh(------) +--R +-+ +--R \|2 +--R (157) ------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 250 +a0037:= integrate(t0037,x) +--R +--R +--R +-+ 2 +-+ +-+ +--R (- 3\|2 + 4)cos(x) + (- 8\|2 + 12)cos(x) - 6\|2 + 8 +--R log(-------------------------------------------------------) +--R 2 +--R cos(x) - 2 +--R (158) ------------------------------------------------------------ +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 250 +m0037:= a0037-r0037 +--R +--R +--R (159) +--R +-+ 2 +-+ +-+ +--R (- 3\|2 + 4)cos(x) + (- 8\|2 + 12)cos(x) - 6\|2 + 8 cos(x) +--R log(-------------------------------------------------------) - 2atanh(------) +--R 2 +-+ +--R cos(x) - 2 \|2 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 250 +d0037:= D(m0037,x) +--R +--R +--R 2sin(x) +--R (160) - ----------- +--R 2 +--R cos(x) - 2 +--R Type: Expression(Integer) +--E 185 + + +\end{chunk} +\subsection{Problem 38} +\begin{chunk}{*} + +--S 186 of 250 +t0038:= (1+x^2)/((1-x^2)*sqrt(1+x^4)) +--R +--R +--R 2 +--R - x - 1 +--R (161) ----------------- +--R +------+ +--R 2 | 4 +--R (x - 1)\|x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 250 +r0038:= atanh(sqrt(2)*x/sqrt(1+x^4))/sqrt(2) +--R +--R +--R +-+ +--R x\|2 +--R atanh(---------) +--R +------+ +--R | 4 +--R \|x + 1 +--R (162) ---------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 250 +a0038:= integrate(t0038,x) +--R +--R +--R +------+ +--R +-+ | 4 +--R +-+ \|2 \|x + 1 - 2x +--R \|2 log(------------------) +--R 2 +--R x - 1 +--R (163) - --------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 250 +m0038:= a0038-r0038 +--R +--R +--R +------+ +--R +-+ | 4 +-+ +--R \|2 \|x + 1 - 2x x\|2 +--R - log(------------------) - atanh(---------) +--R 2 +------+ +--R x - 1 | 4 +--R \|x + 1 +--R (164) -------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 250 +d0038:= D(m0038,x) +--R +--R +--R (165) 0 +--R Type: Expression(Integer) +--E 190 + + +\end{chunk} +\subsection{Problem 39} +\begin{chunk}{*} + +--S 191 of 250 +t0039:= (1-x^2)/((1+x^2)*sqrt(1+x^4)) +--R +--R +--R 2 +--R - x + 1 +--R (166) ----------------- +--R +------+ +--R 2 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 250 +r0039:= atan(sqrt(2)*x/sqrt(1+x^4))/sqrt(2) +--R +--R +--R +-+ +--R x\|2 +--R atan(---------) +--R +------+ +--R | 4 +--R \|x + 1 +--R (167) --------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 250 +a0039:= integrate(t0039,x) +--R +--R +--R +-+ 2x +--R \|2 atan(-------------) +--R +------+ +--R +-+ | 4 +--R \|2 \|x + 1 +--R (168) ----------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 250 +m0039:= a0039-r0039 +--R +--R +--R +-+ +--R x\|2 2x +--R - atan(---------) + atan(-------------) +--R +------+ +------+ +--R | 4 +-+ | 4 +--R \|x + 1 \|2 \|x + 1 +--R (169) --------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 250 +d0039:= D(m0039,x) +--R +--R +--R (170) 0 +--R Type: Expression(Integer) +--E 195 + + +\end{chunk} +\subsection{Problem 40} +\begin{chunk}{*} + +--S 196 of 250 +t0040:= log(sin(x))/(1+sin(x)) +--R +--R +--R log(sin(x)) +--R (171) ----------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 250 +r0040:= -x-atanh(cos(x))-cos(x)*log(sin(x))/(1+sin(x)) +--R +--R +--R - cos(x)log(sin(x)) + (- sin(x) - 1)atanh(cos(x)) - x sin(x) - x +--R (172) ---------------------------------------------------------------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 250 +a0040:= integrate(t0040,x) +--R +--R +--R (173) +--R - 2cos(x)log(sin(x)) + (- sin(x) - 1)log(cos(x) + 1) +--R + +--R sin(x) +--R (sin(x) + 1)log(cos(x) - 1) + (2sin(x) + 2)atan(----------) +--R cos(x) - 1 +--R + +--R sin(x) +--R (2sin(x) + 2)atan(----------) - 4x sin(x) - 4x +--R cos(x) + 1 +--R / +--R 2sin(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 250 +m0040:= a0040-r0040 +--R +--R +--R (174) +--R sin(x) +--R - log(cos(x) + 1) + log(cos(x) - 1) + 2atanh(cos(x)) + 2atan(----------) +--R cos(x) - 1 +--R + +--R sin(x) +--R 2atan(----------) - 2x +--R cos(x) + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 250 +d0040:= D(m0040,x) +--R +--R +--R 4 2 2 4 +--R sin(x) + 2cos(x) sin(x) + cos(x) - 1 +--R (175) -------------------------------------------------------- +--R 4 2 2 4 2 +--R sin(x) + (2cos(x) + 2)sin(x) + cos(x) - 2cos(x) + 1 +--R Type: Expression(Integer) +--E 200 + + +\end{chunk} +\subsection{Problem 41} +\begin{chunk}{*} + +--S 201 of 250 +t0041:= log(sin(x))*sqrt(1+sin(x)) +--R +--R +--R +----------+ +--R (176) log(sin(x))\|sin(x) + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 250 +r0041:= 4*cos(x)/sqrt(1+sin(x))-2*cos(x)*log(sin(x))/sqrt(1+sin(x))-_ + 4*atanh(cos(x)/sqrt(1+sin(x))) +--R +--R +--R +----------+ cos(x) +--R - 4\|sin(x) + 1 atanh(-------------) - 2cos(x)log(sin(x)) + 4cos(x) +--R +----------+ +--R \|sin(x) + 1 +--R (177) ------------------------------------------------------------------- +--R +----------+ +--R \|sin(x) + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 250 +a0041:= integrate(t0041,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 203 + +--S 204 of 250 +--m0041:= a0041-r0041 +--E 204 + +--S 205 of 250 +--d0041:= D(m0041,x) +--E 205 + + +\end{chunk} +\subsection{Problem 42} +\begin{chunk}{*} + +--S 206 of 250 +t0042:= sec(x)/sqrt(sec(x)^4-1) +--R +--R +--R sec(x) +--R (178) -------------- +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 250 +r0042:= -atanh(sqrt(sec(x)^4-1)/(sqrt(2)*sec(x)*tan(x)))/sqrt(2) +--R +--R +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R atanh(----------------) +--R +-+ +--R \|2 sec(x)tan(x) +--R (179) - ----------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 250 +a0042:= integrate(t0042,x) +--R +--R +--R (180) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 5 +-+ 4 +-+ 3 +--R - 8\|2 cos(x) - 24\|2 cos(x) - 20\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 12\|2 cos(x) + 4\|2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 3 2 +--R - 32cos(x) - 128cos(x) - 193cos(x) - 128cos(x) - 33 +--R / +--R 6 5 4 2 +--R cos(x) + 4cos(x) + 5cos(x) - 5cos(x) - 4cos(x) - 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 250 +m0042:= a0042-r0042 +--R +--R +--R (181) +--R - +--R log +--R +-+ 5 +-+ 4 +-+ 3 +--R - 8\|2 cos(x) - 24\|2 cos(x) - 20\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 12\|2 cos(x) + 4\|2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 3 2 +--R - 32cos(x) - 128cos(x) - 193cos(x) - 128cos(x) - 33 +--R / +--R 6 5 4 2 +--R cos(x) + 4cos(x) + 5cos(x) - 5cos(x) - 4cos(x) - 1 +--R + +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R 2atanh(----------------) +--R +-+ +--R \|2 sec(x)tan(x) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 250 +d0042:= D(m0042,x) +--R +--R +--R (182) +--R +-+ 5 +-+ 4 +-+ 3 +--R - 32\|2 cos(x) - 128\|2 cos(x) - 194\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 126\|2 cos(x) - 36\|2 cos(x) + 2\|2 +--R * +--R 2 2 +--R sec(x) sin(x)tan(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16\|2 cos(x) + 64\|2 cos(x) + 97\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 63\|2 cos(x) + 18\|2 cos(x) - \|2 +--R * +--R 4 +--R sec(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16\|2 cos(x) - 64\|2 cos(x) - 97\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 63\|2 cos(x) - 18\|2 cos(x) + \|2 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 32cos(x) - 48cos(x) - 80cos(x) + 48cos(x) +--R + +--R - 16cos(x) - 32 +--R * +--R 2 2 +--R sec(x) sin(x)tan(x) +--R + +--R 6 5 4 3 2 +--R 16cos(x) - 16cos(x) + 24cos(x) + 40cos(x) - 24cos(x) +--R + +--R 8cos(x) + 16 +--R * +--R 4 +--R sec(x) +--R + +--R 6 5 4 3 2 +--R - 16cos(x) + 16cos(x) - 24cos(x) - 40cos(x) + 24cos(x) +--R + +--R - 8cos(x) - 16 +--R * +--R sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R + +--R 6 5 4 2 +--R (64cos(x) + 256cos(x) + 322cos(x) - 320cos(x) - 256cos(x) - 66) +--R * +--R 2 +--R sec(x)tan(x) +--R + +--R 6 5 4 2 +--R - 32cos(x) - 128cos(x) - 161cos(x) + 160cos(x) + 128cos(x) +--R + +--R 33 +--R * +--R 5 +--R sec(x) +--R + +--R 6 5 4 2 +--R (32cos(x) + 128cos(x) + 161cos(x) - 160cos(x) - 128cos(x) - 33) +--R * +--R sec(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 64\|2 cos(x) + 64\|2 cos(x) - 32\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|2 cos(x) - 64\|2 cos(x) + 32\|2 cos(x) + 32\|2 +--R * +--R 2 +--R sec(x)tan(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 +--R * +--R 5 +--R sec(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 +--R * +--R sec(x) +--R / +--R 6 5 4 2 +--R 64cos(x) + 256cos(x) + 322cos(x) - 320cos(x) - 256cos(x) +--R + +--R - 66 +--R * +--R 2 2 +--R sec(x) tan(x) +--R + +--R 6 5 4 2 +--R - 32cos(x) - 128cos(x) - 161cos(x) + 160cos(x) + 128cos(x) +--R + +--R 33 +--R * +--R 4 +--R sec(x) +--R + +--R 6 5 4 2 +--R 32cos(x) + 128cos(x) + 161cos(x) - 160cos(x) - 128cos(x) - 33 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 64\|2 cos(x) + 64\|2 cos(x) - 32\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|2 cos(x) - 64\|2 cos(x) + 32\|2 cos(x) + 32\|2 +--R * +--R 2 2 +--R sec(x) tan(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 +--R * +--R 4 +--R sec(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 32\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) - 16\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) + 16\|2 +--R * +--R +-----------+ +--R | 4 +--R \|sec(x) - 1 +--R Type: Expression(Integer) +--E 210 + + +\end{chunk} +\subsection{Problem 43} +\begin{chunk}{*} + +--S 211 of 250 +t0043:= tan(x)/sqrt(1+tan(x)^4) +--R +--R +--R tan(x) +--R (183) -------------- +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 250 +r0043:= -atanh((1-tan(x)^2)/(sqrt(2)*sqrt(1+tan(x)^4)))/(2*sqrt(2)) +--R +--R +--R 2 +--R tan(x) - 1 +--R atanh(------------------) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R (184) ------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 250 +a0043:= integrate(t0043,x) +--R +--R +--R (185) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R 128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 250 +m0043:= a0043-r0043 +--R +--R +--R (186) +--R log +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 8 6 4 2 +--R 128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17 +--R + +--R 2 +--R tan(x) - 1 +--R - 4atanh(------------------) +--R +-----------+ +--R +-+ | 4 +--R \|2 \|tan(x) + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 250 +d0043:= D(m0043,x) +--R +--R +--R (187) +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 64\|2 cos(x) + 96\|2 cos(x) - 56\|2 cos(x) + 12\|2 cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R sin(x) |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R 9 7 5 3 +--R (128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17cos(x))sin(x) +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R + +--R 10 8 6 4 2 +--R (- 128cos(x) + 256cos(x) - 224cos(x) + 96cos(x) - 17cos(x) )tan(x) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +-+ 4 +--R 128\|2 cos(x) - 320\|2 cos(x) + 368\|2 cos(x) - 232\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 80\|2 cos(x) - 12\|2 +--R * +--R tan(x) +--R / +--R 10 8 6 4 2 +--R (128cos(x) - 256cos(x) + 224cos(x) - 96cos(x) + 17cos(x) ) +--R * +--R +-----------------------+ +--R | 4 2 +--R |2cos(x) - 2cos(x) + 1 +--R |----------------------- +--R | 4 +--R \| cos(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +-+ 4 +--R - 128\|2 cos(x) + 320\|2 cos(x) - 368\|2 cos(x) + 232\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 80\|2 cos(x) + 12\|2 +--R * +--R +-----------+ +--R | 4 +--R \|tan(x) + 1 +--R Type: Expression(Integer) +--E 215 + + +\end{chunk} +\subsection{Problem 44} +\begin{chunk}{*} + +--S 216 of 250 +t0044:= sin(x)/sqrt(1-sin(x)^6) +--R +--R +--R sin(x) +--R (188) ---------------- +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 250 +r0044:= atanh((sqrt(3)*cos(x)*(1+sin(x)^2))/(2*sqrt(1-sin(x)^6)))/(2*sqrt(3)) +--R +--R +--R +-+ 2 +-+ +--R \|3 cos(x)sin(x) + \|3 cos(x) +--R atanh(------------------------------) +--R +-------------+ +--R | 6 +--R 2\|- sin(x) + 1 +--R (189) ------------------------------------- +--R +-+ +--R 2\|3 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 250 +a0044:= integrate(t0044,x) +--R +--R +--R (190) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R - \|3 cos(x) - 2\|3 cos(x) + \|3 cos(x) + 4\|3 cos(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 +--R 7cos(x) - 24cos(x) + 24 +--R / +--R 4 +--R cos(x) +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 250 +m0044:= a0044-r0044 +--R +--R +--R (191) +--R - +--R log +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R - \|3 cos(x) - 2\|3 cos(x) + \|3 cos(x) + 4\|3 cos(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 +--R 7cos(x) - 24cos(x) + 24 +--R / +--R 4 +--R cos(x) +--R + +--R +-+ 2 +-+ +--R \|3 cos(x)sin(x) + \|3 cos(x) +--R - 2atanh(------------------------------) +--R +-------------+ +--R | 6 +--R 2\|- sin(x) + 1 +--R / +--R +-+ +--R 4\|3 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 250 +d0044:= D(m0044,x) +--R +--R +--R (192) +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x) - 64\|3 cos(x) +--R + +--R +-+ +--R - 32\|3 +--R * +--R 7 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 12\|3 cos(x) + 24\|3 cos(x) - 12\|3 cos(x) - 48\|3 cos(x) +--R + +--R +-+ 2 +--R - 24\|3 cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 24\|3 cos(x) + 48\|3 cos(x) - 24\|3 cos(x) - 96\|3 cos(x) +--R + +--R +-+ 2 +--R - 48\|3 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 12\|3 cos(x) + 24\|3 cos(x) - 28\|3 cos(x) - 80\|3 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 8\|3 cos(x) + 64\|3 cos(x) + 32\|3 +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R + +--R 7 6 5 4 2 +--R 7cos(x) + 14cos(x) - 17cos(x) - 48cos(x) + 48cos(x) +--R + +--R 24cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 7cos(x) + 14cos(x) - 10cos(x) - 34cos(x) - 17cos(x) +--R + +--R 3 2 +--R 24cos(x) + 48cos(x) + 24cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 21cos(x) + 42cos(x) - 51cos(x) - 144cos(x) + 144cos(x) +--R + +--R 3 +--R 72cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 6 5 4 2 +--R - 7cos(x) - 14cos(x) + 17cos(x) + 48cos(x) - 48cos(x) +--R + +--R - 24cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 14cos(x) + 28cos(x) - 41cos(x) - 110cos(x) + 17cos(x) +--R + +--R 4 3 2 +--R 144cos(x) + 48cos(x) - 48cos(x) - 24cos(x) +--R * +--R sin(x) +--R * +--R +-------------------------------------------+ +--R | 4 2 +--R | 16cos(x) - 48cos(x) + 48 +--R |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 4 2 7 +--R (- 112cos(x) + 384cos(x) - 384)sin(x) +--R + +--R 6 4 2 5 +--R (- 84cos(x) + 288cos(x) - 288cos(x) )sin(x) +--R + +--R 6 4 2 3 +--R (- 168cos(x) + 576cos(x) - 576cos(x) )sin(x) +--R + +--R 6 4 2 +--R (- 84cos(x) + 400cos(x) - 672cos(x) + 384)sin(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ 9 +--R (- 16\|3 cos(x) + 80\|3 cos(x) - 144\|3 cos(x) + 96\|3 cos(x))sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 16\|3 cos(x) + 64\|3 cos(x) - 64\|3 cos(x) - 48\|3 cos(x) +--R + +--R +-+ +--R 96\|3 cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R (- 48\|3 cos(x) + 240\|3 cos(x) - 432\|3 cos(x) + 288\|3 cos(x) ) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ 3 +--R (16\|3 cos(x) - 80\|3 cos(x) + 144\|3 cos(x) - 96\|3 cos(x))sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 32\|3 cos(x) + 176\|3 cos(x) - 368\|3 cos(x) + 336\|3 cos(x) +--R + +--R +-+ +--R - 96\|3 cos(x) +--R * +--R sin(x) +--R / +--R 7 6 5 4 2 +--R 28cos(x) + 56cos(x) - 68cos(x) - 192cos(x) + 192cos(x) +--R + +--R 96cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 21cos(x) + 42cos(x) - 51cos(x) - 144cos(x) + 144cos(x) +--R + +--R 3 +--R 72cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 8 7 6 4 +--R 42cos(x) + 84cos(x) - 102cos(x) - 288cos(x) + 288cos(x) +--R + +--R 3 +--R 144cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 21cos(x) + 42cos(x) - 79cos(x) - 200cos(x) + 68cos(x) +--R + +--R 4 3 2 +--R 336cos(x) + 72cos(x) - 192cos(x) - 96cos(x) +--R * +--R +-------------------------------------------+ +--R +-------------+ | 4 2 +--R | 6 | 16cos(x) - 48cos(x) + 48 +--R \|- sin(x) + 1 |------------------------------------------- +--R | 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 64\|3 cos(x) + 320\|3 cos(x) - 576\|3 cos(x) + 384\|3 cos(x)) +--R * +--R 6 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 48\|3 cos(x) + 240\|3 cos(x) - 432\|3 cos(x) +--R + +--R +-+ 3 +--R 288\|3 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 96\|3 cos(x) + 480\|3 cos(x) - 864\|3 cos(x) +--R + +--R +-+ 3 +--R 576\|3 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ 3 +--R - 48\|3 cos(x) + 304\|3 cos(x) - 752\|3 cos(x) + 864\|3 cos(x) +--R + +--R +-+ +--R - 384\|3 cos(x) +--R * +--R +-------------+ +--R | 6 +--R \|- sin(x) + 1 +--R Type: Expression(Integer) +--E 220 + + +\end{chunk} +\subsection{Problem 45} +\begin{chunk}{*} + +--S 221 of 250 +t0045:= sqrt(sqrt(sec(x)+1)-sqrt(sec(x)-1)) +--R +--R +--R +-----------------------------+ +--R | +----------+ +----------+ +--R (193) \|\|sec(x) + 1 - \|sec(x) - 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 250 +r0045:= sqrt(2)*cot(x)*sqrt(-1+sec(x))*sqrt(1+sec(x))*_ + (sqrt(-1+sqrt(2))*_ + atan((sqrt(-2+2*sqrt(2))*(-sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (2*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x)))))-_ + sqrt(1+sqrt(2))*_ + atan((sqrt(2+2*sqrt(2))*(-sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (2*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x)))))-_ + sqrt(1+sqrt(2))*_ + atanh((sqrt(-2+2*sqrt(2))*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))+_ + sqrt(-1+sqrt(2))*_ + atanh((sqrt(2+2*sqrt(2))*sqrt(-sqrt(-1+sec(x))+sqrt(1+sec(x))))/_ + (sqrt(2)-sqrt(-1+sec(x))+sqrt(1+sec(x))))) +--R +--R +--R (194) +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 - 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R +---------+ +-----------------------------+ +--R | +-+ | +----------+ +----------+ +--R \|2\|2 + 2 \|\|sec(x) + 1 - \|sec(x) - 1 +--R atanh(--------------------------------------------) +--R +----------+ +----------+ +-+ +--R \|sec(x) + 1 - \|sec(x) - 1 + \|2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 + 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R +---------+ +-----------------------------+ +--R | +-+ | +----------+ +----------+ +--R \|2\|2 - 2 \|\|sec(x) + 1 - \|sec(x) - 1 +--R atanh(--------------------------------------------) +--R +----------+ +----------+ +-+ +--R \|sec(x) + 1 - \|sec(x) - 1 + \|2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 + 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R atan +--R +---------+ +---------+ +--R | +-+ +----------+ | +-+ +----------+ +--R \|2\|2 + 2 \|sec(x) + 1 - \|2\|2 + 2 \|sec(x) - 1 +--R + +--R +---------+ +--R +-+ | +-+ +--R - \|2 \|2\|2 + 2 +--R / +--R +-----------------------------+ +--R | +----------+ +----------+ +--R 2\|\|sec(x) + 1 - \|sec(x) - 1 +--R + +--R +--------+ +--R +-+ | +-+ +----------+ +----------+ +--R \|2 cot(x)\|\|2 - 1 \|sec(x) - 1 \|sec(x) + 1 +--R * +--R atan +--R +---------+ +---------+ +--R | +-+ +----------+ | +-+ +----------+ +--R \|2\|2 - 2 \|sec(x) + 1 - \|2\|2 - 2 \|sec(x) - 1 +--R + +--R +---------+ +--R +-+ | +-+ +--R - \|2 \|2\|2 - 2 +--R / +--R +-----------------------------+ +--R | +----------+ +----------+ +--R 2\|\|sec(x) + 1 - \|sec(x) - 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 250 +a0045:= integrate(t0045,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (residue poly has multiple non-linear factors) +--R +--R Continuing to read the file... +--R +--E 223 + +--S 224 of 250 +--m0045:= a0045-r0045 +--E 224 + +--S 225 of 250 +--d0045:= D(m0045,x) +--E 225 + + +\end{chunk} +\subsection{Problem 46} +\begin{chunk}{*} + +--S 226 of 250 +t0046:= x*log(x^2+1)*atan(x)^2 +--R +--R +--R 2 2 +--R (195) x atan(x) log(x + 1) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 250 +r0046:= x*atan(x)*(3-log(1+x^2))-1/4*(6-log(1+x^2))*log(1+x^2)-_ + 1/2*atan(x)^2*(3+x^2-(1+x^2)*log(1+x^2)) +--R +--R +--R (196) +--R 2 2 2 2 2 +--R log(x + 1) + ((2x + 2)atan(x) - 4x atan(x) - 6)log(x + 1) +--R + +--R 2 2 +--R (- 2x - 6)atan(x) + 12x atan(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 250 +a0046:= integrate(t0046,x) +--R +--R +--R (197) +--R 2 2 2 2x 2 2x 2 +--R 2log(x + 1) + ((x + 1)atan(------) + 4x atan(------) - 12)log(x + 1) +--R 2 2 +--R x - 1 x - 1 +--R + +--R 2 2x 2 2x +--R (- x - 3)atan(------) - 12x atan(------) +--R 2 2 +--R x - 1 x - 1 +--R / +--R 8 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 250 +m0046:= a0046-r0046 +--R +--R +--R (198) +--R 2 2 2 2x 2 +--R (- 4x - 4)atan(x) + 8x atan(x) + (x + 1)atan(------) +--R 2 +--R x - 1 +--R + +--R 2x +--R 4x atan(------) +--R 2 +--R x - 1 +--R * +--R 2 +--R log(x + 1) +--R + +--R 2 2 2 2x 2 +--R (4x + 12)atan(x) - 24x atan(x) + (- x - 3)atan(------) +--R 2 +--R x - 1 +--R + +--R 2x +--R - 12x atan(------) +--R 2 +--R x - 1 +--R / +--R 8 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 250 +d0046:= D(m0046,x) +--R +--R +--R 2 2x 2 2 +--R (- 4x atan(x) + x atan(------) )log(x + 1) +--R 2 +--R x - 1 +--R (199) -------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 230 + + +\end{chunk} +\subsection{Problem 47} +\begin{chunk}{*} + +--S 231 of 250 +t0047:= atan(x*sqrt(1+x^2)) +--R +--R +--R +------+ +--R | 2 +--R (200) atan(x\|x + 1 ) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 250 +r0047:= 1/2*atan(sqrt(1+x^2)/x^2)+x*atan(x*sqrt(1+x^2))+_ + 1/2*sqrt(3)*atanh((sqrt(3)*sqrt(1+x^2))/(2+x^2)) +--R +--R +--R +------+ +------+ +--R +-+ | 2 +------+ | 2 +--R +-+ \|3 \|x + 1 | 2 \|x + 1 +--R \|3 atanh(-------------) + 2x atan(x\|x + 1 ) + atan(---------) +--R 2 2 +--R x + 2 x +--R (201) ---------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 250 +a0047:= integrate(t0047,x) +--R +--R +--R (202) +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 2 +--R ((2x + 1)\|3 - 2x - 4x)\|x + 1 + (- 2x - 2x)\|3 + 2x + 5x +--R + +--R 2 +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 +--R ((- 2x - 1)\|3 - 2x - 4x)\|x + 1 + (2x + 2x)\|3 + 2x +--R + +--R 2 +--R 5x + 2 +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 2x\|x + 1 \|x + 1 - x +--R - 2x atan(-----------) + 2atan(--------------------------------------) +--R 4 2 +------+ +--R x + x - 1 +-+ | 2 +-+ 2 +--R (\|3 - 2x)\|x + 1 - x\|3 + 2x + 2 +--R + +--R +------+ +--R | 2 +--R \|x + 1 - x +--R - 2atan(--------------------------------------) +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|3 + 2x)\|x + 1 - x\|3 - 2x - 2 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 250 +m0047:= a0047-r0047 +--R +--R +--R (203) +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 2 +--R ((2x + 1)\|3 - 2x - 4x)\|x + 1 + (- 2x - 2x)\|3 + 2x + 5x +--R + +--R 2 +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +------+ +--R 2 +-+ 3 | 2 3 +-+ 4 +--R ((- 2x - 1)\|3 - 2x - 4x)\|x + 1 + (2x + 2x)\|3 + 2x +--R + +--R 2 +--R 5x + 2 +--R + +--R +------+ +------+ +--R +-+ | 2 +------+ | 2 +--R +-+ \|3 \|x + 1 | 2 \|x + 1 +--R - 2\|3 atanh(-------------) - 4x atan(x\|x + 1 ) - 2atan(---------) +--R 2 2 +--R x + 2 x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 2x\|x + 1 \|x + 1 - x +--R - 2x atan(-----------) + 2atan(--------------------------------------) +--R 4 2 +------+ +--R x + x - 1 +-+ | 2 +-+ 2 +--R (\|3 - 2x)\|x + 1 - x\|3 + 2x + 2 +--R + +--R +------+ +--R | 2 +--R \|x + 1 - x +--R - 2atan(--------------------------------------) +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|3 + 2x)\|x + 1 - x\|3 - 2x - 2 +--R / +--R 4 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 250 +d0047:= D(m0047,x) +--R +--R +--R +------+ +--R +------+ | 2 +--R | 2 2x\|x + 1 +--R - 2atan(x\|x + 1 ) - atan(-----------) +--R 4 2 +--R x + x - 1 +--R (204) --------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 235 + + +\end{chunk} +\subsection{Problem 48} +\begin{chunk}{*} + +--S 236 of 250 +t0048:= atan(sqrt(x+1)-sqrt(x)) +--R +--R +--R +-----+ +-+ +--R (205) atan(\|x + 1 - \|x ) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 250 +r0048:= sqrt(x)/2+(1+x)*atan(sqrt(1+x)-sqrt(x)) +--R +--R +--R +-----+ +-+ +-+ +--R (2x + 2)atan(\|x + 1 - \|x ) + \|x +--R (206) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 250 +a0048:= integrate(t0048,x) +--R +--R +--R (207) +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +-+ +-----+ +--R ((x + 1)\|x + 1 + (- x - 1)\|x )atan(----------------) + \|x \|x + 1 - x +--R +-+ +-----+ +--R \|x \|x + 1 - x +--R -------------------------------------------------------------------------- +--R +-----+ +-+ +--R 2\|x + 1 - 2\|x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 250 +m0048:= a0048-r0048 +--R +--R +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +--R (- 2x - 2)atan(\|x + 1 - \|x ) + (x + 1)atan(----------------) +--R +-+ +-----+ +--R \|x \|x + 1 - x +--I (208) --------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 250 +d0048:= D(m0048,x) +--R +--R +--R +-----+ +-+ +--R +-----+ +-+ \|x + 1 - \|x +--R - 2atan(\|x + 1 - \|x ) + atan(----------------) +--R +-+ +-----+ +--R \|x \|x + 1 - x +--I (209) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 240 + + +\end{chunk} +\subsection{Problem 49} +\begin{chunk}{*} + +--S 241 of 250 +t0049:= asin(x/sqrt(1-x^2)) +--R +--R +--R x +--I (210) asin(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 250 +r0049:= x*asin(x/sqrt(1-x^2))+atan(sqrt(1-2*x^2)) +--R +--R +--R +---------+ +--R | 2 x +--I (211) atan(\|- 2x + 1 ) + x asin(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 250 +a0049:= integrate(t0049,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 243 + +--S 244 of 250 +--m0049:= a0049-r0049 +--E 244 + +--S 245 of 250 +--d0049:= D(m0049,x) +--E 245 + + +\end{chunk} +\subsection{Problem 50} +\begin{chunk}{*} + +)clear all + +--S 246 of 250 +t0050:= atan(x*sqrt(1-x^2)) +--R +--R +--R +--------+ +--R | 2 +--R (1) atan(x\|- x + 1 ) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 250 +r0050:= x*atan(x*sqrt(1-x^2))-_ + sqrt(1/2*(1+sqrt(5)))*atan(sqrt(1/2*(1+sqrt(5)))*sqrt(1-x^2))+_ + sqrt(1/2*(-1+sqrt(5)))*atanh(sqrt(1/2*(-1+sqrt(5)))*sqrt(1-x^2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--R | +-+ \|- x + 1 \|\|5 - 1 +--R \|\|5 - 1 atanh(----------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--------+ +--R | +-+ \|- x + 1 \|\|5 + 1 +-+ | 2 +--R - \|\|5 + 1 atan(----------------------) + x\|2 atan(x\|- x + 1 ) +--R +-+ +--R \|2 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 250 +a0050:= integrate(t0050,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--------+ +--R | +-+ +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R \|\|5 - 1 log((\|2 \|5 + \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R +--------+ +--------+ +--R +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R log((- \|2 \|5 - \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 + 2x\|2 \|- x + 1 +--R - 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (2x - 2)\|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 - 2x\|2 \|- x + 1 +--R 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (- 2x + 2)\|2 +--R + +--R +--------+ +--R | 2 +--R +-+ 2x\|- x + 1 +--R 2x\|2 atan(-------------) +--R 4 2 +--R x - x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 250 +m0050:= a0050-r0050 +--R +--R +--R (4) +--R +--------+ +--------+ +--------+ +--R | +-+ +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R \|\|5 - 1 log((\|2 \|5 + \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R - +--R +--------+ +--R | +-+ +--R \|\|5 - 1 +--R * +--R +--------+ +--------+ +--R +-+ +-+ +-+ | 2 | +-+ +-+ 2 +--R log((- \|2 \|5 - \|2 )\|- x + 1 \|\|5 - 1 + \|5 - 2x + 3) +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--R | +-+ \|- x + 1 \|\|5 - 1 +--R - 4\|\|5 - 1 atanh(----------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +--------+ | 2 | +-+ +--------+ +--R | +-+ \|- x + 1 \|\|5 + 1 +-+ | 2 +--R 4\|\|5 + 1 atan(----------------------) - 4x\|2 atan(x\|- x + 1 ) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 + 2x\|2 \|- x + 1 +--R - 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (2x - 2)\|2 +--R + +--R +--------+ +--------+ +--------+ +--R +--------+ +-+ | 2 | +-+ +-+ | 2 +--R | +-+ (\|5 - 1)\|- x + 1 \|\|5 + 1 - 2x\|2 \|- x + 1 +--R 2\|\|5 + 1 atan(----------------------------------------------------) +--R +--------+ +--R +-+ | +-+ 2 +-+ +--R (x\|5 - x)\|\|5 + 1 + (- 2x + 2)\|2 +--R + +--R +--------+ +--R | 2 +--R +-+ 2x\|- x + 1 +--R 2x\|2 atan(-------------) +--R 4 2 +--R x - x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 250 +d0050:= D(m0050,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 2x\|- x + 1 +--R - 2atan(x\|- x + 1 ) + atan(-------------) +--R 4 2 +--R x - x + 1 +--R (5) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 250 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Charlwood, Kevin +``Integration on Computer Algebra Systems'' +Electronic Journal of Mathematics and Technology (2008) +\verb|www.freepatentsonline.com/article/| +\verb|Electronic-journal-Mathematics-Technology/188213666.html| +\bibitem{2} +Rich, Albert +``Charlwood Integration Problems'' +\verb|www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf| +\end{thebibliography} +\end{document} + + diff --git a/src/axiom-website/CATS/charlwood.input.pdf b/src/axiom-website/CATS/charlwood.input.pdf new file mode 100644 index 0000000..07e52ce Binary files /dev/null and b/src/axiom-website/CATS/charlwood.input.pdf differ diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index d2ad926..f5a42a0 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -129,7 +129,7 @@ Each Axiom result is differenced from the published result and reduced to a constant (usually 0).
- +