diff --git a/changelog b/changelog index d594f03..40de2e7 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100610 tpd src/axiom-website/patches.html 20100610.04.tpd.patch +20100610 tpd src/input/Makefile rule-based trig integration +20100610 tpd src/input/richtrig600-699.input rule-based trig integration 20100610 tpd src/axiom-website/patches.html 20100610.03.tpd.patch 20100610 tpd src/input/Makefile rule-based trig integration 20100610 tpd src/input/richtrig500-599.input rule-based trig integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index b8c72a5..c8c6d9d 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2878,6 +2878,8 @@ books/bookvol10.5 start of numeric analysis of BLAS/LAPACK
src/input/richtrig400-499.input rule-based trig integration
20100610.03.tpd.patch src/input/richtrig500-599.input rule-based trig integration
+20100610.04.tpd.patch +src/input/richtrig600-699.input rule-based trig integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 446be95..080c479 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -382,6 +382,7 @@ REGRES= ackermann.regress \ richtrig300-399.regress \ richtrig400-499.regress \ richtrig500-599.regress \ + richtrig600-699.regress \ robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -707,6 +708,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richtrig300-399.input \ ${OUT}/richtrig400-499.input \ ${OUT}/richtrig500-599.input \ + ${OUT}/richtrig600-699.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1061,6 +1063,7 @@ DOCFILES= \ ${DOC}/richtrig300-399.input.dvi \ ${DOC}/richtrig400-499.input.dvi \ ${DOC}/richtrig500-599.input.dvi \ + ${DOC}/richtrig600-699.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ ${DOC}/romnum.as.dvi ${DOC}/roots.input.dvi \ diff --git a/src/input/richtrig600-699.input.pamphlet b/src/input/richtrig600-699.input.pamphlet new file mode 100644 index 0000000..b3a8cf0 --- /dev/null +++ b/src/input/richtrig600-699.input.pamphlet @@ -0,0 +1,15974 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richtrig600-699.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig600-699.output +)spool richtrig600-699.output +)set message auto off +)clear all + +--S 1 of 534 +t0600:= sin(x)^3/(a+b*cos(x)^2) +--R +--R +--R 3 +--R sin(x) +--R (1) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--E 1 + +--S 2 of 534 +r0600:= -(a+b)*atan(b^(1/2)*cos(x)/a^(1/2))/a^(1/2)/b^(3/2)+cos(x)/b +--R +--R +--R +-+ +--R cos(x)\|b +-+ +-+ +--R (- b - a)atan(----------) + cos(x)\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R +-+ +-+ +--R b\|a \|b +--R Type: Expression Integer +--E 2 + +--S 3 of 534 +a0600:= integrate(t0600,x) +--R +--R +--R (3) +--R [ +--R (b + a) +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-----+ +--R 2cos(x)\|- a b +--R / +--R +-----+ +--R 2b\|- a b +--R , +--R +---+ +--R (b cos(x) - a)\|a b +---+ +--R (- b - a)atan(--------------------) + cos(x)\|a b +--R a b cos(x) + a b +--R --------------------------------------------------] +--R +---+ +--R b\|a b +--R Type: Union(List Expression Integer,...) +--E 3 + +--S 4 of 534 +m0600a:= a0600.1-r0600 +--R +--R +--R (4) +--R +-+ +-+ +--R (b + a)\|a \|b +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R +-----+ cos(x)\|b +--R (2b + 2a)\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression Integer +--E 4 + +--S 5 of 534 +d0600a:= D(m0600a,x) +--R +--R +--R (5) 0 +--R Type: Expression Integer +--E 5 + +--S 6 of 534 +m0600b:= a0600.2-r0600 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ (b cos(x) - a)\|a b +---+ cos(x)\|b +--R (- b - a)\|a \|b atan(--------------------) + (b + a)\|a b atan(----------) +--R a b cos(x) + a b +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R +-+ +-+ +---+ +--R b\|a \|b \|a b +--R Type: Expression Integer +--E 6 + +--S 7 of 534 +d0600b:= D(m0600b,x) +--R +--R +--R (7) 0 +--R Type: Expression Integer +--E 7 + +--S 8 of 534 +t0601:= sin(x)^4/(a+b*cos(x)^2) +--R +--R +--R 4 +--R sin(x) +--R (8) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--E 8 + +--S 9 of 534 +r0601:= -a*x/b^2-3/2*x/b+(a+b)^(3/2)*atan(a^(1/2)*tan(x)/(a+b)^(1/2))/a^(1/2)/b^2+1/2*cos(x)*sin(x)/b +--R +--R +--R (9) +--R +-+ +--R +-----+ tan(x)\|a +-+ +--R (2b + 2a)\|b + a atan(----------) + (b cos(x)sin(x) + (- 3b - 2a)x)\|a +--R +-----+ +--R \|b + a +--R ----------------------------------------------------------------------- +--R 2 +-+ +--R 2b \|a +--R Type: Expression Integer +--E 9 + +--S 10 of 534 +a0601:= integrate(t0601,x) +--R +--R +--R (10) +--R [ +--R +-------+ +--R |- b - a 2 +--R +-------+ - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R |- b - a \| a +--R (b + a) |------- log(-------------------------------------------------) +--R \| a 2 +--R b cos(x) + a +--R + +--R b cos(x)sin(x) + (- 3b - 2a)x +--R / +--R 2 +--R 2b +--R , +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +--R |b + a \| a +--R (2b + 2a) |----- atan(----------------) + b cos(x)sin(x) + (- 3b - 2a)x +--R \| a (b + a)cos(x) +--R -----------------------------------------------------------------------] +--R 2 +--R 2b +--R Type: Union(List Expression Integer,...) +--E 10 + +--S 11 of 534 +m0601a:= a0601.1-r0601 +--R +--R +--R (11) +--R +-------+ +--R |- b - a +-+ +--R (b + a) |------- \|a +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R \| a +--R log(-------------------------------------------------) +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R +-----+ tan(x)\|a +--R (- 2b - 2a)\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R / +--R 2 +-+ +--R 2b \|a +--R Type: Expression Integer +--E 11 + +--S 12 of 534 +d0601a:= D(m0601a,x) +--R +--R +--R (12) +--R 3 2 2 3 3 2 +--R (- 2a b - 4a b - 2a b)cos(x) sin(x)tan(x) +--R + +--R 3 2 2 3 3 3 2 2 3 +--R ((- 2a b - 4a b - 2a b)cos(x) + (2a b + 4a b + 2a b)cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 3 2 2 3 2 2 2 3 4 2 +--R ((- a b - 2a b - a b)cos(x) + a b + 2a b + a )sin(x) +--R + +--R 4 3 2 2 3 4 2 2 3 4 2 2 2 +--R (b + 3a b + 3a b + a b)cos(x) + (a b + 2a b + a )cos(x) - a b +--R + +--R 3 4 +--R - 2a b - a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 2 3 2 3 2 2 3 4 2 +--R ((- b - 3a b - 3a b - a b)cos(x) + a b + 3a b + 3a b + a )sin(x) +--R + +--R 3 2 2 3 4 3 2 2 3 4 2 2 2 +--R (a b + 2a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) - a b +--R + +--R 3 4 +--R - 2a b - a +--R / +--R 2 3 3 3 2 2 +--R (2a b cos(x) + 2a b cos(x))sin(x)tan(x) +--R + +--R 4 2 3 3 2 3 3 2 +--R ((2a b + 2a b )cos(x) + (2a b + 2a b )cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 4 2 3 4 3 2 2 3 2 2 +--R ((- a b - 2a b )cos(x) - 2a b cos(x) + a b )tan(x) +--R + +--R 5 4 2 3 4 2 3 3 2 2 2 3 3 2 +--R (- b - 3a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) + a b + a b +--R Type: Expression Integer +--E 12 + +--S 13 of 534 +m0601b:= a0601.2-r0601 +--R +--R +--R (13) +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +-+ +--R +-+ |b + a \| a +-----+ tan(x)\|a +--R (b + a)\|a |----- atan(----------------) + (- b - a)\|b + a atan(----------) +--R \| a (b + a)cos(x) +-----+ +--R \|b + a +--R ----------------------------------------------------------------------------- +--R 2 +-+ +--R b \|a +--R Type: Expression Integer +--E 13 + +--S 14 of 534 +d0601b:= D(m0601b,x) +--R +--R +--R (14) +--R 2 2 2 2 2 2 2 +--R (- b - 2a b - a )cos(x) tan(x) + (b + 2a b + a )sin(x) +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (a b sin(x) + (a b + a b)cos(x) )tan(x) + (a b + a b)sin(x) +--R + +--R 3 2 2 2 +--R (b + 2a b + a b)cos(x) +--R Type: Expression Integer +--E 14 + +--S 15 of 534 +t0602:= sin(x)^5/(a+b*cos(x)^2) +--R +--R +--R 5 +--R sin(x) +--R (15) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--E 15 + +--S 16 of 534 +r0602:= -(a+b)^2*atan(b^(1/2)*cos(x)/a^(1/2))/a^(1/2)/b^(5/2)+a*cos(x)/b^2+2*cos(x)/b-1/3*cos(x)^3/b +--R +--R +--R (16) +--R +-+ +--R 2 2 cos(x)\|b +--R (- 3b - 6a b - 3a )atan(----------) +--R +-+ +--R \|a +--R + +--R 3 +-+ +-+ +--R (- b cos(x) + (6b + 3a)cos(x))\|a \|b +--R / +--R 2 +-+ +-+ +--R 3b \|a \|b +--R Type: Expression Integer +--E 16 + +--S 17 of 534 +a0602:= integrate(t0602,x) +--R +--R +--R (17) +--R [ +--R 2 2 +--R (3b + 6a b + 3a ) +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R 3 +-----+ +--R (- 2b cos(x) + (12b + 6a)cos(x))\|- a b +--R / +--R 2 +-----+ +--R 6b \|- a b +--R , +--R +--R +---+ +--R 2 2 (b cos(x) - a)\|a b +--R (- 3b - 6a b - 3a )atan(--------------------) +--R a b cos(x) + a b +--R + +--R 3 +---+ +--R (- b cos(x) + (6b + 3a)cos(x))\|a b +--R / +--R 2 +---+ +--R 3b \|a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 17 + +--S 18 of 534 +m0602a:= a0602.1-r0602 +--R +--R +--R (18) +--R 2 2 +-+ +-+ +--R (b + 2a b + a )\|a \|b +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R 2 2 +-----+ cos(x)\|b +--R (2b + 4a b + 2a )\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 2b \|- a b \|a \|b +--R Type: Expression Integer +--E 18 + +--S 19 of 534 +d0602a:= D(m0602a,x) +--R +--R +--R (19) 0 +--R Type: Expression Integer +--E 19 + +--S 20 of 534 +m0602b:= a0602.2-r0602 +--R +--R +--R (20) +--R +---+ +--R 2 2 +-+ +-+ (b cos(x) - a)\|a b +--R (- b - 2a b - a )\|a \|b atan(--------------------) +--R a b cos(x) + a b +--R + +--R +-+ +--R 2 2 +---+ cos(x)\|b +--R (b + 2a b + a )\|a b atan(----------) +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R b \|a \|b \|a b +--R Type: Expression Integer +--E 20 + +--S 21 of 534 +d0602b:= D(m0602b,x) +--R +--R +--R (21) 0 +--R Type: Expression Integer +--E 21 + +--S 22 of 534 +t0603:= sin(x)^6/(a+b*cos(x)^2) +--R +--R +--R 6 +--R sin(x) +--R (22) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--E 22 + +--S 23 of 534 +r0603:= -1/2*a*x/b^2-7/8*x/b-(a+b)^2*x/b^3+(a+b)^(5/2)*atan(a^(1/2)*tan(x)/(a+b)^(1/2))/a^(1/2)/b^3+1/2*a*cos(x)*sin(x)/b^2+7/8*cos(x)*sin(x)/b+1/4*cos(x)*sin(x)^3/b +--R +--R +--R (23) +--R +-+ +--R 2 2 +-----+ tan(x)\|a +--R (8b + 16a b + 8a )\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-+ +--R (2b cos(x)sin(x) + (7b + 4a b)cos(x)sin(x) + (- 15b - 20a b - 8a )x)\|a +--R / +--R 3 +-+ +--R 8b \|a +--R Type: Expression Integer +--E 23 + +--S 24 of 534 +a0603:= integrate(t0603,x) +--R +--R +--R (24) +--R [ +--R +-------+ +--R 2 2 |- b - a +--R (4b + 8a b + 4a ) |------- +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R \| a +--R log(-------------------------------------------------) +--R 2 +--R b cos(x) + a +--R + +--R 2 3 2 2 2 +--R (- 2b cos(x) + (9b + 4a b)cos(x))sin(x) + (- 15b - 20a b - 8a )x +--R / +--R 3 +--R 8b +--R , +--R +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +--R 2 2 |b + a \| a +--R (8b + 16a b + 8a ) |----- atan(----------------) +--R \| a (b + a)cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2b cos(x) + (9b + 4a b)cos(x))sin(x) + (- 15b - 20a b - 8a )x +--R / +--R 3 +--R 8b +--R ] +--R Type: Union(List Expression Integer,...) +--E 24 + +--S 25 of 534 +m0603a:= a0603.1-r0603 +--R +--R +--R (25) +--R +-------+ +--R 2 2 |- b - a +-+ +--R (2b + 4a b + 2a ) |------- \|a +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R \| a +--R log(-------------------------------------------------) +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R 2 2 +-----+ tan(x)\|a +--R (- 4b - 8a b - 4a )\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 3 2 +-+ +--R (- b cos(x)sin(x) + (- b cos(x) + b cos(x))sin(x))\|a +--R / +--R 3 +-+ +--R 4b \|a +--R Type: Expression Integer +--E 25 + +--S 26 of 534 +d0603a:= D(m0603a,x) +--R +--R +--R (26) +--R 2 3 3 3 2 5 +--R (2a b cos(x) + 2a b cos(x))sin(x) +--R + +--R 2 3 3 3 2 3 +--R (- 2a b cos(x) - 2a b cos(x))sin(x) +--R + +--R 2 3 7 2 3 3 2 5 +--R - 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 24a b - 22a b - 8a b)cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 3 3 2 5 +--R ((2a b + 2a b )cos(x) + (2a b + 2a b )cos(x))sin(x) +--R + +--R 4 2 3 3 2 3 3 2 3 +--R ((- 2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x))sin(x) +--R + +--R 4 2 3 7 4 3 2 5 +--R (- 2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 22a b - 22a b - 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 +--R (8a b + 24a b + 24a b + 8a b)cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 4 2 3 4 3 2 2 3 2 4 +--R ((- a b - 2a b )cos(x) - 2a b cos(x) + a b )sin(x) +--R + +--R 4 2 3 4 4 2 3 3 2 4 2 +--R (a b + 2a b )cos(x) + (- 4a b - 12a b - 10a b - 4a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R 4a b + 11a b + 12a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 8 4 2 3 3 2 6 +--R (a b + 2a b )cos(x) + (- a b - 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (4b + 16a b + 24a b + 13a b + 4a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 4 5 +--R (4a b + 13a b + 12a b + 4a )cos(x) - 4a b - 12a b - 12a b - 4a +--R * +--R 2 +--R tan(x) +--R + +--R 5 4 2 3 4 2 3 3 2 2 2 3 +--R (- b - 3a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) + a b +--R + +--R 3 2 +--R a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 2 3 4 +--R (b + 3a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 4 2 3 +--R (- 4b - 16a b - 22a b - 14a b - 4a b)cos(x) + 4a b + 15a b +--R + +--R 3 2 4 5 +--R 23a b + 16a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 8 5 4 3 2 6 +--R (b + 3a b + 2a b )cos(x) + (- b - 3a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (4a b + 9a b + 9a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 2 3 3 2 4 5 +--R (- 4a b - 7a b + a b + 8a b + 4a )cos(x) - 4a b - 12a b - 12a b - 4a +--R / +--R 2 4 3 3 3 2 +--R (8a b cos(x) + 8a b cos(x))sin(x)tan(x) +--R + +--R 5 2 4 3 2 4 3 3 +--R ((8a b + 8a b )cos(x) + (8a b + 8a b )cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 5 2 4 4 3 3 2 3 3 2 +--R ((- 4a b - 8a b )cos(x) - 8a b cos(x) + 4a b )tan(x) +--R + +--R 6 5 2 4 4 2 4 3 3 2 2 4 3 3 +--R (- 4b - 12a b - 8a b )cos(x) + (- 8a b - 8a b )cos(x) + 4a b + 4a b +--R Type: Expression Integer +--E 26 + +--S 27 of 534 +m0603b:= a0603.2-r0603 +--R +--R +--R (27) +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +--R 2 2 +-+ |b + a \| a +--R (4b + 8a b + 4a )\|a |----- atan(----------------) +--R \| a (b + a)cos(x) +--R + +--R +-+ +--R 2 2 +-----+ tan(x)\|a +--R (- 4b - 8a b - 4a )\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 3 2 +-+ +--R (- b cos(x)sin(x) + (- b cos(x) + b cos(x))sin(x))\|a +--R / +--R 3 +-+ +--R 4b \|a +--R Type: Expression Integer +--E 27 + +--S 28 of 534 +d0603b:= D(m0603b,x) +--R +--R +--R (28) +--R 2 6 2 2 2 2 4 +--R a b sin(x) + ((a b + a b)cos(x) - a b)sin(x) +--R + +--R 2 4 2 2 2 2 2 6 +--R (- a b cos(x) - a b cos(x) )sin(x) + (- a b - a b)cos(x) +--R + +--R 2 2 4 3 2 2 3 2 +--R (a b + a b)cos(x) + (- 4b - 12a b - 12a b - 4a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 6 3 2 2 2 2 2 4 +--R (a b + a b)sin(x) + ((b + 2a b + a b)cos(x) - a b - a b)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 +--R (- a b - a b)cos(x) + (- b - a b )cos(x) + 4b + 12a b + 12a b +--R + +--R 3 +--R 4a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- b - 2a b - a b)cos(x) + (b + 2a b + a b)cos(x) +--R / +--R 2 2 2 3 2 2 2 2 3 2 2 2 +--R (4a b sin(x) + (4a b + 4a b )cos(x) )tan(x) + (4a b + 4a b )sin(x) +--R + +--R 4 3 2 2 2 +--R (4b + 8a b + 4a b )cos(x) +--R Type: Expression Integer +--E 28 + +--S 29 of 534 +t0604:= sin(x)^7/(a+b*cos(x)^2) +--R +--R +--R 7 +--R sin(x) +--R (29) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression Integer +--E 29 + +--S 30 of 534 +r0604:= -(a+b)^3*atan(b^(1/2)*cos(x)/a^(1/2))/a^(1/2)/b^(7/2)+a*cos(x)/b^2+2*cos(x)/b+(a+b)^2*cos(x)/b^3-1/3*a*cos(x)^3/b^2-cos(x)^3/b+1/5*cos(x)^5/b +--R +--R +--R (30) +--R +-+ +--R 3 2 2 3 cos(x)\|b +--R (- 15b - 45a b - 45a b - 15a )atan(----------) +--R +-+ +--R \|a +--R + +--R 2 5 2 3 2 2 +-+ +-+ +--R (3b cos(x) + (- 15b - 5a b)cos(x) + (45b + 45a b + 15a )cos(x))\|a \|b +--R / +--R 3 +-+ +-+ +--R 15b \|a \|b +--R Type: Expression Integer +--E 30 + +--S 31 of 534 +a0604:= integrate(t0604,x) +--R +--R +--R (31) +--R [ +--R 3 2 2 3 +--R (15b + 45a b + 45a b + 15a ) +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R 2 5 2 3 2 2 +--R (6b cos(x) + (- 30b - 10a b)cos(x) + (90b + 90a b + 30a )cos(x)) +--R * +--R +-----+ +--R \|- a b +--R / +--R 3 +-----+ +--R 30b \|- a b +--R , +--R +--R +---+ +--R 3 2 2 3 (b cos(x) - a)\|a b +--R (- 15b - 45a b - 45a b - 15a )atan(--------------------) +--R a b cos(x) + a b +--R + +--R 2 5 2 3 2 2 +---+ +--R (3b cos(x) + (- 15b - 5a b)cos(x) + (45b + 45a b + 15a )cos(x))\|a b +--R / +--R 3 +---+ +--R 15b \|a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 31 + +--S 32 of 534 +m0604a:= a0604.1-r0604 +--R +--R +--R (32) +--R 3 2 2 3 +-+ +-+ +--R (b + 3a b + 3a b + a )\|a \|b +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R 3 2 2 3 +-----+ cos(x)\|b +--R (2b + 6a b + 6a b + 2a )\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R 3 +-----+ +-+ +-+ +--R 2b \|- a b \|a \|b +--R Type: Expression Integer +--E 32 + +--S 33 of 534 +d0604a:= D(m0604a,x) +--R +--R +--R (33) 0 +--R Type: Expression Integer +--E 33 + +--S 34 of 534 +m0604b:= a0604.2-r0604 +--R +--R +--R (34) +--R +---+ +--R 3 2 2 3 +-+ +-+ (b cos(x) - a)\|a b +--R (- b - 3a b - 3a b - a )\|a \|b atan(--------------------) +--R a b cos(x) + a b +--R + +--R +-+ +--R 3 2 2 3 +---+ cos(x)\|b +--R (b + 3a b + 3a b + a )\|a b atan(----------) +--R +-+ +--R \|a +--R / +--R 3 +-+ +-+ +---+ +--R b \|a \|b \|a b +--R Type: Expression Integer +--E 34 + +--S 35 of 534 +d0604b:= D(m0604b,x) +--R +--R +--R (35) 0 +--R Type: Expression Integer +--E 35 + +--S 36 of 534 +t0605:= sin(x)^2/(a-a*cos(x)^2) +--R +--R +--R 2 +--R sin(x) +--R (36) - ------------- +--R 2 +--R a cos(x) - a +--R Type: Expression Integer +--E 36 + +--S 37 of 534 +r0605:= x/a +--R +--R +--R x +--R (37) - +--R a +--R Type: Fraction Polynomial Integer +--E 37 + +--S 38 of 534 +a0605:= integrate(t0605,x) +--R +--R +--R x +--R (38) - +--R a +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 534 +m0605:= a0605-r0605 +--R +--R +--R (39) 0 +--R Type: Expression Integer +--E 39 + +--S 40 of 534 +d0605:= D(m0605,x) +--R +--R +--R (40) 0 +--R Type: Expression Integer +--E 40 + +--S 41 of 534 +t0606:= sin(x)^4/(a-a*cos(x)^2) +--R +--R +--R 4 +--R sin(x) +--R (41) - ------------- +--R 2 +--R a cos(x) - a +--R Type: Expression Integer +--E 41 + +--S 42 of 534 +r0606:= -1/2*(-x+cos(x)*sin(x))/a +--R +--R +--R - cos(x)sin(x) + x +--R (42) ------------------ +--R 2a +--R Type: Expression Integer +--E 42 + +--S 43 of 534 +a0606:= integrate(t0606,x) +--R +--R +--R - cos(x)sin(x) + x +--R (43) ------------------ +--R 2a +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 534 +m0606:= a0606-r0606 +--R +--R +--R (44) 0 +--R Type: Expression Integer +--E 44 + +--S 45 of 534 +d0606:= D(m0606,x) +--R +--R +--R (45) 0 +--R Type: Expression Integer +--E 45 + +--S 46 of 534 +t0607:= tan(x)/(1+cos(x)^2) +--R +--R +--R tan(x) +--R (46) ----------- +--R 2 +--R cos(x) + 1 +--R Type: Expression Integer +--E 46 + +--S 47 of 534 +r0607:= atanh(1+2*cos(x)^2) +--R +--R +--R 2 +--R (47) atanh(2cos(x) + 1) +--R Type: Expression Integer +--E 47 + +--S 48 of 534 +a0607:= integrate(t0607,x) +--R +--R +--R 2 +--R 2cos(x) + 2 2cos(x) +--R log(---------------------) - 2log(- ----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R (48) ----------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 534 +m0607:= a0607-r0607 +--R +--R +--R (49) +--R 2 +--R 2cos(x) + 2 2cos(x) 2 +--R log(---------------------) - 2log(- ----------) - 2atanh(2cos(x) + 1) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R ---------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 49 + +--S 50 of 534 +d0607:= D(m0607,x) +--R +--R +--R (50) 0 +--R Type: Expression Integer +--E 50 + +--S 51 of 534 +t0608:= cos(a+b*x)^3*sin(a+b*x)^n +--R +--R +--R 3 n +--R (51) cos(b x + a) sin(b x + a) +--R Type: Expression Integer +--E 51 + +--S 52 of 534 +r0608:= sin(a+b*x)^(1+n)/b/(1+n)-sin(a+b*x)^(3+n)/b/(3+n) +--R +--R +--R n + 3 n + 1 +--R (- n - 1)sin(b x + a) + (n + 3)sin(b x + a) +--R (52) ----------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Expression Integer +--E 52 + +--S 53 of 534 +a0608:= integrate(t0608,x) +--R +--R +--R 2 n log(sin(b x + a)) +--R ((n + 1)cos(b x + a) + 2)sin(b x + a)%e +--R (53) ----------------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 534 +m0608:= a0608-r0608 +--R +--R +--R (54) +--R 2 n log(sin(b x + a)) +--R ((n + 1)cos(b x + a) + 2)sin(b x + a)%e +--R + +--R n + 3 n + 1 +--R (n + 1)sin(b x + a) + (- n - 3)sin(b x + a) +--R / +--R 2 +--R b n + 4b n + 3b +--R Type: Expression Integer +--E 54 + +--S 55 of 534 +d0608:= D(m0608,x) +--R +--R +--R (55) +--R 2 3 +--R (- 2cos(b x + a)sin(b x + a) + (n + 1)cos(b x + a) + 2cos(b x + a)) +--R * +--R n log(sin(b x + a)) +--R %e +--R + +--R n + 2 n +--R (n + 3)cos(b x + a)sin(b x + a) + (- n - 3)cos(b x + a)sin(b x + a) +--R / +--R n + 3 +--R Type: Expression Integer +--E 55 + +--S 56 of 534 +t0609:= cos(a+b*x)^5*sin(a+b*x)^n +--R +--R +--R 5 n +--R (56) cos(b x + a) sin(b x + a) +--R Type: Expression Integer +--E 56 + +--S 57 of 534 +r0609:= sin(a+b*x)^(1+n)/b/(1+n)-2*sin(a+b*x)^(3+n)/b/(3+n)+sin(a+b*x)^(5+n)/b/(5+n) +--R +--R +--R (57) +--R 2 n + 5 2 n + 3 +--R (n + 4n + 3)sin(b x + a) + (- 2n - 12n - 10)sin(b x + a) +--R + +--R 2 n + 1 +--R (n + 8n + 15)sin(b x + a) +--R / +--R 3 2 +--R b n + 9b n + 23b n + 15b +--R Type: Expression Integer +--E 57 + +--S 58 of 534 +a0609:= integrate(t0609,x) +--R +--R +--R (58) +--R 2 4 2 +--R ((n + 4n + 3)cos(b x + a) + (4n + 4)cos(b x + a) + 8)sin(b x + a) +--R * +--R n log(sin(b x + a)) +--R %e +--R / +--R 3 2 +--R b n + 9b n + 23b n + 15b +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 534 +m0609:= a0609-r0609 +--R +--R +--R (59) +--R 2 4 2 +--R ((n + 4n + 3)cos(b x + a) + (4n + 4)cos(b x + a) + 8)sin(b x + a) +--R * +--R n log(sin(b x + a)) +--R %e +--R + +--R 2 n + 5 2 n + 3 +--R (- n - 4n - 3)sin(b x + a) + (2n + 12n + 10)sin(b x + a) +--R + +--R 2 n + 1 +--R (- n - 8n - 15)sin(b x + a) +--R / +--R 3 2 +--R b n + 9b n + 23b n + 15b +--R Type: Expression Integer +--E 59 + +--S 60 of 534 +d0609:= D(m0609,x) +--R +--R +--R (60) +--R 3 2 +--R ((- 4n - 12)cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 2 5 3 +--R (n + 4n + 3)cos(b x + a) + (4n + 4)cos(b x + a) + 8cos(b x + a) +--R * +--R n log(sin(b x + a)) +--R %e +--R + +--R 2 n + 4 +--R (- n - 8n - 15)cos(b x + a)sin(b x + a) +--R + +--R 2 n + 2 +--R (2n + 16n + 30)cos(b x + a)sin(b x + a) +--R + +--R 2 n +--R (- n - 8n - 15)cos(b x + a)sin(b x + a) +--R / +--R 2 +--R n + 8n + 15 +--R Type: Expression Integer +--E 60 + +--S 61 of 534 +t0610:= cos(a+b*x)^m*sin(a+b*x)^3 +--R +--R +--R 3 m +--R (61) sin(b x + a) cos(b x + a) +--R Type: Expression Integer +--E 61 + +--S 62 of 534 +r0610:= -cos(a+b*x)^(1+m)/b/(1+m)+cos(a+b*x)^(3+m)/b/(3+m) +--R +--R +--R m + 3 m + 1 +--R (m + 1)cos(b x + a) + (- m - 3)cos(b x + a) +--R (62) ----------------------------------------------------- +--R 2 +--R b m + 4b m + 3b +--R Type: Expression Integer +--E 62 + +--S 63 of 534 +a0610:= integrate(t0610,x) +--R +--R +--R 3 m log(cos(b x + a)) +--R ((m + 1)cos(b x + a) + (- m - 3)cos(b x + a))%e +--R (63) ------------------------------------------------------------------- +--R 2 +--R b m + 4b m + 3b +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 534 +m0610:= a0610-r0610 +--R +--R +--R (64) +--R 3 m log(cos(b x + a)) +--R ((m + 1)cos(b x + a) + (- m - 3)cos(b x + a))%e +--R + +--R m + 3 m + 1 +--R (- m - 1)cos(b x + a) + (m + 3)cos(b x + a) +--R / +--R 2 +--R b m + 4b m + 3b +--R Type: Expression Integer +--E 64 + +--S 65 of 534 +d0610:= D(m0610,x) +--R +--R +--R (65) +--R 2 m log(cos(b x + a)) +--R (- cos(b x + a) + 1)sin(b x + a)%e +--R + +--R m + 2 m +--R sin(b x + a)cos(b x + a) - sin(b x + a)cos(b x + a) +--R Type: Expression Integer +--E 65 + +--S 66 of 534 +t0611:= cos(a+b*x)^m*sin(a+b*x)^5 +--R +--R +--R 5 m +--R (66) sin(b x + a) cos(b x + a) +--R Type: Expression Integer +--E 66 + +--S 67 of 534 +r0611:= -cos(a+b*x)^(1+m)/b/(1+m)+2*cos(a+b*x)^(3+m)/b/(3+m)-cos(a+b*x)^(5+m)/b/(5+m) +--R +--R +--R (67) +--R 2 m + 5 2 m + 3 +--R (- m - 4m - 3)cos(b x + a) + (2m + 12m + 10)cos(b x + a) +--R + +--R 2 m + 1 +--R (- m - 8m - 15)cos(b x + a) +--R / +--R 3 2 +--R b m + 9b m + 23b m + 15b +--R Type: Expression Integer +--E 67 + +--S 68 of 534 +a0611:= integrate(t0611,x) +--R +--R +--R (68) +--R 2 5 2 3 +--R (- m - 4m - 3)cos(b x + a) + (2m + 12m + 10)cos(b x + a) +--R + +--R 2 +--R (- m - 8m - 15)cos(b x + a) +--R * +--R m log(cos(b x + a)) +--R %e +--R / +--R 3 2 +--R b m + 9b m + 23b m + 15b +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 534 +m0611:= a0611-r0611 +--R +--R +--R (69) +--R 2 5 2 3 +--R (- m - 4m - 3)cos(b x + a) + (2m + 12m + 10)cos(b x + a) +--R + +--R 2 +--R (- m - 8m - 15)cos(b x + a) +--R * +--R m log(cos(b x + a)) +--R %e +--R + +--R 2 m + 5 2 m + 3 +--R (m + 4m + 3)cos(b x + a) + (- 2m - 12m - 10)cos(b x + a) +--R + +--R 2 m + 1 +--R (m + 8m + 15)cos(b x + a) +--R / +--R 3 2 +--R b m + 9b m + 23b m + 15b +--R Type: Expression Integer +--E 69 + +--S 70 of 534 +d0611:= D(m0611,x) +--R +--R +--R (70) +--R 4 2 m log(cos(b x + a)) +--R (cos(b x + a) - 2cos(b x + a) + 1)sin(b x + a)%e +--R + +--R m + 4 m + 2 +--R - sin(b x + a)cos(b x + a) + 2sin(b x + a)cos(b x + a) +--R + +--R m +--R - sin(b x + a)cos(b x + a) +--R Type: Expression Integer +--E 70 + +--S 71 of 534 +t0612:= csc(a+b*x)*sec(a+b*x)^2 +--R +--R +--R 2 +--R (71) csc(b x + a)sec(b x + a) +--R Type: Expression Integer +--E 71 + +--S 72 of 534 +r0612:= -atanh(cos(a+b*x))/b+sec(a+b*x)/b +--R +--R +--R - atanh(cos(b x + a)) + sec(b x + a) +--R (72) ------------------------------------ +--R b +--R Type: Expression Integer +--E 72 + +--S 73 of 534 +a0612:= integrate(t0612,x) +--R +--R +--R sin(b x + a) +--R cos(b x + a)log(----------------) + cos(b x + a) + 1 +--R cos(b x + a) + 1 +--R (73) ---------------------------------------------------- +--R b cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 534 +m0612:= a0612-r0612 +--R +--R +--R (74) +--R sin(b x + a) +--R cos(b x + a)log(----------------) + cos(b x + a)atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R + +--R - cos(b x + a)sec(b x + a) + cos(b x + a) + 1 +--R / +--R b cos(b x + a) +--R Type: Expression Integer +--E 74 + +--S 75 of 534 +d0612:= D(m0612,x) +--R +--R +--R (75) +--R 4 2 +--R (- cos(b x + a) + cos(b x + a) )sec(b x + a)sin(b x + a)tan(b x + a) +--R + +--R 3 2 2 5 +--R (cos(b x + a) + cos(b x + a) - 1)sin(b x + a) + cos(b x + a) +--R + +--R 3 +--R - cos(b x + a) +--R / +--R 4 2 +--R (cos(b x + a) - cos(b x + a) )sin(b x + a) +--R Type: Expression Integer +--E 75 + +--S 76 of 534 +t0613:= csc(a+b*x)^2*sec(a+b*x) +--R +--R +--R 2 +--R (76) csc(b x + a) sec(b x + a) +--R Type: Expression Integer +--E 76 + +--S 77 of 534 +r0613:= atanh(sin(a+b*x))/b-csc(a+b*x)/b +--R +--R +--R atanh(sin(b x + a)) - csc(b x + a) +--R (77) ---------------------------------- +--R b +--R Type: Expression Integer +--E 77 + +--S 78 of 534 +a0613:= integrate(t0613,x) +--R +--R +--R (78) +--R sin(b x + a) + cos(b x + a) + 1 +--R sin(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - sin(b x + a)log(-------------------------------) - 1 +--R cos(b x + a) + 1 +--R / +--R b sin(b x + a) +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 534 +m0613:= a0613-r0613 +--R +--R +--R (79) +--R sin(b x + a) + cos(b x + a) + 1 +--R sin(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - sin(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R - sin(b x + a)atanh(sin(b x + a)) + csc(b x + a)sin(b x + a) - 1 +--R / +--R b sin(b x + a) +--R Type: Expression Integer +--E 79 + +--S 80 of 534 +d0613:= D(m0613,x) +--R +--R +--R (80) +--R 6 +--R (- cot(b x + a)csc(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2cos(b x + a) + 2)cot(b x + a)csc(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) + 2 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - 2cos(b x + a) - 1)cot(b x + a)csc(b x + a) +--R + +--R 3 2 +--R - 2cos(b x + a) - 2cos(b x + a) - cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R cos(b x + a) + 2cos(b x + a) + cos(b x + a) +--R / +--R 6 2 4 +--R sin(b x + a) + (- cos(b x + a) - 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 2 +--R (cos(b x + a) + 2cos(b x + a) + 1)sin(b x + a) +--R Type: Expression Integer +--E 80 + +--S 81 of 534 +t0614:= cos(a+b*x)*cot(a+b*x) +--R +--R +--R (81) cos(b x + a)cot(b x + a) +--R Type: Expression Integer +--E 81 + +--S 82 of 534 +r0614:= -(atanh(cos(a+b*x))-cos(a+b*x))/b +--R +--R +--R - atanh(cos(b x + a)) + cos(b x + a) +--R (82) ------------------------------------ +--R b +--R Type: Expression Integer +--E 82 + +--S 83 of 534 +a0614:= integrate(t0614,x) +--R +--R +--R sin(b x + a) +--R log(----------------) + cos(b x + a) +--R cos(b x + a) + 1 +--R (83) ------------------------------------ +--R b +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 534 +m0614:= a0614-r0614 +--R +--R +--R sin(b x + a) +--R log(----------------) + atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R (84) ------------------------------------------- +--R b +--R Type: Expression Integer +--E 84 + +--S 85 of 534 +d0614:= D(m0614,x) +--R +--R +--R 2 3 +--R cos(b x + a)sin(b x + a) + cos(b x + a) - cos(b x + a) +--R (85) -------------------------------------------------------- +--R 2 +--R (cos(b x + a) - 1)sin(b x + a) +--R Type: Expression Integer +--E 85 + +--S 86 of 534 +t0615:= cos(a+b*x)*cot(a+b*x)^3 +--R +--R +--R 3 +--R (86) cos(b x + a)cot(b x + a) +--R Type: Expression Integer +--E 86 + +--S 87 of 534 +r0615:= 3/2*atanh(cos(a+b*x))/b-3/2*cos(a+b*x)/b-1/2*cos(a+b*x)*cot(a+b*x)^2/b +--R +--R +--R 2 +--R 3atanh(cos(b x + a)) - cos(b x + a)cot(b x + a) - 3cos(b x + a) +--R (87) ---------------------------------------------------------------- +--R 2b +--R Type: Expression Integer +--E 87 + +--S 88 of 534 +a0615:= integrate(t0615,x) +--R +--R +--R (88) +--R 2 sin(b x + a) 3 +--R (- 3cos(b x + a) + 3)log(----------------) - 2cos(b x + a) +--R cos(b x + a) + 1 +--R + +--R 2 +--R - 2cos(b x + a) + 3cos(b x + a) + 2 +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 534 +m0615:= a0615-r0615 +--R +--R +--R (89) +--R 2 sin(b x + a) +--R (- 3cos(b x + a) + 3)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (- 3cos(b x + a) + 3)atanh(cos(b x + a)) +--R + +--R 3 2 3 +--R (cos(b x + a) - cos(b x + a))cot(b x + a) + cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) + 2 +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Expression Integer +--E 89 + +--S 90 of 534 +d0615:= D(m0615,x) +--R +--R +--R (90) +--R 4 2 2 4 +--R (- cos(b x + a) + 2cos(b x + a) - 1)cot(b x + a) - cos(b x + a) +--R + +--R 3 2 +--R - 3cos(b x + a) + 3cos(b x + a) + 3cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 3 3 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2cos(b x + a))cot(b x + a) +--R + +--R 5 3 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2cos(b x + a))cot(b x + a) +--R * +--R sin(b x + a) +--R + +--R 5 3 +--R - 3cos(b x + a) + 6cos(b x + a) - 3cos(b x + a) +--R / +--R 4 2 +--R (2cos(b x + a) - 4cos(b x + a) + 2)sin(b x + a) +--R Type: Expression Integer +--E 90 + +--S 91 of 534 +t0616:= sin(a+b*x)*tan(a+b*x) +--R +--R +--R (91) sin(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 91 + +--S 92 of 534 +r0616:= (atanh(sin(a+b*x))-sin(a+b*x))/b +--R +--R +--R atanh(sin(b x + a)) - sin(b x + a) +--R (92) ---------------------------------- +--R b +--R Type: Expression Integer +--E 92 + +--S 93 of 534 +a0616:= integrate(t0616,x) +--R +--R +--R (93) +--R sin(b x + a) + cos(b x + a) + 1 +--R log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - log(-------------------------------) - sin(b x + a) +--R cos(b x + a) + 1 +--R / +--R b +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 534 +m0616:= a0616-r0616 +--R +--R +--R (94) +--R sin(b x + a) + cos(b x + a) + 1 +--R log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - log(-------------------------------) - atanh(sin(b x + a)) +--R cos(b x + a) + 1 +--R / +--R b +--R Type: Expression Integer +--E 94 + +--S 95 of 534 +d0616:= D(m0616,x) +--R +--R +--R (95) +--R 4 2 2 +--R - 2sin(b x + a) + (- 2cos(b x + a) - cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 +--R - cos(b x + a) + cos(b x + a) +--R / +--R 4 2 2 +--R sin(b x + a) + (- cos(b x + a) - 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) + 2cos(b x + a) + 1 +--R Type: Expression Integer +--E 95 + +--S 96 of 534 +t0617:= sin(a+b*x)*tan(a+b*x)^3 +--R +--R +--R 3 +--R (96) sin(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 96 + +--S 97 of 534 +r0617:= -3/2*atanh(sin(a+b*x))/b+3/2*sin(a+b*x)/b+1/2*sin(a+b*x)*tan(a+b*x)^2/b +--R +--R +--R 2 +--R - 3atanh(sin(b x + a)) + sin(b x + a)tan(b x + a) + 3sin(b x + a) +--R (97) ------------------------------------------------------------------ +--R 2b +--R Type: Expression Integer +--E 97 + +--S 98 of 534 +a0617:= integrate(t0617,x) +--R +--R +--R (98) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (2cos(b x + a) + 1)sin(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 534 +m0617:= a0617-r0617 +--R +--R +--R (99) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R 3cos(b x + a) atanh(sin(b x + a)) +--R + +--R 2 2 +--R - cos(b x + a) sin(b x + a)tan(b x + a) +--R + +--R 2 +--R (- cos(b x + a) + 1)sin(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Expression Integer +--E 99 + +--S 100 of 534 +d0617:= D(m0617,x) +--R +--R +--R (100) +--R 3 5 +--R - 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 3 +--R (2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R (- 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) )sin(b x + a) +--R * +--R 3 +--R tan(b x + a) +--R + +--R 4 4 +--R - cos(b x + a) sin(b x + a) +--R + +--R 6 5 4 2 +--R (cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) )sin(b x + a) +--R + +--R 6 5 4 +--R - cos(b x + a) - 2cos(b x + a) - cos(b x + a) +--R * +--R 2 +--R tan(b x + a) +--R + +--R 3 5 +--R - 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 3 +--R (2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R (- 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) )sin(b x + a) +--R * +--R tan(b x + a) +--R + +--R 6 +--R 2sin(b x + a) +--R + +--R 4 3 2 +--R (- cos(b x + a) + 6cos(b x + a) - cos(b x + a) - 4cos(b x + a) - 4) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R cos(b x + a) + 8cos(b x + a) + 4cos(b x + a) - 8cos(b x + a) +--R + +--R 4cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) - 2cos(b x + a) - 3cos(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R / +--R 3 4 +--R 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 2 +--R (- 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 4cos(b x + a) + 2cos(b x + a) +--R Type: Expression Integer +--E 100 + +--S 101 of 534 +t0618:= sin(a+b*x)^2*tan(a+b*x)^2 +--R +--R +--R 2 2 +--R (101) sin(b x + a) tan(b x + a) +--R Type: Expression Integer +--E 101 + +--S 102 of 534 +r0618:= -3/2*x+3/2*tan(a+b*x)/b-1/2*sin(a+b*x)^2*tan(a+b*x)/b +--R +--R +--R 2 +--R (- sin(b x + a) + 3)tan(b x + a) - 3b x +--R (102) ---------------------------------------- +--R 2b +--R Type: Expression Integer +--E 102 + +--S 103 of 534 +a0618:= integrate(t0618,x) +--R +--R +--R 2 +--R (cos(b x + a) + 2)sin(b x + a) - 3b x cos(b x + a) +--R (103) --------------------------------------------------- +--R 2b cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 534 +m0618:= a0618-r0618 +--R +--R +--R (104) +--R 2 +--R (cos(b x + a)sin(b x + a) - 3cos(b x + a))tan(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2)sin(b x + a) +--R / +--R 2b cos(b x + a) +--R Type: Expression Integer +--E 104 + +--S 105 of 534 +d0618:= D(m0618,x) +--R +--R +--R (105) +--R 2 2 2 2 +--R (cos(b x + a) sin(b x + a) - 3cos(b x + a) )tan(b x + a) +--R + +--R 3 2 4 +--R 2cos(b x + a) sin(b x + a)tan(b x + a) + 2sin(b x + a) + cos(b x + a) +--R + +--R 2 +--R - cos(b x + a) +--R / +--R 2 +--R 2cos(b x + a) +--R Type: Expression Integer +--E 105 + +--S 106 of 534 +t0619:= sec(a+b*x)^2*tan(a+b*x)^n +--R +--R +--R 2 n +--R (106) sec(b x + a) tan(b x + a) +--R Type: Expression Integer +--E 106 + +--S 107 of 534 +r0619:= tan(a+b*x)^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R tan(b x + a) +--R (107) ----------------- +--R b n + b +--R Type: Expression Integer +--E 107 + +--S 108 of 534 +a0619:= integrate(t0619,x) +--R +--R +--R sin(b x + a) +--R n log(------------) +--R cos(b x + a) +--R sin(b x + a)%e +--R (108) --------------------------------- +--R (b n + b)cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 534 +m0619:= a0619-r0619 +--R +--R +--R sin(b x + a) +--R n log(------------) +--R cos(b x + a) n + 1 +--R sin(b x + a)%e - cos(b x + a)tan(b x + a) +--R (109) ----------------------------------------------------------------- +--R (b n + b)cos(b x + a) +--R Type: Expression Integer +--E 109 + +--S 110 of 534 +d0619:= D(m0619,x) +--R +--R +--R (110) +--R sin(b x + a) +--R n log(------------) +--R 2 2 cos(b x + a) +--R (sin(b x + a) + cos(b x + a) )%e +--R + +--R 2 2 2 n +--R (- cos(b x + a) tan(b x + a) - cos(b x + a) )tan(b x + a) +--R / +--R 2 +--R cos(b x + a) +--R Type: Expression Integer +--E 110 + +--S 111 of 534 +t0620:= sec(a+b*x)^n*tan(a+b*x)^3 +--R +--R +--R 3 n +--R (111) tan(b x + a) sec(b x + a) +--R Type: Expression Integer +--E 111 + +--S 112 of 534 +r0620:= -sec(a+b*x)^n/b/n+sec(a+b*x)^(2+n)/b/(2+n) +--R +--R +--R n + 2 n +--R n sec(b x + a) + (- n - 2)sec(b x + a) +--R (112) -------------------------------------------- +--R 2 +--R b n + 2b n +--R Type: Expression Integer +--E 112 + +--S 113 of 534 +a0620:= integrate(t0620,x) +--R +--R +--R 1 +--R n log(-------------) +--R 2 +--R cos(b x + a) +--R -------------------- +--R 2 2 +--R ((- n - 2)cos(b x + a) + n)%e +--R (113) -------------------------------------------------- +--R 2 2 +--R (b n + 2b n)cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 534 +m0620:= a0620-r0620 +--R +--R +--R (114) +--R 1 +--R n log(-------------) +--R 2 +--R cos(b x + a) +--R -------------------- +--R 2 2 +--R ((- n - 2)cos(b x + a) + n)%e +--R + +--R 2 n + 2 2 n +--R - n cos(b x + a) sec(b x + a) + (n + 2)cos(b x + a) sec(b x + a) +--R / +--R 2 2 +--R (b n + 2b n)cos(b x + a) +--R Type: Expression Integer +--E 114 + +--S 115 of 534 +d0620:= D(m0620,x) +--R +--R +--R (115) +--R 1 +--R n log(-------------) +--R 2 +--R cos(b x + a) +--R -------------------- +--R 2 2 +--R (- cos(b x + a) + 1)sin(b x + a)%e +--R + +--R 3 n + 1 +--R - cos(b x + a) sec(b x + a)tan(b x + a)sec(b x + a) +--R + +--R 3 n - 1 +--R cos(b x + a) sec(b x + a)tan(b x + a)sec(b x + a) +--R / +--R 3 +--R cos(b x + a) +--R Type: Expression Integer +--E 115 + +--S 116 of 534 +t0621:= sec(a+b*x)^4*tan(a+b*x)^n +--R +--R +--R 4 n +--R (116) sec(b x + a) tan(b x + a) +--R Type: Expression Integer +--E 116 + +--S 117 of 534 +r0621:= tan(a+b*x)^(1+n)/b/(1+n)+tan(a+b*x)^(3+n)/b/(3+n) +--R +--R +--R n + 3 n + 1 +--R (n + 1)tan(b x + a) + (n + 3)tan(b x + a) +--R (117) --------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Expression Integer +--E 117 + +--S 118 of 534 +a0621:= integrate(t0621,x) +--R +--R +--R sin(b x + a) +--R n log(------------) +--R 2 cos(b x + a) +--R (2cos(b x + a) + n + 1)sin(b x + a)%e +--R (118) --------------------------------------------------------- +--R 2 3 +--R (b n + 4b n + 3b)cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 534 +m0621:= a0621-r0621 +--R +--R +--R (119) +--R sin(b x + a) +--R n log(------------) +--R 2 cos(b x + a) +--R (2cos(b x + a) + n + 1)sin(b x + a)%e +--R + +--R 3 n + 3 +--R (- n - 1)cos(b x + a) tan(b x + a) +--R + +--R 3 n + 1 +--R (- n - 3)cos(b x + a) tan(b x + a) +--R / +--R 2 3 +--R (b n + 4b n + 3b)cos(b x + a) +--R Type: Expression Integer +--E 119 + +--S 120 of 534 +d0621:= D(m0621,x) +--R +--R +--R (120) +--R 2 2 4 +--R (2cos(b x + a) + n + 3)sin(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R (n + 1)cos(b x + a) +--R * +--R sin(b x + a) +--R n log(------------) +--R cos(b x + a) +--R %e +--R + +--R 4 2 4 +--R ((- n - 3)cos(b x + a) tan(b x + a) + (- n - 3)cos(b x + a) ) +--R * +--R n + 2 +--R tan(b x + a) +--R + +--R 4 2 4 n +--R ((- n - 3)cos(b x + a) tan(b x + a) + (- n - 3)cos(b x + a) )tan(b x + a) +--R / +--R 4 +--R (n + 3)cos(b x + a) +--R Type: Expression Integer +--E 120 + +--S 121 of 534 +t0622:= sec(a+b*x)*tan(a+b*x)^2 +--R +--R +--R 2 +--R (121) sec(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 121 + +--S 122 of 534 +r0622:= -1/2*atanh(sin(a+b*x))/b+1/2*sec(a+b*x)*tan(a+b*x)/b +--R +--R +--R - atanh(sin(b x + a)) + sec(b x + a)tan(b x + a) +--R (122) ------------------------------------------------ +--R 2b +--R Type: Expression Integer +--E 122 + +--S 123 of 534 +a0622:= integrate(t0622,x) +--R +--R +--R (123) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a) log(-------------------------------) + sin(b x + a) +--R cos(b x + a) + 1 +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 534 +m0622:= a0622-r0622 +--R +--R +--R (124) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 2 +--R cos(b x + a) atanh(sin(b x + a)) - cos(b x + a) sec(b x + a)tan(b x + a) +--R + +--R sin(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Expression Integer +--E 124 + +--S 125 of 534 +d0622:= D(m0622,x) +--R +--R +--R (125) +--R 3 4 +--R - 2cos(b x + a) sec(b x + a)sin(b x + a) +--R + +--R 5 4 3 +--R (2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) )sec(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (- 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) )sec(b x + a) +--R * +--R 2 +--R tan(b x + a) +--R + +--R 6 +--R 2sin(b x + a) +--R + +--R 3 3 2 +--R - cos(b x + a) sec(b x + a) + 2cos(b x + a) - cos(b x + a) +--R + +--R - 4cos(b x + a) - 4 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) )sec(b x + a) +--R + +--R 5 3 +--R 2cos(b x + a) - 4cos(b x + a) + 4cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (- cos(b x + a) - 2cos(b x + a) - cos(b x + a) )sec(b x + a) +--R + +--R 6 3 2 +--R cos(b x + a) + 2cos(b x + a) + cos(b x + a) +--R / +--R 3 4 +--R 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 2 +--R (- 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 4cos(b x + a) + 2cos(b x + a) +--R Type: Expression Integer +--E 125 + +--S 126 of 534 +t0623:= sec(1/2*x)^3*tan(1/2*x)^2 +--R +--R +--R x 3 x 2 +--R (126) sec(-) tan(-) +--R 2 2 +--R Type: Expression Integer +--E 126 + +--S 127 of 534 +r0623:= -1/4*atanh(sin(1/2*x))+1/4*sec(1/2*x)*tan(1/2*x)+1/2*sec(1/2*x)*tan(1/2*x)^3 +--R +--R +--R x x x 3 x x +--R - atanh(sin(-)) + 2sec(-)tan(-) + sec(-)tan(-) +--R 2 2 2 2 2 +--R (127) ----------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 127 + +--S 128 of 534 +a0623:= integrate(t0623,x) +--R +--R +--R (128) +--R x x x x +--R sin(-) + cos(-) + 1 sin(-) - cos(-) - 1 +--R x 4 2 2 x 4 2 2 +--R - cos(-) log(-------------------) + cos(-) log(-------------------) +--R 2 x 2 x +--R cos(-) + 1 cos(-) + 1 +--R 2 2 +--R + +--R x 2 x +--R (- cos(-) + 2)sin(-) +--R 2 2 +--R / +--R x 4 +--R 4cos(-) +--R 2 +--R Type: Union(Expression Integer,...) +--E 128 + +--S 129 of 534 +m0623:= a0623-r0623 +--R +--R +--R (129) +--R x x x x +--R sin(-) + cos(-) + 1 sin(-) - cos(-) - 1 +--R x 4 2 2 x 4 2 2 +--R - cos(-) log(-------------------) + cos(-) log(-------------------) +--R 2 x 2 x +--R cos(-) + 1 cos(-) + 1 +--R 2 2 +--R + +--R x 4 x x 4 x x 3 x 4 x x +--R cos(-) atanh(sin(-)) - 2cos(-) sec(-)tan(-) - cos(-) sec(-)tan(-) +--R 2 2 2 2 2 2 2 2 +--R + +--R x 2 x +--R (- cos(-) + 2)sin(-) +--R 2 2 +--R / +--R x 4 +--R 4cos(-) +--R 2 +--R Type: Expression Integer +--E 129 + +--S 130 of 534 +d0623:= D(m0623,x) +--R +--R +--R (130) +--R x 5 x x 4 +--R - 8cos(-) sec(-)sin(-) +--R 2 2 2 +--R + +--R x 7 x 6 x 5 x x 2 +--R (8cos(-) + 16cos(-) + 16cos(-) )sec(-)sin(-) +--R 2 2 2 2 2 +--R + +--R x 7 x 6 x 5 x +--R (- 8cos(-) - 16cos(-) - 8cos(-) )sec(-) +--R 2 2 2 2 +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R x 5 x x 4 +--R - 8cos(-) sec(-)sin(-) +--R 2 2 2 +--R + +--R x 7 x 6 x 5 x x 2 +--R (8cos(-) + 16cos(-) + 16cos(-) )sec(-)sin(-) +--R 2 2 2 2 2 +--R + +--R x 7 x 6 x 5 x +--R (- 8cos(-) - 16cos(-) - 8cos(-) )sec(-) +--R 2 2 2 2 +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R x 2 x 6 +--R (- 2cos(-) + 8)sin(-) +--R 2 2 +--R + +--R x 5 x x 5 x 4 x 3 x 2 x +--R - cos(-) sec(-) + 2cos(-) + cos(-) + 4cos(-) - 2cos(-) - 16cos(-) +--R 2 2 2 2 2 2 2 +--R + +--R - 16 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 7 x 6 x 5 x x 7 x 6 +--R (cos(-) + 2cos(-) + 2cos(-) )sec(-) + 2cos(-) + 2cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 3 x 2 x +--R - 2cos(-) - 8cos(-) + 2cos(-) + 16cos(-) + 8 +--R 2 2 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 7 x 6 x 5 x x 8 x 6 x 5 +--R (- cos(-) - 2cos(-) - cos(-) )sec(-) + cos(-) - 2cos(-) - 2cos(-) +--R 2 2 2 2 2 2 2 +--R + +--R x 4 x 3 x 2 +--R cos(-) + 4cos(-) + 2cos(-) +--R 2 2 2 +--R / +--R x 5 x 4 x 7 x 6 x 5 x 2 x 7 +--R 8cos(-) sin(-) + (- 8cos(-) - 16cos(-) - 16cos(-) )sin(-) + 8cos(-) +--R 2 2 2 2 2 2 2 +--R + +--R x 6 x 5 +--R 16cos(-) + 8cos(-) +--R 2 2 +--R Type: Expression Integer +--E 130 + +--S 131 of 534 +t0624:= cot(a+b*x)^n*csc(a+b*x)^2 +--R +--R +--R 2 n +--R (131) csc(b x + a) cot(b x + a) +--R Type: Expression Integer +--E 131 + +--S 132 of 534 +r0624:= -cot(a+b*x)^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R cot(b x + a) +--R (132) - ----------------- +--R b n + b +--R Type: Expression Integer +--E 132 + +--S 133 of 534 +a0624:= integrate(t0624,x) +--R +--R +--R cos(b x + a) +--R n log(------------) +--R sin(b x + a) +--R cos(b x + a)%e +--R (133) - --------------------------------- +--R (b n + b)sin(b x + a) +--R Type: Union(Expression Integer,...) +--E 133 + +--S 134 of 534 +m0624:= a0624-r0624 +--R +--R +--R cos(b x + a) +--R n log(------------) +--R sin(b x + a) n + 1 +--R - cos(b x + a)%e + sin(b x + a)cot(b x + a) +--R (134) ------------------------------------------------------------------- +--R (b n + b)sin(b x + a) +--R Type: Expression Integer +--E 134 + +--S 135 of 534 +d0624:= D(m0624,x) +--R +--R +--R (135) +--R cos(b x + a) +--R n log(------------) +--R 2 2 sin(b x + a) +--R (sin(b x + a) + cos(b x + a) )%e +--R + +--R 2 2 n +--R (- cot(b x + a) - 1)sin(b x + a) cot(b x + a) +--R / +--R 2 +--R sin(b x + a) +--R Type: Expression Integer +--E 135 + +--S 136 of 534 +t0625:= cot(a+b*x)^3*csc(a+b*x)^n +--R +--R +--R 3 n +--R (136) cot(b x + a) csc(b x + a) +--R Type: Expression Integer +--E 136 + +--S 137 of 534 +r0625:= csc(a+b*x)^n/b/n-csc(a+b*x)^(2+n)/b/(2+n) +--R +--R +--R n + 2 n +--R - n csc(b x + a) + (n + 2)csc(b x + a) +--R (137) -------------------------------------------- +--R 2 +--R b n + 2b n +--R Type: Expression Integer +--E 137 + +--S 138 of 534 +a0625:= integrate(t0625,x) +--R +--R +--R 1 +--R n log(- -----------------) +--R 2 +--R cos(b x + a) - 1 +--R -------------------------- +--R 2 2 +--R ((n + 2)cos(b x + a) - 2)%e +--R (138) ------------------------------------------------------ +--R 2 2 2 +--R (b n + 2b n)cos(b x + a) - b n - 2b n +--R Type: Union(Expression Integer,...) +--E 138 + +--S 139 of 534 +m0625:= a0625-r0625 +--R +--R +--R (139) +--R 1 +--R n log(- -----------------) +--R 2 +--R cos(b x + a) - 1 +--R -------------------------- +--R 2 2 +--R ((n + 2)cos(b x + a) - 2)%e +--R + +--R 2 n + 2 +--R (n cos(b x + a) - n)csc(b x + a) +--R + +--R 2 n +--R ((- n - 2)cos(b x + a) + n + 2)csc(b x + a) +--R / +--R 2 2 2 +--R (b n + 2b n)cos(b x + a) - b n - 2b n +--R Type: Expression Integer +--E 139 + +--S 140 of 534 +d0625:= D(m0625,x) +--R +--R +--R (140) +--R 1 +--R n log(- -----------------) +--R 2 +--R cos(b x + a) - 1 +--R -------------------------- +--R 3 2 +--R cos(b x + a) sin(b x + a)%e +--R + +--R 4 2 +--R (- cos(b x + a) + 2cos(b x + a) - 1)cot(b x + a)csc(b x + a) +--R * +--R n + 1 +--R csc(b x + a) +--R + +--R 4 2 +--R (cos(b x + a) - 2cos(b x + a) + 1)cot(b x + a)csc(b x + a) +--R * +--R n - 1 +--R csc(b x + a) +--R / +--R 4 2 +--R cos(b x + a) - 2cos(b x + a) + 1 +--R Type: Expression Integer +--E 140 + +--S 141 of 534 +t0626:= cot(a+b*x)^2*csc(a+b*x) +--R +--R +--R 2 +--R (141) cot(b x + a) csc(b x + a) +--R Type: Expression Integer +--E 141 + +--S 142 of 534 +r0626:= 1/2*atanh(cos(a+b*x))/b-1/2*cot(a+b*x)*csc(a+b*x)/b +--R +--R +--R atanh(cos(b x + a)) - cot(b x + a)csc(b x + a) +--R (142) ---------------------------------------------- +--R 2b +--R Type: Expression Integer +--E 142 + +--S 143 of 534 +a0626:= integrate(t0626,x) +--R +--R +--R 2 sin(b x + a) +--R (- cos(b x + a) + 1)log(----------------) + cos(b x + a) +--R cos(b x + a) + 1 +--R (143) --------------------------------------------------------- +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Union(Expression Integer,...) +--E 143 + +--S 144 of 534 +m0626:= a0626-r0626 +--R +--R +--R (144) +--R 2 sin(b x + a) +--R (- cos(b x + a) + 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (- cos(b x + a) + 1)atanh(cos(b x + a)) +--R + +--R 2 +--R (cos(b x + a) - 1)cot(b x + a)csc(b x + a) + cos(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Expression Integer +--E 144 + +--S 145 of 534 +d0626:= D(m0626,x) +--R +--R +--R (145) +--R 3 2 2 +--R (- cos(b x + a) + cos(b x + a) + cos(b x + a) + 1)sin(b x + a) +--R + +--R 4 2 2 4 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2)cot(b x + a) - cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) - 1 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 5 3 +--R - cos(b x + a) + 2cos(b x + a) - cos(b x + a) +--R / +--R 4 2 +--R (2cos(b x + a) - 4cos(b x + a) + 2)sin(b x + a) +--R Type: Expression Integer +--E 145 + +--S 146 of 534 +t0627:= cot(a+b*x)^2*csc(a+b*x)^3 +--R +--R +--R 2 3 +--R (146) cot(b x + a) csc(b x + a) +--R Type: Expression Integer +--E 146 + +--S 147 of 534 +r0627:= 1/8*atanh(cos(a+b*x))/b-1/8*cot(a+b*x)*csc(a+b*x)/b-1/4*cot(a+b*x)^3*csc(a+b*x)/b +--R +--R +--R 3 +--R atanh(cos(b x + a)) + (- 2cot(b x + a) - cot(b x + a))csc(b x + a) +--R (147) ------------------------------------------------------------------- +--R 8b +--R Type: Expression Integer +--E 147 + +--S 148 of 534 +a0627:= integrate(t0627,x) +--R +--R +--R (148) +--R 4 2 sin(b x + a) +--R (- cos(b x + a) + 2cos(b x + a) - 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 3 +--R - cos(b x + a) - cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Union(Expression Integer,...) +--E 148 + +--S 149 of 534 +m0627:= a0627-r0627 +--R +--R +--R (149) +--R 4 2 sin(b x + a) +--R (- cos(b x + a) + 2cos(b x + a) - 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 4 2 +--R (- cos(b x + a) + 2cos(b x + a) - 1)atanh(cos(b x + a)) +--R + +--R 4 2 3 +--R (2cos(b x + a) - 4cos(b x + a) + 2)cot(b x + a) +--R + +--R 4 2 +--R (cos(b x + a) - 2cos(b x + a) + 1)cot(b x + a) +--R * +--R csc(b x + a) +--R + +--R 3 +--R - cos(b x + a) - cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Expression Integer +--E 149 + +--S 150 of 534 +d0627:= D(m0627,x) +--R +--R +--R (150) +--R 5 4 3 2 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) - 6cos(b x + a) +--R + +--R - cos(b x + a) - 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 4 2 +--R (- 8cos(b x + a) + 24cos(b x + a) - 24cos(b x + a) + 8) +--R * +--R 4 +--R cot(b x + a) +--R + +--R 6 4 2 +--R (- 8cos(b x + a) + 24cos(b x + a) - 24cos(b x + a) + 8) +--R * +--R 2 +--R cot(b x + a) +--R + +--R 6 4 2 +--R - cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) + 1 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 7 5 3 +--R - cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) + cos(b x + a) +--R / +--R 6 4 2 +--R (8cos(b x + a) - 24cos(b x + a) + 24cos(b x + a) - 8)sin(b x + a) +--R Type: Expression Integer +--E 150 + +--S 151 of 534 +t0628:= cot(a+b*x)^4*csc(a+b*x) +--R +--R +--R 4 +--R (151) cot(b x + a) csc(b x + a) +--R Type: Expression Integer +--E 151 + +--S 152 of 534 +r0628:= -3/8*atanh(cos(a+b*x))/b+3/8*cot(a+b*x)*csc(a+b*x)/b-1/4*cot(a+b*x)^3*csc(a+b*x)/b +--R +--R +--R (152) +--R 3 +--R - 3atanh(cos(b x + a)) + (- 2cot(b x + a) + 3cot(b x + a))csc(b x + a) +--R ----------------------------------------------------------------------- +--R 8b +--R Type: Expression Integer +--E 152 + +--S 153 of 534 +a0628:= integrate(t0628,x) +--R +--R +--R (153) +--R 4 2 sin(b x + a) +--R (3cos(b x + a) - 6cos(b x + a) + 3)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 3 +--R - 5cos(b x + a) + 3cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Union(Expression Integer,...) +--E 153 + +--S 154 of 534 +m0628:= a0628-r0628 +--R +--R +--R (154) +--R 4 2 sin(b x + a) +--R (3cos(b x + a) - 6cos(b x + a) + 3)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 4 2 +--R (3cos(b x + a) - 6cos(b x + a) + 3)atanh(cos(b x + a)) +--R + +--R 4 2 3 +--R (2cos(b x + a) - 4cos(b x + a) + 2)cot(b x + a) +--R + +--R 4 2 +--R (- 3cos(b x + a) + 6cos(b x + a) - 3)cot(b x + a) +--R * +--R csc(b x + a) +--R + +--R 3 +--R - 5cos(b x + a) + 3cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Expression Integer +--E 154 + +--S 155 of 534 +d0628:= D(m0628,x) +--R +--R +--R (155) +--R 5 4 3 2 +--R 3cos(b x + a) - 5cos(b x + a) - 6cos(b x + a) - 6cos(b x + a) +--R + +--R 3cos(b x + a) + 3 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 4 2 +--R (- 8cos(b x + a) + 24cos(b x + a) - 24cos(b x + a) + 8) +--R * +--R 4 +--R cot(b x + a) +--R + +--R 6 4 2 +--R 3cos(b x + a) - 9cos(b x + a) + 9cos(b x + a) - 3 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 7 5 3 +--R 3cos(b x + a) - 9cos(b x + a) + 9cos(b x + a) - 3cos(b x + a) +--R / +--R 6 4 2 +--R (8cos(b x + a) - 24cos(b x + a) + 24cos(b x + a) - 8)sin(b x + a) +--R Type: Expression Integer +--E 155 + +--S 156 of 534 +t0629:= cot(3*x)^4*csc(3*x) +--R +--R +--R 4 +--R (156) cot(3x) csc(3x) +--R Type: Expression Integer +--E 156 + +--S 157 of 534 +r0629:= -1/8*atanh(cos(3*x))+1/8*cot(3*x)*csc(3*x)-1/12*cot(3*x)^3*csc(3*x) +--R +--R +--R 3 +--R - 3atanh(cos(3x)) + (- 2cot(3x) + 3cot(3x))csc(3x) +--R (157) --------------------------------------------------- +--R 24 +--R Type: Expression Integer +--E 157 + +--S 158 of 534 +a0629:= integrate(t0629,x) +--R +--R +--R 4 2 sin(3x) 3 +--R (3cos(3x) - 6cos(3x) + 3)log(-----------) - 5cos(3x) + 3cos(3x) +--R cos(3x) + 1 +--R (158) ------------------------------------------------------------------ +--R 4 2 +--R 24cos(3x) - 48cos(3x) + 24 +--R Type: Union(Expression Integer,...) +--E 158 + +--S 159 of 534 +m0629:= a0629-r0629 +--R +--R +--R (159) +--R 4 2 sin(3x) +--R (3cos(3x) - 6cos(3x) + 3)log(-----------) +--R cos(3x) + 1 +--R + +--R 4 2 +--R (3cos(3x) - 6cos(3x) + 3)atanh(cos(3x)) +--R + +--R 4 2 3 +--R (2cos(3x) - 4cos(3x) + 2)cot(3x) +--R + +--R 4 2 +--R (- 3cos(3x) + 6cos(3x) - 3)cot(3x) +--R * +--R csc(3x) +--R + +--R 3 +--R - 5cos(3x) + 3cos(3x) +--R / +--R 4 2 +--R 24cos(3x) - 48cos(3x) + 24 +--R Type: Expression Integer +--E 159 + +--S 160 of 534 +d0629:= D(m0629,x) +--R +--R +--R (160) +--R 5 4 3 2 2 +--R (3cos(3x) - 5cos(3x) - 6cos(3x) - 6cos(3x) + 3cos(3x) + 3)sin(3x) +--R + +--R 6 4 2 4 6 +--R (- 8cos(3x) + 24cos(3x) - 24cos(3x) + 8)cot(3x) + 3cos(3x) +--R + +--R 4 2 +--R - 9cos(3x) + 9cos(3x) - 3 +--R * +--R csc(3x)sin(3x) +--R + +--R 7 5 3 +--R 3cos(3x) - 9cos(3x) + 9cos(3x) - 3cos(3x) +--R / +--R 6 4 2 +--R (8cos(3x) - 24cos(3x) + 24cos(3x) - 8)sin(3x) +--R Type: Expression Integer +--E 160 + +--S 161 of 534 +t0630:= cot(x)^4*csc(x)^3 +--R +--R +--R 4 3 +--R (161) cot(x) csc(x) +--R Type: Expression Integer +--E 161 + +--S 162 of 534 +r0630:= -1/16*atanh(cos(x))+1/16*cot(x)*csc(x)-1/24*cot(x)^3*csc(x)-1/6*cot(x)^5*csc(x) +--R +--R +--R 5 3 +--R - 3atanh(cos(x)) + (- 8cot(x) - 2cot(x) + 3cot(x))csc(x) +--R (162) ---------------------------------------------------------- +--R 48 +--R Type: Expression Integer +--E 162 + +--S 163 of 534 +a0630:= integrate(t0630,x) +--R +--R +--R (163) +--R 6 4 2 sin(x) 5 3 +--R (3cos(x) - 9cos(x) + 9cos(x) - 3)log(----------) + 3cos(x) + 8cos(x) +--R cos(x) + 1 +--R + +--R - 3cos(x) +--R / +--R 6 4 2 +--R 48cos(x) - 144cos(x) + 144cos(x) - 48 +--R Type: Union(Expression Integer,...) +--E 163 + +--S 164 of 534 +m0630:= a0630-r0630 +--R +--R +--R (164) +--R 6 4 2 sin(x) +--R (3cos(x) - 9cos(x) + 9cos(x) - 3)log(----------) +--R cos(x) + 1 +--R + +--R 6 4 2 +--R (3cos(x) - 9cos(x) + 9cos(x) - 3)atanh(cos(x)) +--R + +--R 6 4 2 5 +--R (8cos(x) - 24cos(x) + 24cos(x) - 8)cot(x) +--R + +--R 6 4 2 3 +--R (2cos(x) - 6cos(x) + 6cos(x) - 2)cot(x) +--R + +--R 6 4 2 +--R (- 3cos(x) + 9cos(x) - 9cos(x) + 3)cot(x) +--R * +--R csc(x) +--R + +--R 5 3 +--R 3cos(x) + 8cos(x) - 3cos(x) +--R / +--R 6 4 2 +--R 48cos(x) - 144cos(x) + 144cos(x) - 48 +--R Type: Expression Integer +--E 164 + +--S 165 of 534 +d0630:= D(m0630,x) +--R +--R +--R (165) +--R 7 6 5 4 3 2 +--R cos(x) + cos(x) - 3cos(x) + 13cos(x) + 3cos(x) + 3cos(x) +--R + +--R - cos(x) - 1 +--R * +--R 2 +--R sin(x) +--R + +--R 8 6 4 2 6 +--R (- 16cos(x) + 64cos(x) - 96cos(x) + 64cos(x) - 16)cot(x) +--R + +--R 8 6 4 2 4 +--R (- 16cos(x) + 64cos(x) - 96cos(x) + 64cos(x) - 16)cot(x) +--R + +--R 8 6 4 2 +--R cos(x) - 4cos(x) + 6cos(x) - 4cos(x) + 1 +--R * +--R csc(x)sin(x) +--R + +--R 9 7 5 3 +--R cos(x) - 4cos(x) + 6cos(x) - 4cos(x) + cos(x) +--R / +--R 8 6 4 2 +--R (16cos(x) - 64cos(x) + 96cos(x) - 64cos(x) + 16)sin(x) +--R Type: Expression Integer +--E 165 + +--S 166 of 534 +t0631:= cos(x)^(2/3)/sin(x)^(8/3) +--R +--R +--R 3+------+2 +--R \|cos(x) +--R (166) ----------------- +--R 2 3+------+2 +--R sin(x) \|sin(x) +--R Type: Expression Integer +--E 166 + +--S 167 of 534 +r0631:= -3/5*cos(x)^(5/3)/sin(x)^(5/3) +--R +--R +--R 3+------+2 +--R 3cos(x)\|cos(x) +--R (167) - ----------------- +--R 3+------+2 +--R 5sin(x)\|sin(x) +--R Type: Expression Integer +--E 167 + +--S 168 of 534 +--a0631:= integrate(t0631,x) +--E 168 + +--S 169 of 534 +--m0631:= a0631-r0631 +--E 169 + +--S 170 of 534 +--d0631:= D(m0631,x) +--E 170 + +--S 171 of 534 +t0632:= sin(x)^(2/3)/cos(x)^(8/3) +--R +--R +--R 3+------+2 +--R \|sin(x) +--R (168) ----------------- +--R 2 3+------+2 +--R cos(x) \|cos(x) +--R Type: Expression Integer +--E 171 + +--S 172 of 534 +r0632:= 3/5*sin(x)^(5/3)/cos(x)^(5/3) +--R +--R +--R 3+------+2 +--R 3sin(x)\|sin(x) +--R (169) ----------------- +--R 3+------+2 +--R 5cos(x)\|cos(x) +--R Type: Expression Integer +--E 172 + +--S 173 of 534 +--a0632:= integrate(t0632,x) +--E 173 + +--S 174 of 534 +--m0632:= a0632-r0632 +--E 174 + +--S 175 of 534 +--d0632:= D(m0632,x) +--E 175 + +--S 176 of 534 +t0633:= sin(x)^(1/2)/cos(x)^(1/2) +--R +--R +--R +------+ +--R \|sin(x) +--R (170) --------- +--R +------+ +--R \|cos(x) +--R Type: Expression Integer +--E 176 + +--S 177 of 534 +r0633:= -1/2*atan(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+1/2*atan(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+1/4*log(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2)-1/4*log(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2) +--R +--R +--R (171) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - \|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R \|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +-+ \|2 \|sin(x) - \|cos(x) +--R 2\|2 atan(-------------------------) + 2\|2 atan(-------------------------) +--R +------+ +------+ +--R \|cos(x) \|cos(x) +--R / +--R 4 +--R Type: Expression Integer +--E 177 + +--S 178 of 534 +a0633:= integrate(t0633,x) +--R +--R +--R >> Error detected within library code: +--R Imaginary part is nonzero. Cannot retract. +--R +--R Continuing to read the file... +--R +--E 178 + +--S 179 of 534 +m0633:= a0633-r0633 +--R +--R +--R (172) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R \|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - \|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +--R - 2\|2 atan(-------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) - \|cos(x) +--R - 2\|2 atan(-------------------------) + 4a0633 +--R +------+ +--R \|cos(x) +--R / +--R 4 +--R Type: Expression Integer +--E 179 + +--S 180 of 534 +d0633:= D(m0633,x) +--R +--R +--R (173) +--R 2 2 +--R (- 3cos(x)sin(x) - cos(x) )tan(x) +--R + +--R 2 2 2 +--R (sin(x) - 2cos(x)sin(x) - cos(x) )tan(x) + 3sin(x) - cos(x)sin(x) +--R * +--R +------+ +------+ +--R \|cos(x) \|sin(x) +--R / +--R 2 2 2 2 +--R 2cos(x) sin(x)tan(x) + 4cos(x) sin(x)tan(x) - 4cos(x)sin(x) +--R + +--R 2 +--R 2cos(x) sin(x) +--R Type: Expression Integer +--E 180 + +--S 181 of 534 +t0634:= sin(x)^(5/2)/cos(x)^(1/2) +--R +--R +--R 2 +------+ +--R sin(x) \|sin(x) +--R (174) ---------------- +--R +------+ +--R \|cos(x) +--R Type: Expression Integer +--E 181 + +--S 182 of 534 +r0634:= -3/8*atan(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+3/8*atan(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+3/16*log(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2)-3/16*log(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2)-1/2*cos(x)^(1/2)*sin(x)^(3/2) +--R +--R +--R (175) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - 3\|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R 3\|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +--R 6\|2 atan(-------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) - \|cos(x) +------+ +------+ +--R 6\|2 atan(-------------------------) - 8sin(x)\|cos(x) \|sin(x) +--R +------+ +--R \|cos(x) +--R / +--R 16 +--R Type: Expression Integer +--E 182 + +--S 183 of 534 +a0634:= integrate(t0634,x) +--R +--R +--R >> Error detected within library code: +--R Imaginary part is nonzero. Cannot retract. +--R +--R Continuing to read the file... +--R +--E 183 + +--S 184 of 534 +m0634:= a0634-r0634 +--R +--R +--R (176) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R 3\|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - 3\|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +--R - 6\|2 atan(-------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) - \|cos(x) +------+ +------+ +--R - 6\|2 atan(-------------------------) + 8sin(x)\|cos(x) \|sin(x) +--R +------+ +--R \|cos(x) +--R + +--R 16a0634 +--R / +--R 16 +--R Type: Expression Integer +--E 184 + +--S 185 of 534 +d0634:= D(m0634,x) +--R +--R +--R (177) +--R 3 3 2 2 +--R (- 2cos(x)sin(x) + (6cos(x) - 9cos(x))sin(x) - 3cos(x) )tan(x) +--R + +--R 3 2 3 2 +--R (- 4cos(x)sin(x) + 3sin(x) + (12cos(x) - 6cos(x))sin(x) - 3cos(x) ) +--R * +--R tan(x) +--R + +--R 4 3 2 2 +--R 4sin(x) - 2cos(x)sin(x) + (- 12cos(x) + 9)sin(x) +--R + +--R 3 +--R (6cos(x) - 3cos(x))sin(x) +--R / +--R 2 +------+ +------+ +--R (8cos(x)tan(x) + 16cos(x)tan(x) - 16sin(x) + 8cos(x))\|cos(x) \|sin(x) +--R Type: Expression Integer +--E 185 + +--S 186 of 534 +t0635:= sec(x)^(3/2)*sin(x) +--R +--R +--R +------+ +--R (178) sec(x)sin(x)\|sec(x) +--R Type: Expression Integer +--E 186 + +--S 187 of 534 +r0635:= 2*sec(x)^(1/2) +--R +--R +--R +------+ +--R (179) 2\|sec(x) +--R Type: Expression Integer +--E 187 + +--S 188 of 534 +a0635:= integrate(t0635,x) +--R +--R +--R +-------+ +--R 2 | 1 +--R (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (180) ------------------------ +--R 2 +--R 2cos(x) +--R Type: Union(Expression Integer,...) +--E 188 + +--S 189 of 534 +m0635:= a0635-r0635 +--R +--R +--R +-------+ +--R 2 +------+ 2 | 1 +--R - 4cos(x) \|sec(x) + (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (181) ---------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Expression Integer +--E 189 + +--S 190 of 534 +d0635:= D(m0635,x) +--R +--R +--R +-------+3 +--R 2 +------+ 5 | 1 +--R (2cos(x) - 5)sin(x)\|sec(x) - 4cos(x) sec(x)tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R (182) --------------------------------------------------------------- +--R +-------+3 +--R 5 | 1 +------+ +--R 4cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression Integer +--E 190 + +--S 191 of 534 +t0636:= sec(x)^(5/2)*sin(x) +--R +--R +--R 2 +------+ +--R (183) sec(x) sin(x)\|sec(x) +--R Type: Expression Integer +--E 191 + +--S 192 of 534 +r0636:= 2/3*sec(x)^(3/2) +--R +--R +--R +------+ +--R 2sec(x)\|sec(x) +--R (184) ---------------- +--R 3 +--R Type: Expression Integer +--E 192 + +--S 193 of 534 +a0636:= integrate(t0636,x) +--R +--R +--R +-------+ +--R 2 | 1 +--R (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (185) ------------------------ +--R 3 +--R 6cos(x) +--R Type: Union(Expression Integer,...) +--E 193 + +--S 194 of 534 +m0636:= a0636-r0636 +--R +--R +--R +-------+ +--R 3 +------+ 2 | 1 +--R - 4cos(x) sec(x)\|sec(x) + (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (186) ---------------------------------------------------- +--R 3 +--R 6cos(x) +--R Type: Expression Integer +--E 194 + +--S 195 of 534 +d0636:= D(m0636,x) +--R +--R +--R +-------+3 +--R 2 +------+ 6 2 | 1 +--R (6cos(x) - 7)sin(x)\|sec(x) - 12cos(x) sec(x) tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R (187) ----------------------------------------------------------------- +--R +-------+3 +--R 6 | 1 +------+ +--R 12cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression Integer +--E 195 + +--S 196 of 534 +t0637:= sec(x)^(5/2)*sin(x)^3 +--R +--R +--R 2 3 +------+ +--R (188) sec(x) sin(x) \|sec(x) +--R Type: Expression Integer +--E 196 + +--S 197 of 534 +r0637:= 2/sec(x)^(1/2)+2/3*sec(x)^(3/2) +--R +--R +--R 2 +--R 2sec(x) + 6 +--R (189) ------------ +--R +------+ +--R 3\|sec(x) +--R Type: Expression Integer +--E 197 + +--S 198 of 534 +a0637:= integrate(t0637,x) +--R +--R +--R +-------+ +--R 2 | 1 +--R (6cos(x) + 2) |------- +--R 4| 2 +--R \|cos(x) +--R (190) ------------------------ +--R 3cos(x) +--R Type: Union(Expression Integer,...) +--E 198 + +--S 199 of 534 +m0637:= a0637-r0637 +--R +--R +--R +-------+ +--R 2 | 1 +------+ 2 +--R (6cos(x) + 2) |------- \|sec(x) - 2cos(x)sec(x) - 6cos(x) +--R 4| 2 +--R \|cos(x) +--R (191) ------------------------------------------------------------ +--R +------+ +--R 3cos(x)\|sec(x) +--R Type: Expression Integer +--E 199 + +--S 200 of 534 +d0637:= D(m0637,x) +--R +--R +--R (192) +--R 2 +------+ +--R (- cos(x) + 1)sin(x)\|sec(x) +--R + +--R +-------+3 +--R 4 2 4 | 1 +--R (- cos(x) sec(x) + cos(x) )tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R / +--R +-------+3 +--R 4 | 1 +------+ +--R cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression Integer +--E 200 + +--S 201 of 534 +t0638:= sec(x)^(9/2)*sin(x)^3 +--R +--R +--R 4 3 +------+ +--R (193) sec(x) sin(x) \|sec(x) +--R Type: Expression Integer +--E 201 + +--S 202 of 534 +r0638:= -2/3*sec(x)^(3/2)+2/7*sec(x)^(7/2) +--R +--R +--R 3 +------+ +--R (6sec(x) - 14sec(x))\|sec(x) +--R (194) ------------------------------ +--R 21 +--R Type: Expression Integer +--E 202 + +--S 203 of 534 +a0638:= integrate(t0638,x) +--R +--R +--R +-------+ +--R 4 2 | 1 +--R (- 14cos(x) + 13cos(x) - 3) |------- +--R 4| 2 +--R \|cos(x) +--R (195) --------------------------------------- +--R 5 +--R 42cos(x) +--R Type: Union(Expression Integer,...) +--E 203 + +--S 204 of 534 +m0638:= a0638-r0638 +--R +--R +--R (196) +--R 5 3 5 +------+ +--R (- 12cos(x) sec(x) + 28cos(x) sec(x))\|sec(x) +--R + +--R +-------+ +--R 4 2 | 1 +--R (- 14cos(x) + 13cos(x) - 3) |------- +--R 4| 2 +--R \|cos(x) +--R / +--R 5 +--R 42cos(x) +--R Type: Expression Integer +--E 204 + +--S 205 of 534 +d0638:= D(m0638,x) +--R +--R +--R (197) +--R 4 2 +------+ +--R (- 42cos(x) + 91cos(x) - 33)sin(x)\|sec(x) +--R + +--R +-------+3 +--R 8 4 8 2 | 1 +--R (- 84cos(x) sec(x) + 84cos(x) sec(x) )tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R / +--R +-------+3 +--R 8 | 1 +------+ +--R 84cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression Integer +--E 205 + +--S 206 of 534 +t0639:= x*sin(a+b*x)^2*cos(a+b*x)^2 +--R +--R +--R 2 2 +--R (198) x cos(b x + a) sin(b x + a) +--R Type: Expression Integer +--E 206 + +--S 207 of 534 +r0639:= -1/128*(-8*b^2*x^2+cos(4*a+4*b*x)+4*x*sin(4*a+4*b*x)*b)/b^2 +--R +--R +--R 2 2 +--R - 4b x sin(4b x + 4a) - cos(4b x + 4a) + 8b x +--R (199) ---------------------------------------------- +--R 2 +--R 128b +--R Type: Expression Integer +--E 207 + +--S 208 of 534 +a0639:= integrate(t0639,x) +--R +--R +--R (200) +--R 3 4 +--R (- 4b x cos(b x + a) + 2b x cos(b x + a))sin(b x + a) - cos(b x + a) +--R + +--R 2 2 2 +--R cos(b x + a) + b x +--R / +--R 2 +--R 16b +--R Type: Union(Expression Integer,...) +--E 208 + +--S 209 of 534 +m0639:= a0639-r0639 +--R +--R +--R (201) +--R 4b x sin(4b x + 4a) +--R + +--R 3 +--R (- 32b x cos(b x + a) + 16b x cos(b x + a))sin(b x + a) + cos(4b x + 4a) +--R + +--R 4 2 +--R - 8cos(b x + a) + 8cos(b x + a) +--R / +--R 2 +--R 128b +--R Type: Expression Integer +--E 209 + +--S 210 of 534 +d0639:= D(m0639,x) +--R +--R +--R (202) +--R 2 2 4 +--R (6x cos(b x + a) - x)sin(b x + a) + x cos(4b x + 4a) - 2x cos(b x + a) +--R + +--R 2 +--R x cos(b x + a) +--R / +--R 8 +--R Type: Expression Integer +--E 210 + +--S 211 of 534 +t0640:= x^2*sin(a+b*x)^2*cos(a+b*x)^2 +--R +--R +--R 2 2 2 +--R (203) x cos(b x + a) sin(b x + a) +--R Type: Expression Integer +--E 211 + +--S 212 of 534 +r0640:= -1/768*(-32*b^3*x^3+12*b*x*cos(4*a+4*b*x)-3*sin(4*a+4*b*x)+24*x^2*sin(4*a+4*b*x)*b^2)/b^3 +--R +--R +--R 2 2 3 3 +--R (- 24b x + 3)sin(4b x + 4a) - 12b x cos(4b x + 4a) + 32b x +--R (204) ------------------------------------------------------------ +--R 3 +--R 768b +--R Type: Expression Integer +--E 212 + +--S 213 of 534 +a0640:= integrate(t0640,x) +--R +--R +--R (205) +--R 2 2 3 2 2 +--R ((- 48b x + 6)cos(b x + a) + (24b x - 3)cos(b x + a))sin(b x + a) +--R + +--R 4 2 3 3 +--R - 24b x cos(b x + a) + 24b x cos(b x + a) + 8b x - 3b x +--R / +--R 3 +--R 192b +--R Type: Union(Expression Integer,...) +--E 213 + +--S 214 of 534 +m0640:= a0640-r0640 +--R +--R +--R (206) +--R 2 2 +--R (8b x - 1)sin(4b x + 4a) +--R + +--R 2 2 3 2 2 +--R ((- 64b x + 8)cos(b x + a) + (32b x - 4)cos(b x + a))sin(b x + a) +--R + +--R 4 2 +--R 4b x cos(4b x + 4a) - 32b x cos(b x + a) + 32b x cos(b x + a) - 4b x +--R / +--R 3 +--R 256b +--R Type: Expression Integer +--E 214 + +--S 215 of 534 +d0640:= D(m0640,x) +--R +--R +--R (207) +--R 2 2 2 2 2 2 +--R ((48b x - 6)cos(b x + a) - 8b x + 1)sin(b x + a) +--R + +--R 2 2 2 2 4 +--R 8b x cos(4b x + 4a) + (- 16b x - 6)cos(b x + a) +--R + +--R 2 2 2 +--R (8b x + 7)cos(b x + a) - 1 +--R / +--R 2 +--R 64b +--R Type: Expression Integer +--E 215 + +--S 216 of 534 +t0641:= x^3*sin(a+b*x)^2*cos(a+b*x)^2 +--R +--R +--R 3 2 2 +--R (208) x cos(b x + a) sin(b x + a) +--R Type: Expression Integer +--E 216 + +--S 217 of 534 +r0641:= -1/1024*(-32*x^4*b^4-3*cos(4*a+4*b*x)+24*b^2*x^2*cos(4*a+4*b*x)-12*x*sin(4*a+4*b*x)*b+32*x^3*sin(4*a+4*b*x)*b^3)/b^4 +--R +--R +--R (209) +--R 3 3 2 2 4 4 +--R (- 32b x + 12b x)sin(4b x + 4a) + (- 24b x + 3)cos(4b x + 4a) + 32b x +--R ------------------------------------------------------------------------ +--R 4 +--R 1024b +--R Type: Expression Integer +--E 217 + +--S 218 of 534 +a0641:= integrate(t0641,x) +--R +--R +--R (210) +--R 3 3 3 3 3 +--R ((- 32b x + 12b x)cos(b x + a) + (16b x - 6b x)cos(b x + a)) +--R * +--R sin(b x + a) +--R + +--R 2 2 4 2 2 2 4 4 2 2 +--R (- 24b x + 3)cos(b x + a) + (24b x - 3)cos(b x + a) + 4b x - 3b x +--R / +--R 4 +--R 128b +--R Type: Union(Expression Integer,...) +--E 218 + +--S 219 of 534 +m0641:= a0641-r0641 +--R +--R +--R (211) +--R 3 3 +--R (32b x - 12b x)sin(4b x + 4a) +--R + +--R 3 3 3 3 3 +--R ((- 256b x + 96b x)cos(b x + a) + (128b x - 48b x)cos(b x + a)) +--R * +--R sin(b x + a) +--R + +--R 2 2 2 2 4 +--R (24b x - 3)cos(4b x + 4a) + (- 192b x + 24)cos(b x + a) +--R + +--R 2 2 2 2 2 +--R (192b x - 24)cos(b x + a) - 24b x +--R / +--R 4 +--R 1024b +--R Type: Expression Integer +--E 219 + +--S 220 of 534 +d0641:= D(m0641,x) +--R +--R +--R (212) +--R 2 3 2 2 3 2 +--R ((48b x - 18x)cos(b x + a) - 8b x + 3x)sin(b x + a) +--R + +--R 2 3 2 3 4 +--R 8b x cos(4b x + 4a) + (- 16b x - 18x)cos(b x + a) +--R + +--R 2 3 2 +--R (8b x + 21x)cos(b x + a) - 3x +--R / +--R 2 +--R 64b +--R Type: Expression Integer +--E 220 + +--S 221 of 534 +t0642:= x*sec(a+b*x)*tan(a+b*x) +--R +--R +--R (213) x sec(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 221 + +--S 222 of 534 +r0642:= -atanh(sin(a+b*x))/b^2+x*sec(a+b*x)/b +--R +--R +--R - atanh(sin(b x + a)) + b x sec(b x + a) +--R (214) ---------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 222 + +--S 223 of 534 +a0642:= integrate(t0642,x) +--R +--R +--R (215) +--R sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a)log(-------------------------------) + b x +--R cos(b x + a) + 1 +--R / +--R 2 +--R b cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 223 + +--S 224 of 534 +m0642:= a0642-r0642 +--R +--R +--R (216) +--R sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R cos(b x + a)atanh(sin(b x + a)) - b x cos(b x + a)sec(b x + a) + b x +--R / +--R 2 +--R b cos(b x + a) +--R Type: Expression Integer +--E 224 + +--S 225 of 534 +d0642:= D(m0642,x) +--R +--R +--R (217) +--R 2 4 +--R - b x cos(b x + a) sec(b x + a)sin(b x + a) +--R + +--R 4 3 2 +--R (b x cos(b x + a) + 2b x cos(b x + a) + 2b x cos(b x + a) ) +--R * +--R 2 +--R sec(b x + a)sin(b x + a) +--R + +--R 4 3 2 +--R (- b x cos(b x + a) - 2b x cos(b x + a) - b x cos(b x + a) ) +--R * +--R sec(b x + a) +--R * +--R tan(b x + a) +--R + +--R 5 +--R b x sin(b x + a) +--R + +--R 2 2 +--R (- cos(b x + a) sec(b x + a) + 2cos(b x + a) + cos(b x + a)) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 2 3 +--R (- b x cos(b x + a) - 2b x cos(b x + a) - 2b x)sin(b x + a) +--R + +--R 4 3 2 +--R (cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) )sec(b x + a) +--R + +--R 4 2 +--R 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 2 +--R (b x cos(b x + a) + 2b x cos(b x + a) + b x)sin(b x + a) +--R + +--R 4 3 2 +--R (- cos(b x + a) - 2cos(b x + a) - cos(b x + a) )sec(b x + a) +--R + +--R 5 2 +--R cos(b x + a) + 2cos(b x + a) + cos(b x + a) +--R / +--R 2 4 +--R b cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 2 +--R (- b cos(b x + a) - 2b cos(b x + a) - 2b cos(b x + a) )sin(b x + a) +--R + +--R 4 3 2 +--R b cos(b x + a) + 2b cos(b x + a) + b cos(b x + a) +--R Type: Expression Integer +--E 225 + +--S 226 of 534 +t0643:= x^2*sec(a+b*x)*tan(a+b*x) +--R +--R +--R 2 +--R (218) x sec(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 226 + +--S 227 of 534 +r0643:= 4*%i*x*atan(exp(1)^(%i*b*x+%i*a))/b^2-2*%i*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^3+2*%i*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^3+x^2*sec(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 534 +a0643:= integrate(t0643,x) +--R +--R +--R x +--R ++ 2 +--R (219) | %L sec(%L b + a)tan(%L b + a)d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 228 + +--S 229 of 534 +m0643:= a0643-r0643 +--R +--R +--R x +--R ++ 2 +--R (220) | %L sec(%L b + a)tan(%L b + a)d%L - r0643 +--R ++ +--R Type: Expression Integer +--E 229 + +--S 230 of 534 +d0643:= D(m0643,x) +--R +--R +--R 2 +--R (221) x sec(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 230 + +--S 231 of 534 +t0644:= x^3*sec(a+b*x)*tan(a+b*x) +--R +--R +--R 3 +--R (222) x sec(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 231 + +--S 232 of 534 +r0644:= 6*%i*x^2*atan(exp(1)^(%i*b*x+%i*a))/b^2-6*%i*x*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^3+6*%i*x*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^3+6*polylog(3,-%i*exp(1)^(%i*b*x+%i*a))/b^4-6*polylog(3,%i*exp(1)^(%i*b*x+%i*a))/b^4+x^3*sec(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 534 +a0644:= integrate(t0644,x) +--R +--R +--R x +--R ++ 3 +--R (223) | %L sec(%L b + a)tan(%L b + a)d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 233 + +--S 234 of 534 +m0644:= a0644-r0644 +--R +--R +--R x +--R ++ 3 +--R (224) | %L sec(%L b + a)tan(%L b + a)d%L - r0644 +--R ++ +--R Type: Expression Integer +--E 234 + +--S 235 of 534 +d0644:= D(m0644,x) +--R +--R +--R 3 +--R (225) x sec(b x + a)tan(b x + a) +--R Type: Expression Integer +--E 235 + +--S 236 of 534 +t0645:= x^3*sec(a+b*x)^2*tan(a+b*x) +--R +--R +--R 3 2 +--R (226) x sec(b x + a) tan(b x + a) +--R Type: Expression Integer +--E 236 + +--S 237 of 534 +r0645:= 3/2*%i*x^2/b^2-3*x*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b^3+3/2*%i*polylog(2,-exp(1)^(2*%i*a+2*%i*b*x))/b^4+1/2*x^3*sec(a+b*x)^2/b-3/2*x^2*tan(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 534 +a0645:= integrate(t0645,x) +--R +--R +--R x +--R ++ 3 2 +--R (227) | %L sec(%L b + a) tan(%L b + a)d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 238 + +--S 239 of 534 +m0645:= a0645-r0645 +--R +--R +--R x +--R ++ 3 2 +--R (228) | %L sec(%L b + a) tan(%L b + a)d%L - r0645 +--R ++ +--R Type: Expression Integer +--E 239 + +--S 240 of 534 +d0645:= D(m0645,x) +--R +--R +--R 3 2 +--R (229) x sec(b x + a) tan(b x + a) +--R Type: Expression Integer +--E 240 + +--S 241 of 534 +t0646:= x*csc(a+b*x)*cot(a+b*x) +--R +--R +--R (230) x cot(b x + a)csc(b x + a) +--R Type: Expression Integer +--E 241 + +--S 242 of 534 +r0646:= -atanh(cos(a+b*x))/b^2-x*csc(a+b*x)/b +--R +--R +--R - atanh(cos(b x + a)) - b x csc(b x + a) +--R (231) ---------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 242 + +--S 243 of 534 +a0646:= integrate(t0646,x) +--R +--R +--R sin(b x + a) +--R sin(b x + a)log(----------------) - b x +--R cos(b x + a) + 1 +--R (232) --------------------------------------- +--R 2 +--R b sin(b x + a) +--R Type: Union(Expression Integer,...) +--E 243 + +--S 244 of 534 +m0646:= a0646-r0646 +--R +--R +--R (233) +--R sin(b x + a) +--R sin(b x + a)log(----------------) + sin(b x + a)atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R + +--R b x csc(b x + a)sin(b x + a) - b x +--R / +--R 2 +--R b sin(b x + a) +--R Type: Expression Integer +--E 244 + +--S 245 of 534 +d0646:= D(m0646,x) +--R +--R +--R (234) +--R 3 +--R cos(b x + a)sin(b x + a) +--R + +--R 2 2 +--R ((- b x cos(b x + a) + b x)cot(b x + a) + cos(b x + a) - 1) +--R * +--R 2 +--R csc(b x + a)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) - cos(b x + a) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 3 +--R b x cos(b x + a) - b x cos(b x + a) +--R / +--R 2 2 +--R (b cos(b x + a) - b)sin(b x + a) +--R Type: Expression Integer +--E 245 + +--S 246 of 534 +t0647:= x^2*csc(a+b*x)*cot(a+b*x) +--R +--R +--R 2 +--R (235) x cot(b x + a)csc(b x + a) +--R Type: Expression Integer +--E 246 + +--S 247 of 534 +r0647:= -4*x*atanh(exp(1)^(%i*b*x+%i*a))/b^2-x^2*csc(a+b*x)/b+2*%i*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^3-2*%i*polylog(2,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 534 +a0647:= integrate(t0647,x) +--R +--R +--R x +--R ++ 2 +--R (236) | %L cot(%L b + a)csc(%L b + a)d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 248 + +--S 249 of 534 +m0647:= a0647-r0647 +--R +--R +--R x +--R ++ 2 +--R (237) | %L cot(%L b + a)csc(%L b + a)d%L - r0647 +--R ++ +--R Type: Expression Integer +--E 249 + +--S 250 of 534 +d0647:= D(m0647,x) +--R +--R +--R 2 +--R (238) x cot(b x + a)csc(b x + a) +--R Type: Expression Integer +--E 250 + +--S 251 of 534 +t0648:= x^3*csc(a+b*x)*cot(a+b*x) +--R +--R +--R 3 +--R (239) x cot(b x + a)csc(b x + a) +--R Type: Expression Integer +--E 251 + +--S 252 of 534 +r0648:= -6*x^2*atanh(exp(1)^(%i*b*x+%i*a))/b^2-x^3*csc(a+b*x)/b+6*%i*x*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^3-6*%i*x*polylog(2,exp(1)^(%i*b*x+%i*a))/b^3-6*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^4+6*polylog(3,exp(1)^(%i*b*x+%i*a))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 534 +a0648:= integrate(t0648,x) +--R +--R +--R x +--R ++ 3 +--R (240) | %L cot(%L b + a)csc(%L b + a)d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 253 + +--S 254 of 534 +m0648:= a0648-r0648 +--R +--R +--R x +--R ++ 3 +--R (241) | %L cot(%L b + a)csc(%L b + a)d%L - r0648 +--R ++ +--R Type: Expression Integer +--E 254 + +--S 255 of 534 +d0648:= D(m0648,x) +--R +--R +--R 3 +--R (242) x cot(b x + a)csc(b x + a) +--R Type: Expression Integer +--E 255 + +--S 256 of 534 +t0649:= x^3*csc(a+b*x)^2*cot(a+b*x) +--R +--R +--R 3 2 +--R (243) x cot(b x + a)csc(b x + a) +--R Type: Expression Integer +--E 256 + +--S 257 of 534 +r0649:= -3/2*%i*x^2/b^2-3/2*x^2*cot(a+b*x)/b^2-1/2*x^3*csc(a+b*x)^2/b+3*x*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b^3-3/2*%i*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 257 + +--S 258 of 534 +a0649:= integrate(t0649,x) +--R +--R +--R x +--R ++ 3 2 +--R (244) | %L cot(%L b + a)csc(%L b + a) d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 258 + +--S 259 of 534 +m0649:= a0649-r0649 +--R +--R +--R x +--R ++ 3 2 +--R (245) | %L cot(%L b + a)csc(%L b + a) d%L - r0649 +--R ++ +--R Type: Expression Integer +--E 259 + +--S 260 of 534 +d0649:= D(m0649,x) +--R +--R +--R 3 2 +--R (246) x cot(b x + a)csc(b x + a) +--R Type: Expression Integer +--E 260 + +--S 261 of 534 +t0650:= x*csc(x)*sec(x) +--R +--R +--R (247) x csc(x)sec(x) +--R Type: Expression Integer +--E 261 + +--S 262 of 534 +r0650:= -2*x*atanh(exp(2*%i*x))+1/2*%i*polylog(2,-exp(2*%i*x))-1/2*%i*polylog(2,exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 262 + +--S 263 of 534 +a0650:= integrate(t0650,x) +--R +--R +--R x +--R ++ +--R (248) | %L csc(%L)sec(%L)d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 263 + +--S 264 of 534 +m0650:= a0650-r0650 +--R +--R +--R x +--R ++ +--R (249) | %L csc(%L)sec(%L)d%L - r0650 +--R ++ +--R Type: Expression Integer +--E 264 + +--S 265 of 534 +d0650:= D(m0650,x) +--R +--R +--R (250) x csc(x)sec(x) +--R Type: Expression Integer +--E 265 + +--S 266 of 534 +t0651:= x*csc(x)*sec(x)^2 +--R +--R +--R 2 +--R (251) x csc(x)sec(x) +--R Type: Expression Integer +--E 266 + +--S 267 of 534 +r0651:= -2*atanh(tan(1/2*x))+x*log(1-exp(1)^(%i*x))-x*log(1+exp(1)^(%i*x))+%i*polylog(2,-exp(1)^(%i*x))-%i*polylog(2,exp(1)^(%i*x))+x*sec(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 534 +a0651:= integrate(t0651,x) +--R +--R +--R x +--R ++ 2 +--R (252) | %L csc(%L)sec(%L) d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 268 + +--S 269 of 534 +m0651:= a0651-r0651 +--R +--R +--R x +--R ++ 2 +--R (253) | %L csc(%L)sec(%L) d%L - r0651 +--R ++ +--R Type: Expression Integer +--E 269 + +--S 270 of 534 +d0651:= D(m0651,x) +--R +--R +--R 2 +--R (254) x csc(x)sec(x) +--R Type: Expression Integer +--E 270 + +--S 271 of 534 +t0652:= x*csc(x)*sec(x)^3 +--R +--R +--R 3 +--R (255) x csc(x)sec(x) +--R Type: Expression Integer +--E 271 + +--S 272 of 534 +r0652:= x*log(1-exp(1)^(2*%i*x))-x*log(1+exp(1)^(2*%i*x))+1/2*%i*polylog(2,-exp(1)^(2*%i*x))-1/2*%i*polylog(2,exp(1)^(2*%i*x))+1/2*x*sec(x)^2-1/2*tan(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 534 +a0652:= integrate(t0652,x) +--R +--R +--R x +--R ++ 3 +--R (256) | %L csc(%L)sec(%L) d%L +--R ++ +--R Type: Union(Expression Integer,...) +--E 273 + +--S 274 of 534 +m0652:= a0652-r0652 +--R +--R +--R x +--R ++ 3 +--R (257) | %L csc(%L)sec(%L) d%L - r0652 +--R ++ +--R Type: Expression Integer +--E 274 + +--S 275 of 534 +d0652:= D(m0652,x) +--R +--R +--R 3 +--R (258) x csc(x)sec(x) +--R Type: Expression Integer +--E 275 + +--S 276 of 534 +t0653:= x*sin(a+b*x)*cos(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (259) x cos(b x + a)sin(b x + a)\|cos(b x + a) +--R Type: Expression Integer +--E 276 + +--S 277 of 534 +r0653:= -2/25*(5*x*cos(a+b*x)^(5/2)*b-6*EllipticE(1/2*a+1/2*b*x,2)-2*cos(a+b*x)^(3/2)*sin(a+b*x))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 534 +a0653:= integrate(t0653,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 278 + +--S 279 of 534 +m0653:= a0653-r0653 +--R +--R +--R (260) - r0653 + a0653 +--R Type: Polynomial Integer +--E 279 + +--S 280 of 534 +d0653:= D(m0653,x) +--R +--R +--R (261) 0 +--R Type: Polynomial Integer +--E 280 + +--S 281 of 534 +t0654:= x*sin(a+b*x)*cos(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (262) x sin(b x + a)\|cos(b x + a) +--R Type: Expression Integer +--E 281 + +--S 282 of 534 +r0654:= -2/9*(3*x*cos(a+b*x)^(3/2)*b-2*EllipticF(1/2*a+1/2*b*x,2)-2*cos(a+b*x)^(1/2)*sin(a+b*x))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 534 +a0654:= integrate(t0654,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 283 + +--S 284 of 534 +m0654:= a0654-r0654 +--R +--R +--R (263) - r0654 + a0654 +--R Type: Polynomial Integer +--E 284 + +--S 285 of 534 +d0654:= D(m0654,x) +--R +--R +--R (264) 0 +--R Type: Polynomial Integer +--E 285 + +--S 286 of 534 +t0655:= x*sin(a+b*x)/cos(a+b*x)^(1/2) +--R +--R +--R x sin(b x + a) +--R (265) --------------- +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression Integer +--E 286 + +--S 287 of 534 +r0655:= -2*(x*cos(a+b*x)^(1/2)*b-2*EllipticE(1/2*a+1/2*b*x,2))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 534 +a0655:= integrate(t0655,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 288 + +--S 289 of 534 +m0655:= a0655-r0655 +--R +--R +--R (266) - r0655 + a0655 +--R Type: Polynomial Integer +--E 289 + +--S 290 of 534 +d0655:= D(m0655,x) +--R +--R +--R (267) 0 +--R Type: Polynomial Integer +--E 290 + +--S 291 of 534 +t0656:= x*sin(a+b*x)/cos(a+b*x)^(3/2) +--R +--R +--R x sin(b x + a) +--R (268) --------------------------- +--R +------------+ +--R cos(b x + a)\|cos(b x + a) +--R Type: Expression Integer +--E 291 + +--S 292 of 534 +r0656:= 2*x/b/cos(a+b*x)^(1/2)-4*EllipticF(1/2*a+1/2*b*x,2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 292 + +--S 293 of 534 +a0656:= integrate(t0656,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 293 + +--S 294 of 534 +m0656:= a0656-r0656 +--R +--R +--R (269) - r0656 + a0656 +--R Type: Polynomial Integer +--E 294 + +--S 295 of 534 +d0656:= D(m0656,x) +--R +--R +--R (270) 0 +--R Type: Polynomial Integer +--E 295 + +--S 296 of 534 +t0657:= x*sin(a+b*x)/cos(a+b*x)^(5/2) +--R +--R +--R x sin(b x + a) +--R (271) ---------------------------- +--R 2 +------------+ +--R cos(b x + a) \|cos(b x + a) +--R Type: Expression Integer +--E 296 + +--S 297 of 534 +r0657:= 2/3*(b*x+2*EllipticE(1/2*a+1/2*b*x,2)*cos(a+b*x)^(3/2)-2*cos(a+b*x)*sin(a+b*x))/b^2/cos(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 534 +a0657:= integrate(t0657,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 298 + +--S 299 of 534 +m0657:= a0657-r0657 +--R +--R +--R (272) - r0657 + a0657 +--R Type: Polynomial Integer +--E 299 + +--S 300 of 534 +d0657:= D(m0657,x) +--R +--R +--R (273) 0 +--R Type: Polynomial Integer +--E 300 + +--S 301 of 534 +t0658:= x*cos(a+b*x)*sin(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (274) x cos(b x + a)sin(b x + a)\|sin(b x + a) +--R Type: Expression Integer +--E 301 + +--S 302 of 534 +r0658:= -2/25*(6*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)-2*cos(a+b*x)*sin(a+b*x)^(3/2)-5*x*sin(a+b*x)^(5/2)*b)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 302 + +--S 303 of 534 +a0658:= integrate(t0658,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 303 + +--S 304 of 534 +m0658:= a0658-r0658 +--R +--R +--R (275) - r0658 + a0658 +--R Type: Polynomial Integer +--E 304 + +--S 305 of 534 +d0658:= D(m0658,x) +--R +--R +--R (276) 0 +--R Type: Polynomial Integer +--E 305 + +--S 306 of 534 +t0659:= x*cos(a+b*x)*sin(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (277) x cos(b x + a)\|sin(b x + a) +--R Type: Expression Integer +--E 306 + +--S 307 of 534 +r0659:= 2/9*(-2*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)+2*cos(a+b*x)*sin(a+b*x)^(1/2)+3*x*sin(a+b*x)^(3/2)*b)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 534 +a0659:= integrate(t0659,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 308 + +--S 309 of 534 +m0659:= a0659-r0659 +--R +--R +--R (278) - r0659 + a0659 +--R Type: Polynomial Integer +--E 309 + +--S 310 of 534 +d0659:= D(m0659,x) +--R +--R +--R (279) 0 +--R Type: Polynomial Integer +--E 310 + +--S 311 of 534 +t0660:= x*cos(a+b*x)/sin(a+b*x)^(1/2) +--R +--R +--R x cos(b x + a) +--R (280) --------------- +--R +------------+ +--R \|sin(b x + a) +--R Type: Expression Integer +--E 311 + +--S 312 of 534 +r0660:= -4*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b^2+2*x*sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 534 +a0660:= integrate(t0660,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 313 + +--S 314 of 534 +m0660:= a0660-r0660 +--R +--R +--R (281) - r0660 + a0660 +--R Type: Polynomial Integer +--E 314 + +--S 315 of 534 +d0660:= D(m0660,x) +--R +--R +--R (282) 0 +--R Type: Polynomial Integer +--E 315 + +--S 316 of 534 +t0661:= x*cos(a+b*x)/sin(a+b*x)^(3/2) +--R +--R +--R x cos(b x + a) +--R (283) --------------------------- +--R +------------+ +--R sin(b x + a)\|sin(b x + a) +--R Type: Expression Integer +--E 316 + +--S 317 of 534 +r0661:= 4*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)/b^2-2*x/b/sin(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 317 + +--S 318 of 534 +a0661:= integrate(t0661,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 318 + +--S 319 of 534 +m0661:= a0661-r0661 +--R +--R +--R (284) - r0661 + a0661 +--R Type: Polynomial Integer +--E 319 + +--S 320 of 534 +d0661:= D(m0661,x) +--R +--R +--R (285) 0 +--R Type: Polynomial Integer +--E 320 + +--S 321 of 534 +t0662:= x*cos(a+b*x)/sin(a+b*x)^(5/2) +--R +--R +--R x cos(b x + a) +--R (286) ---------------------------- +--R 2 +------------+ +--R sin(b x + a) \|sin(b x + a) +--R Type: Expression Integer +--E 321 + +--S 322 of 534 +r0662:= -2/3*(2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2)+b*x+2*cos(a+b*x)*sin(a+b*x))/b^2/sin(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 534 +a0662:= integrate(t0662,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 323 + +--S 324 of 534 +m0662:= a0662-r0662 +--R +--R +--R (287) - r0662 + a0662 +--R Type: Polynomial Integer +--E 324 + +--S 325 of 534 +d0662:= D(m0662,x) +--R +--R +--R (288) 0 +--R Type: Polynomial Integer +--E 325 + +--S 326 of 534 +t0663:= x*sin(a+b*x)*sec(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (289) x sec(b x + a) sin(b x + a)\|sec(b x + a) +--R Type: Expression Integer +--E 326 + +--S 327 of 534 +r0663:= 2/3*(1/cos(a+b*x))^(1/2)*(b*x+2*EllipticE(1/2*a+1/2*b*x,2)*cos(a+b*x)^(3/2)-2*cos(a+b*x)*sin(a+b*x))/cos(a+b*x)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 327 + +--S 328 of 534 +a0663:= integrate(t0663,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 328 + +--S 329 of 534 +m0663:= a0663-r0663 +--R +--R +--R (290) - r0663 + a0663 +--R Type: Polynomial Integer +--E 329 + +--S 330 of 534 +d0663:= D(m0663,x) +--R +--R +--R (291) 0 +--R Type: Polynomial Integer +--E 330 + +--S 331 of 534 +t0664:= x*sin(a+b*x)*sec(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (292) x sec(b x + a)sin(b x + a)\|sec(b x + a) +--R Type: Expression Integer +--E 331 + +--S 332 of 534 +r0664:= -2*(1/cos(a+b*x))^(1/2)*(-b*x+2*EllipticF(1/2*a+1/2*b*x,2)*cos(a+b*x)^(1/2))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 332 + +--S 333 of 534 +a0664:= integrate(t0664,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 333 + +--S 334 of 534 +m0664:= a0664-r0664 +--R +--R +--R (293) - r0664 + a0664 +--R Type: Polynomial Integer +--E 334 + +--S 335 of 534 +d0664:= D(m0664,x) +--R +--R +--R (294) 0 +--R Type: Polynomial Integer +--E 335 + +--S 336 of 534 +t0665:= x*sin(a+b*x)*sec(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (295) x sin(b x + a)\|sec(b x + a) +--R Type: Expression Integer +--E 336 + +--S 337 of 534 +r0665:= -2*x/b/sec(a+b*x)^(1/2)+4*cos(a+b*x)^(1/2)*EllipticE(1/2*a+1/2*b*x,2)*sec(a+b*x)^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 337 + +--S 338 of 534 +a0665:= integrate(t0665,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 338 + +--S 339 of 534 +m0665:= a0665-r0665 +--R +--R +--R (296) - r0665 + a0665 +--R Type: Polynomial Integer +--E 339 + +--S 340 of 534 +d0665:= D(m0665,x) +--R +--R +--R (297) 0 +--R Type: Polynomial Integer +--E 340 + +--S 341 of 534 +t0666:= x*sin(a+b*x)/sec(a+b*x)^(1/2) +--R +--R +--R x sin(b x + a) +--R (298) --------------- +--R +------------+ +--R \|sec(b x + a) +--R Type: Expression Integer +--E 341 + +--S 342 of 534 +r0666:= -2/9*(3*b*x*cos(a+b*x)^(3/2)-2*EllipticF(1/2*a+1/2*b*x,2)-2*sin(a+b*x)*cos(a+b*x)^(1/2))/cos(a+b*x)^(1/2)/(1/cos(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 342 + +--S 343 of 534 +a0666:= integrate(t0666,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 343 + +--S 344 of 534 +m0666:= a0666-r0666 +--R +--R +--R (299) - r0666 + a0666 +--R Type: Polynomial Integer +--E 344 + +--S 345 of 534 +d0666:= D(m0666,x) +--R +--R +--R (300) 0 +--R Type: Polynomial Integer +--E 345 + +--S 346 of 534 +t0667:= x*sin(a+b*x)/sec(a+b*x)^(3/2) +--R +--R +--R x sin(b x + a) +--R (301) --------------------------- +--R +------------+ +--R sec(b x + a)\|sec(b x + a) +--R Type: Expression Integer +--E 346 + +--S 347 of 534 +r0667:= 2/25*(-5*b*x*cos(a+b*x)^(5/2)+6*EllipticE(1/2*a+1/2*b*x,2)+2*sin(a+b*x)*cos(a+b*x)^(3/2))/cos(a+b*x)^(1/2)/(1/cos(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 534 +a0667:= integrate(t0667,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 348 + +--S 349 of 534 +m0667:= a0667-r0667 +--R +--R +--R (302) - r0667 + a0667 +--R Type: Polynomial Integer +--E 349 + +--S 350 of 534 +d0667:= D(m0667,x) +--R +--R +--R (303) 0 +--R Type: Polynomial Integer +--E 350 + +--S 351 of 534 +t0668:= x*cos(a+b*x)*csc(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (304) x cos(b x + a)csc(b x + a) \|csc(b x + a) +--R Type: Expression Integer +--E 351 + +--S 352 of 534 +r0668:= -2/3*(1/sin(a+b*x))^(1/2)*(2*cos(a+b*x)*sin(a+b*x)+b*x+2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2))/sin(a+b*x)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 352 + +--S 353 of 534 +a0668:= integrate(t0668,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 353 + +--S 354 of 534 +m0668:= a0668-r0668 +--R +--R +--R (305) - r0668 + a0668 +--R Type: Polynomial Integer +--E 354 + +--S 355 of 534 +d0668:= D(m0668,x) +--R +--R +--R (306) 0 +--R Type: Polynomial Integer +--E 355 + +--S 356 of 534 +t0669:= x*cos(a+b*x)*csc(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (307) x cos(b x + a)csc(b x + a)\|csc(b x + a) +--R Type: Expression Integer +--E 356 + +--S 357 of 534 +r0669:= 2*(1/sin(a+b*x))^(1/2)*(-b*x+2*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 357 + +--S 358 of 534 +a0669:= integrate(t0669,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 358 + +--S 359 of 534 +m0669:= a0669-r0669 +--R +--R +--R (308) - r0669 + a0669 +--R Type: Polynomial Integer +--E 359 + +--S 360 of 534 +d0669:= D(m0669,x) +--R +--R +--R (309) 0 +--R Type: Polynomial Integer +--E 360 + +--S 361 of 534 +t0670:= x*cos(a+b*x)*csc(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (310) x cos(b x + a)\|csc(b x + a) +--R Type: Expression Integer +--E 361 + +--S 362 of 534 +r0670:= 2*x/b/csc(a+b*x)^(1/2)-4*csc(a+b*x)^(1/2)*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 362 + +--S 363 of 534 +a0670:= integrate(t0670,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 363 + +--S 364 of 534 +m0670:= a0670-r0670 +--R +--R +--R (311) - r0670 + a0670 +--R Type: Polynomial Integer +--E 364 + +--S 365 of 534 +d0670:= D(m0670,x) +--R +--R +--R (312) 0 +--R Type: Polynomial Integer +--E 365 + +--S 366 of 534 +t0671:= x*cos(a+b*x)/csc(a+b*x)^(1/2) +--R +--R +--R x cos(b x + a) +--R (313) --------------- +--R +------------+ +--R \|csc(b x + a) +--R Type: Expression Integer +--E 366 + +--S 367 of 534 +r0671:= -2/9*(-3*b*x*sin(a+b*x)^(3/2)-2*cos(a+b*x)*sin(a+b*x)^(1/2)+2*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/(1/sin(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 367 + +--S 368 of 534 +a0671:= integrate(t0671,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 368 + +--S 369 of 534 +m0671:= a0671-r0671 +--R +--R +--R (314) - r0671 + a0671 +--R Type: Polynomial Integer +--E 369 + +--S 370 of 534 +d0671:= D(m0671,x) +--R +--R +--R (315) 0 +--R Type: Polynomial Integer +--E 370 + +--S 371 of 534 +t0672:= x*cos(a+b*x)/csc(a+b*x)^(3/2) +--R +--R +--R x cos(b x + a) +--R (316) --------------------------- +--R +------------+ +--R csc(b x + a)\|csc(b x + a) +--R Type: Expression Integer +--E 371 + +--S 372 of 534 +r0672:= -2/25*(-5*b*x*sin(a+b*x)^(5/2)-2*cos(a+b*x)*sin(a+b*x)^(3/2)+6*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/(1/sin(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 534 +a0672:= integrate(t0672,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 373 + +--S 374 of 534 +m0672:= a0672-r0672 +--R +--R +--R (317) - r0672 + a0672 +--R Type: Polynomial Integer +--E 374 + +--S 375 of 534 +d0672:= D(m0672,x) +--R +--R +--R (318) 0 +--R Type: Polynomial Integer +--E 375 + +--S 376 of 534 +t0673:= x/(a+b*sin(x)*cos(x)) +--R +--R +--R x +--R (319) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression Integer +--E 376 + +--S 377 of 534 +r0673:= -1/2*(2*%i*x*log((-2*a+(4*a^2-b^2)^(1/2)+%i*b*exp(2*%i*x))/(-2*a+(4*a^2-b^2)^(1/2)))-2*%i*x*log((2*a+(4*a^2-b^2)^(1/2)-%i*b*exp(2*%i*x))/(2*a+(4*a^2-b^2)^(1/2)))+polylog(2,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))-polylog(2,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2))))/(4*a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 534 +a0673:= integrate(t0673,x) +--R +--R +--R x +--R ++ %L +--R (320) | -------------------- d%L +--R ++ b cos(%L)sin(%L) + a +--R Type: Union(Expression Integer,...) +--E 378 + +--S 379 of 534 +m0673:= a0673-r0673 +--R +--R +--R x +--R ++ %L +--R (321) | -------------------- d%L - r0673 +--R ++ b cos(%L)sin(%L) + a +--R Type: Expression Integer +--E 379 + +--S 380 of 534 +d0673:= D(m0673,x) +--R +--R +--R x +--R (322) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression Integer +--E 380 + +--S 381 of 534 +t0674:= x^2/(a+b*sin(x)*cos(x)) +--R +--R +--R 2 +--R x +--R (323) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression Integer +--E 381 + +--S 382 of 534 +r0674:= 1/2*(-2*%i*x^2*log((-2*a+(4*a^2-b^2)^(1/2)+%i*b*exp(2*%i*x))/(-2*a+(4*a^2-b^2)^(1/2)))+2*%i*x^2*log((2*a+(4*a^2-b^2)^(1/2)-%i*b*exp(2*%i*x))/(2*a+(4*a^2-b^2)^(1/2)))-2*x*polylog(2,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))+2*x*polylog(2,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2)))-%i*polylog(3,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))+%i*polylog(3,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2))))/(4*a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 382 + +--S 383 of 534 +a0674:= integrate(t0674,x) +--R +--R +--R x 2 +--R ++ %L +--R (324) | -------------------- d%L +--R ++ b cos(%L)sin(%L) + a +--R Type: Union(Expression Integer,...) +--E 383 + +--S 384 of 534 +m0674:= a0674-r0674 +--R +--R +--R x 2 +--R ++ %L +--R (325) | -------------------- d%L - r0674 +--R ++ b cos(%L)sin(%L) + a +--R Type: Expression Integer +--E 384 + +--S 385 of 534 +d0674:= D(m0674,x) +--R +--R +--R 2 +--R x +--R (326) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression Integer +--E 385 + +--S 386 of 534 +t0675:= x^3/(a+b*sin(x)*cos(x)) +--R +--R +--R 3 +--R x +--R (327) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression Integer +--E 386 + +--S 387 of 534 +r0675:= 1/4*(-4*%i*x^3*log((-2*a+(4*a^2-b^2)^(1/2)+%i*b*exp(2*%i*x))/(-2*a+(4*a^2-b^2)^(1/2)))+4*%i*x^3*log((2*a+(4*a^2-b^2)^(1/2)-%i*b*exp(2*%i*x))/(2*a+(4*a^2-b^2)^(1/2)))-6*x^2*polylog(2,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))+6*x^2*polylog(2,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2)))-6*%i*x*polylog(3,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))+6*%i*x*polylog(3,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2)))+3*polylog(4,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))-3*polylog(4,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2))))/(4*a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 387 + +--S 388 of 534 +a0675:= integrate(t0675,x) +--R +--R +--R x 3 +--R ++ %L +--R (328) | -------------------- d%L +--R ++ b cos(%L)sin(%L) + a +--R Type: Union(Expression Integer,...) +--E 388 + +--S 389 of 534 +m0675:= a0675-r0675 +--R +--R +--R x 3 +--R ++ %L +--R (329) | -------------------- d%L - r0675 +--R ++ b cos(%L)sin(%L) + a +--R Type: Expression Integer +--E 389 + +--S 390 of 534 +d0675:= D(m0675,x) +--R +--R +--R 3 +--R x +--R (330) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression Integer +--E 390 + +--S 391 of 534 +t0676:= (a+b*sin(x))/(b+a*sin(x))^2 +--R +--R +--R b sin(x) + a +--R (331) ---------------------------- +--R 2 2 2 +--R a sin(x) + 2a b sin(x) + b +--R Type: Expression Integer +--E 391 + +--S 392 of 534 +r0676:= -cos(x)/(b+a*sin(x)) +--R +--R +--R cos(x) +--R (332) - ------------ +--R a sin(x) + b +--R Type: Expression Integer +--E 392 + +--S 393 of 534 +a0676:= integrate(t0676,x) +--R +--R +--R - a sin(x) - b cos(x) - b +--R (333) ------------------------- +--R 2 +--R a b sin(x) + b +--R Type: Union(Expression Integer,...) +--E 393 + +--S 394 of 534 +m0676:= a0676-r0676 +--R +--R +--R 1 +--R (334) - - +--R b +--R Type: Expression Integer +--E 394 + +--S 395 of 534 +d0676:= D(m0676,x) +--R +--R +--R (335) 0 +--R Type: Expression Integer +--E 395 + +--S 396 of 534 +t0677:= x*(b+a*sin(x))/(a+b*sin(x))^2 +--R +--R +--R a x sin(x) + b x +--R (336) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 396 + +--S 397 of 534 +r0677:= log(a+b*sin(x))/b-x*cos(x)/(a+b*sin(x)) +--R +--R +--R (b sin(x) + a)log(b sin(x) + a) - b x cos(x) +--R (337) -------------------------------------------- +--R 2 +--R b sin(x) + a b +--R Type: Expression Integer +--E 397 + +--S 398 of 534 +a0677:= integrate(t0677,x) +--R +--R +--R (338) +--R 2b sin(x) + 2a 2 +--R (b sin(x) + a)log(--------------) + (- b sin(x) - a)log(----------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - b x cos(x) +--R / +--R 2 +--R b sin(x) + a b +--R Type: Union(Expression Integer,...) +--E 398 + +--S 399 of 534 +m0677:= a0677-r0677 +--R +--R +--R 2b sin(x) + 2a 2 +--R - log(b sin(x) + a) + log(--------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (339) ----------------------------------------------------------- +--R b +--R Type: Expression Integer +--E 399 + +--S 400 of 534 +d0677:= D(m0677,x) +--R +--R +--R (340) 0 +--R Type: Expression Integer +--E 400 + +--S 401 of 534 +t0678:= x*(b+a*cos(x))/(a+b*cos(x))^2 +--R +--R +--R a x cos(x) + b x +--R (341) ---------------------------- +--R 2 2 2 +--R b cos(x) + 2a b cos(x) + a +--R Type: Expression Integer +--E 401 + +--S 402 of 534 +r0678:= log(a+b*cos(x))/b+x*sin(x)/(a+b*cos(x)) +--R +--R +--R (b cos(x) + a)log(b cos(x) + a) + b x sin(x) +--R (342) -------------------------------------------- +--R 2 +--R b cos(x) + a b +--R Type: Expression Integer +--E 402 + +--S 403 of 534 +a0678:= integrate(t0678,x) +--R +--R +--R (343) +--R 2 - 2b cos(x) - 2a +--R (- b cos(x) - a)log(----------) + (b cos(x) + a)log(----------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R b x sin(x) +--R / +--R 2 +--R b cos(x) + a b +--R Type: Union(Expression Integer,...) +--E 403 + +--S 404 of 534 +m0678:= a0678-r0678 +--R +--R +--R 2 - 2b cos(x) - 2a +--R - log(b cos(x) + a) - log(----------) + log(----------------) +--R cos(x) + 1 cos(x) + 1 +--R (344) ------------------------------------------------------------- +--R b +--R Type: Expression Integer +--E 404 + +--S 405 of 534 +d0678:= D(m0678,x) +--R +--R +--R (345) 0 +--R Type: Expression Integer +--E 405 + +--S 406 of 534 +t0679:= sin(x)/(a+a*sin(x))^(1/2) +--R +--R +--R sin(x) +--R (346) --------------- +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 406 + +--S 407 of 534 +r0679:= 2*(-cos(x)+atanh(cos(1/4*%pi+1/2*x))*sin(1/4*%pi+1/2*x))/(a*(1+sin(x)))^(1/2) +--R +--R +--R 2x + %pi 2x + %pi +--R 2sin(--------)atanh(cos(--------)) - 2cos(x) +--R 4 4 +--R (347) -------------------------------------------- +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 407 + +--S 408 of 534 +a0679:= integrate(t0679,x) +--R +--R +--R (348) +--R [ +--R +-+ +--R |2 +--R (a cos(x) + a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R (- a cos(x) - a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 408 + +--S 409 of 534 +m0679a:= a0679.1-r0679 +--R +--R +--R (349) +--R +-+ +--R |2 +------------+ +--R (a cos(x) + a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x + %pi 2x + %pi 2 +--R (- 4a cos(x) - 4a)sin(--------)atanh(cos(--------)) + 4a cos(x) +--R 4 4 +--R + +--R 4a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression Integer +--E 409 + +--S 410 of 534 +d0679a:= D(m0679a,x) +--R +--R +--R (350) +--R +-+ 2x + %pi 2 +-+ 4 +--R (\|2 cos(--------) - \|2 )sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (\|2 cos(--------) - \|2 )cos(x)sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2\|2 cos(--------) - 2\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +-+ +--R (\|2 cos(--------) - \|2 )cos(x) - 3\|2 cos(--------) + 3\|2 +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 4\|2 cos(--------) + 4\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) - 2\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 2\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (2\|2 cos(--------) - 2\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2\|2 cos(--------) + 2\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (2a cos(--------) - 2a)sin(x) + (2a cos(--------) - 2a)sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 2 +--R ((2a cos(--------) - 2a)cos(x) - 2a cos(--------) + 2a)sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 3 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 6a cos(--------) + 6a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) - 2a cos(--------) + 2a +--R 4 4 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (- 2a\|2 cos(--------) + 2a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R - 2a\|2 cos(--------) + 2a\|2 cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (2a\|2 cos(--------) - 2a\|2 cos(--------))cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (4a\|2 cos(--------) - 4a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R 2a\|2 cos(--------) - 2a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 4a\|2 cos(--------) + 4a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ +-+ 2x + %pi 2 +--R (- 2a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 2 +--R (2a\|2 cos(x) + 2a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (2a\|2 cos(x) + 4a\|2 cos(x) + 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 2a cos(--------) + 2a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (- 4a cos(--------) + 4a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R - 2a cos(--------) + 2a cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (2a cos(--------) - 2a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (4a cos(--------) - 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (2a cos(--------) - 2a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (4a cos(--------) - 4a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2x + %pi 3 +--R (8a cos(--------) - 8a cos(--------))cos(x) + 4a cos(--------) +--R 4 4 4 +--R + +--R 2x + %pi +--R - 4a cos(--------) +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 6a cos(--------) + 6a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 12a cos(--------) + 12a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (6a cos(--------) - 6a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2x + %pi 3 +--R (12a cos(--------) - 12a cos(--------))cos(x) + 6a cos(--------) +--R 4 4 4 +--R + +--R 2x + %pi +--R - 6a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) + (- 8a cos(--------) + 8a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 4a cos(--------) + 4a +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (- 2a cos(x) - 4a cos(x) - 2a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (8a cos(--------) - 8a)cos(x) + (16a cos(--------) - 16a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 8a cos(--------) - 8a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (4a cos(x) + 8a cos(x) + 4a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (- 2a cos(--------) + 2a)cos(x) + (- 4a cos(--------) + 4a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (10a cos(--------) - 10a)cos(x) + (24a cos(--------) - 24a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 12a cos(--------) - 12a +--R 4 +--R * +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (6a cos(x) + 12a cos(x) + 6a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (6a cos(--------) - 6a)cos(x) + (12a cos(--------) - 12a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 +--R (6a cos(--------) - 6a)cos(x) +--R 4 +--R / +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) + 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 2a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) - 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 2a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (2a cos(--------) - 2a)cos(x) + (4a cos(--------) - 4a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 2a cos(--------) - 2a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 2 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8a cos(--------) + 8a)cos(x) - 4a cos(--------) + 4a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) + (- 12a cos(--------) + 12a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 6a cos(--------) + 6a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 410 + +--S 411 of 534 +m0679b:= a0679.2-r0679 +--R +--R +--R (351) +--R +-+ +--R |2 +------------+ +--R (- a cos(x) - a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x + %pi 2x + %pi 2 +--R (- 4a cos(x) - 4a)sin(--------)atanh(cos(--------)) + 4a cos(x) +--R 4 4 +--R + +--R 4a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression Integer +--E 411 + +--S 412 of 534 +d0679b:= D(m0679b,x) +--R +--R +--R (352) +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (\|2 cos(--------) - \|2 )cos(x) + 5\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 5\|2 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (\|2 cos(--------) - \|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) - 3\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 3\|2 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (2\|2 cos(--------) - 2\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (4\|2 cos(--------) - 4\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 9\|2 cos(--------) + 9\|2 )cos(x) - 11\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 11\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 22\|2 cos(--------) + 22\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 35\|2 cos(--------) + 35\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) + 7\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 7\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (10\|2 cos(--------) - 10\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (34\|2 cos(--------) - 34\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (48\|2 cos(--------) - 48\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (34\|2 cos(--------) - 34\|2 )cos(x) + 10\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 10\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (6\|2 cos(--------) - 6\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (6\|2 cos(--------) - 6\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 2x + %pi 2 5 +--R ((4a cos(--------) - 4a)cos(x) + 4a cos(--------) - 4a)sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R ((- 6a cos(--------) + 6a)cos(x) - 6a cos(--------) + 6a) +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (4a cos(--------) - 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (4a cos(--------) - 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 14a cos(--------) + 14a)cos(x) - 14a cos(--------) + 14a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (- 8a cos(--------) + 8a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 34a cos(--------) + 34a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 38a cos(--------) + 38a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) + 6a cos(--------) - 6a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (24a cos(--------) - 24a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (62a cos(--------) - 62a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (62a cos(--------) - 62a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (34a cos(--------) - 34a)cos(x) + 10a cos(--------) - 10a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 5 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 8a cos(--------) + 8a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (8a cos(--------) - 8a)cos(x) + (4a cos(--------) - 4a)cos(x) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (- 4a\|2 cos(--------) + 4a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (- 8a\|2 cos(--------) + 8a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R - 4a\|2 cos(--------) + 4a\|2 cos(--------) +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 3 +--R (4a\|2 cos(--------) - 4a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (20a\|2 cos(--------) - 20a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (28a\|2 cos(--------) - 28a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R 12a\|2 cos(--------) - 12a\|2 cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 24a\|2 cos(--------) + 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 16a\|2 cos(--------) + 16a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 3 +--R (- 8a\|2 cos(--------) + 8a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (- 12a\|2 cos(--------) + 12a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R 4a\|2 cos(--------) - 4a\|2 cos(--------) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 3 +--R (- 12a\|2 cos(--------) + 12a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (- 36a\|2 cos(--------) + 36a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (- 36a\|2 cos(--------) + 36a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R - 12a\|2 cos(--------) + 12a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 8a\|2 cos(--------) + 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 16a\|2 cos(--------) + 16a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 8a\|2 cos(--------) + 8a\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (40a\|2 cos(--------) - 40a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (56a\|2 cos(--------) - 56a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 24a\|2 cos(--------) - 24a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (4a\|2 cos(x) + 20a\|2 cos(x) + 28a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 24a\|2 cos(--------) + 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 28a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 8a\|2 cos(--------) - 8a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi 2 +--R (- 8a\|2 cos(x) - 12a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (24a\|2 cos(--------) - 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 56a\|2 cos(--------) + 56a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 72a\|2 cos(--------) + 72a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 24a\|2 cos(--------) + 24a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) - 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (- 12a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 12a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (- 2a cos(--------) + 2a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 14a cos(--------) + 14a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (- 22a cos(--------) + 22a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R - 10a cos(--------) + 10a cos(--------) +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (2a cos(--------) - 2a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (14a cos(--------) - 14a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (22a cos(--------) - 22a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (10a cos(--------) - 10a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (26a cos(--------) - 26a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (70a cos(--------) - 70a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (62a cos(--------) - 62a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R 18a cos(--------) - 18a cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (- 28a cos(--------) + 28a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 84a cos(--------) + 84a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 84a cos(--------) + 84a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 28a cos(--------) + 28a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 4 +--R (- 8a cos(--------) + 8a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (- 22a cos(--------) + 22a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 18a cos(--------) + 18a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (- 2a cos(--------) + 2a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R 2a cos(--------) - 2a cos(--------) +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 5 +--R (8a cos(--------) - 8a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (50a cos(--------) - 50a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (102a cos(--------) - 102a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (86a cos(--------) - 86a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (26a cos(--------) - 26a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 4 +--R (- 8a cos(--------) + 8a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (- 50a cos(--------) + 50a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 102a cos(--------) + 102a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2x + %pi 3 +--R (- 86a cos(--------) + 86a cos(--------))cos(x) - 26a cos(--------) +--R 4 4 4 +--R + +--R 2x + %pi +--R 26a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 28a cos(--------) + 28a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 44a cos(--------) + 44a)cos(x) - 20a cos(--------) + 20a +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (- 2a cos(x) - 14a cos(x) - 22a cos(x) - 10a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (52a cos(--------) - 52a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (140a cos(--------) - 140a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (124a cos(--------) - 124a)cos(x) + 36a cos(--------) - 36a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (26a cos(x) + 70a cos(x) + 62a cos(x) + 18a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (- 2a cos(--------) + 2a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 30a cos(--------) + 30a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 66a cos(--------) + 66a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 46a cos(--------) + 46a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) + 4a cos(--------) - 4a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 22a cos(x) - 18a cos(x) - 2a cos(x) + 2a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 2x + %pi 2 4 +--R (28a cos(--------) - 28a)cos(x) + (68a cos(--------) - 68a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 3 +--R (- 16a cos(--------) + 16a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 176a cos(--------) + 176a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 172a cos(--------) + 172a)cos(x) - 52a cos(--------) + 52a +--R 4 4 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 50a cos(x) - 102a cos(x) - 86a cos(x) - 26a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 6 2x + %pi 2 5 +--R (- 8a cos(--------) + 8a)cos(x) + (- 50a cos(--------) + 50a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 4 +--R (- 102a cos(--------) + 102a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (- 86a cos(--------) + 86a)cos(x) + (- 26a cos(--------) + 26a)cos(x) +--R 4 4 +--R / +--R +-+ 2x + %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 20a\|2 cos(--------) + 20a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 28a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 12a\|2 cos(--------) + 12a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +-+ 2x + %pi 2 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) - 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) + 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 12a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (2a cos(--------) - 2a)cos(x) + (14a cos(--------) - 14a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (22a cos(--------) - 22a)cos(x) + 10a cos(--------) - 10a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 26a cos(--------) + 26a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 70a cos(--------) + 70a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 62a cos(--------) + 62a)cos(x) - 18a cos(--------) + 18a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (22a cos(--------) - 22a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (18a cos(--------) - 18a)cos(x) + (2a cos(--------) - 2a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 2a cos(--------) + 2a +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (50a cos(--------) - 50a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (102a cos(--------) - 102a)cos(x) + (86a cos(--------) - 86a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 26a cos(--------) - 26a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 412 + +--S 413 of 534 +t0680:= sin(x)/(a-a*sin(x))^(1/2) +--R +--R +--R sin(x) +--R (353) ----------------- +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 413 + +--S 414 of 534 +r0680:= 2*(-cos(x)+atanh(sin(1/4*%pi+1/2*x))*cos(1/4*%pi+1/2*x))/(-a*(sin(x)-1))^(1/2) +--R +--R +--R 2x + %pi 2x + %pi +--R 2cos(--------)atanh(sin(--------)) - 2cos(x) +--R 4 4 +--R (354) -------------------------------------------- +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 414 + +--S 415 of 534 +a0680:= integrate(t0680,x) +--R +--R +--R (355) +--R [ +--R +-+ +--R |2 +--R (a cos(x) + a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R (- a cos(x) - a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 415 + +--S 416 of 534 +m0680a:= a0680.1-r0680 +--R +--R +--R (356) +--R +-+ +--R |2 +--------------+ +--R (a cos(x) + a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi 2x + %pi +--R (- 4a cos(--------)cos(x) - 4a cos(--------))atanh(sin(--------)) +--R 4 4 4 +--R + +--R 2 +--R 4a cos(x) + 4a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression Integer +--E 416 + +--S 417 of 534 +d0680a:= D(m0680a,x) +--R +--R +--R (357) +--R +-+ 2x + %pi 2 +-+ 4 +--R (- \|2 sin(--------) + \|2 )sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (\|2 cos(x)sin(--------) - \|2 cos(x))sin(x) +--R 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 2\|2 cos(x) - \|2 cos(x) + 3\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 2\|2 cos(x) + \|2 cos(x) - 3\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 4\|2 cos(x) - 6\|2 cos(x) - 2\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 6\|2 cos(x) + 2\|2 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2x + %pi 2 +-+ 3 +--R (- 2\|2 cos(x) + 2\|2 cos(x))sin(--------) + 2\|2 cos(x) +--R 4 +--R + +--R +-+ +--R - 2\|2 cos(x) +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ +-+ 2x + %pi 3 +--R (2a\|2 cos(x) + 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ +-+ 2x + %pi +--R (- 2a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 3 +--R (2a\|2 cos(x) + 2a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R (2a\|2 cos(--------)cos(x) + 2a\|2 cos(--------)cos(x)) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ 2x + %pi +--R (- 2a\|2 cos(x) - 2a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R - 2a\|2 cos(--------)cos(x) - 2a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 3 +--R (- 2a\|2 cos(x) - 4a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R 2a\|2 cos(--------)cos(x) + 4a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R 2a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi +--R (2a\|2 cos(x) + 4a\|2 cos(x) + 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R - 2a\|2 cos(--------)cos(x) - 4a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R - 2a\|2 cos(--------)cos(x) +--R 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(sin(--------)) +--R \|a 4 +--R + +--R +-+ +-+ 2x + %pi 2 +-+ +--R (- 4a\|2 cos(x) - 4a\|2 )sin(--------) + 4a\|2 cos(x) +--R 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 2 +--R (- 4a\|2 cos(x) - 4a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ 2x + %pi 2 +-+ +--R 4a\|2 cos(x) + (2a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R 2a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 2a\|2 cos(x) + 2a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2x + %pi 2 +-+ 2 +--R 2a\|2 cos(x) + (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ +--R (2a\|2 cos(--------) - 8a\|2 )cos(x) - 4a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 2x + %pi 2 +--R (- 2a\|2 cos(x) - 4a\|2 cos(x) - 2a\|2 cos(x) )sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +--R 2a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi 2 +--R - 4a\|2 cos(--------) cos(x) - 2a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (2a sin(--------) - 2a)sin(x) + (- 2a sin(--------) + 2a)sin(x) +--R 4 4 +--R + +--R 2 2x + %pi 2 2 2 +--R ((2a cos(x) - 2a)sin(--------) - 2a cos(x) + 2a)sin(x) +--R 4 +--R + +--R 3 2 2x + %pi 2 +--R (4a cos(x) + 6a cos(x) + 4a cos(x) + 2a)sin(--------) +--R 4 +--R + +--R 3 2 +--R - 4a cos(x) - 6a cos(x) - 4a cos(x) - 2a +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 2 2x + %pi 3 +--R (- 2a cos(x) - 4a cos(x) - 2a)sin(--------) +--R 4 +--R + +--R 2 2x + %pi +--R (2a cos(x) + 4a cos(x) + 2a)sin(--------) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x + %pi 3 +--R (- 4a cos(x) - 8a cos(x) - 4a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - 2a cos(--------)cos(x) - 4a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R - 2a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2 2x + %pi +--R (4a cos(x) + 8a cos(x) + 4a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R 2a cos(--------)cos(x) + 4a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R 2a cos(--------)cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R 2 2x + %pi 3 +--R (6a cos(x) + 12a cos(x) + 6a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - 6a cos(--------)cos(x) - 12a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R - 6a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2 2x + %pi +--R (- 6a cos(x) - 12a cos(x) - 6a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R 6a cos(--------)cos(x) + 12a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R 6a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi +--R atanh(sin(--------)) +--R 4 +--R + +--R 2 2x + %pi 2 2 +--R (4a cos(x) + 8a cos(x) + 4a)sin(--------) - 4a cos(x) - 8a cos(x) +--R 4 +--R + +--R - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (8a cos(x) + 16a cos(x) + 8a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 2a cos(--------) - 8a)cos(x) + (- 4a cos(--------) - 16a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 2a cos(--------) - 8a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (2a cos(x) + 4a cos(x) - 10a cos(x) - 24a cos(x) - 12a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2x + %pi 2 2 +--R - 2a cos(x) - 4a cos(x) + (- 4a cos(--------) + 10a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8a cos(--------) + 24a)cos(x) - 4a cos(--------) + 12a +--R 4 4 +--R * +--R sin(x) +--R + +--R 4 3 2 2x + %pi 2 4 +--R (6a cos(x) + 12a cos(x) + 6a cos(x) )sin(--------) - 6a cos(x) +--R 4 +--R + +--R 3 2x + %pi 2 2 +--R - 12a cos(x) + (6a cos(--------) - 6a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R 12a cos(--------) cos(x) + 6a cos(--------) +--R 4 4 +--R / +--R +-+ +-+ 2x + %pi 2 +-+ +-+ +--R ((2a\|2 cos(x) + 2a\|2 )sin(--------) - 2a\|2 cos(x) - 2a\|2 ) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(x) + 2a\|2 cos(x))sin(--------) - 2a\|2 cos(x) +--R 4 +--R + +--R +-+ +--R - 2a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 2a\|2 cos(x) - 4a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 2a\|2 cos(x) + 4a\|2 cos(x) + 2a\|2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 2 2x + %pi 2 2 +--R (- 2a cos(x) - 4a cos(x) - 2a)sin(--------) + 2a cos(x) +--R 4 +--R + +--R 4a cos(x) + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x + %pi 2 2 +--R (- 4a cos(x) - 8a cos(x) - 4a)sin(--------) + 4a cos(x) +--R 4 +--R + +--R 8a cos(x) + 4a +--R * +--R sin(x) +--R + +--R 2 2x + %pi 2 2 +--R (6a cos(x) + 12a cos(x) + 6a)sin(--------) - 6a cos(x) +--R 4 +--R + +--R - 12a cos(x) - 6a +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 417 + +--S 418 of 534 +m0680b:= a0680.2-r0680 +--R +--R +--R (358) +--R +-+ +--R |2 +--------------+ +--R (- a cos(x) - a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi 2x + %pi +--R (- 4a cos(--------)cos(x) - 4a cos(--------))atanh(sin(--------)) +--R 4 4 4 +--R + +--R 2 +--R 4a cos(x) + 4a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression Integer +--E 418 + +--S 419 of 534 +d0680b:= D(m0680b,x) +--R +--R +--R (359) +--R +-+ +-+ 2x + %pi 2 +-+ +-+ +--R ((- \|2 cos(x) - 5\|2 )sin(--------) + \|2 cos(x) + 5\|2 ) +--R 4 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (\|2 cos(x) - 6\|2 cos(x) - 3\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R - \|2 cos(x) + 6\|2 cos(x) + 3\|2 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 2\|2 cos(x) - 4\|2 cos(x) + 9\|2 cos(x) + 11\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 2\|2 cos(x) + 4\|2 cos(x) - 9\|2 cos(x) - 11\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 22\|2 cos(x) - 35\|2 cos(x) - 6\|2 cos(x) + 7\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 22\|2 cos(x) + 35\|2 cos(x) + 6\|2 cos(x) - 7\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 10\|2 cos(x) - 34\|2 cos(x) - 48\|2 cos(x) +--R + +--R +-+ +-+ +--R - 34\|2 cos(x) - 10\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 10\|2 cos(x) + 34\|2 cos(x) + 48\|2 cos(x) + 34\|2 cos(x) +--R + +--R +-+ +--R 10\|2 +--R * +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R (- 6\|2 cos(x) - 6\|2 cos(x) + 6\|2 cos(x) + 6\|2 cos(x)) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 6\|2 cos(x) + 6\|2 cos(x) - 6\|2 cos(x) - 6\|2 cos(x) +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 3 +--R (4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi +--R (- 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (4a\|2 cos(x) + 20a\|2 cos(x) + 28a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R 4a\|2 cos(--------)cos(x) + 8a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R 4a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 4a\|2 cos(x) - 20a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +--R - 12a\|2 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R - 4a\|2 cos(--------)cos(x) - 8a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R - 4a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi 3 +--R (8a\|2 cos(x) + 12a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R 4a\|2 cos(--------)cos(x) + 24a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R 36a\|2 cos(--------)cos(x) + 16a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi +--R (- 8a\|2 cos(x) - 12a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R - 4a\|2 cos(--------)cos(x) - 24a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R - 36a\|2 cos(--------)cos(x) - 16a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) - 12a\|2 ) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R 12a\|2 cos(--------)cos(x) + 36a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R 36a\|2 cos(--------)cos(x) + 12a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (12a\|2 cos(x) + 36a\|2 cos(x) + 36a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R - 12a\|2 cos(--------)cos(x) - 36a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R - 36a\|2 cos(--------)cos(x) - 12a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(sin(--------)) +--R \|a 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 40a\|2 cos(x) - 56a\|2 cos(x) +--R + +--R +-+ +--R - 24a\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2x + %pi 2 +-+ 2 +--R 8a\|2 cos(x) + (4a\|2 cos(--------) + 40a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) + 56a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 24a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 4a\|2 cos(x) - 24a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 2x + %pi 2 +-+ 3 +--R 4a\|2 cos(x) + (4a\|2 cos(--------) + 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (20a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi 2 +-+ +--R 28a\|2 cos(--------) cos(x) + 12a\|2 cos(--------) - 8a\|2 +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) - 24a\|2 cos(x) - 12a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 56a\|2 cos(x) + 72a\|2 cos(x) + 24a\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R 4a\|2 cos(x) + 24a\|2 cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +-+ +--R (12a\|2 cos(--------) - 56a\|2 )cos(x) - 72a\|2 cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 4a\|2 cos(--------) - 24a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) +--R + +--R +-+ 2 +--R - 12a\|2 cos(x) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R 12a\|2 cos(x) + 36a\|2 cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 12a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 36a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi 2 +--R - 36a\|2 cos(--------) cos(x) - 12a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 5 +--R ((4a cos(x) + 4a)sin(--------) - 4a cos(x) - 4a)sin(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R ((6a cos(x) + 6a)sin(--------) - 6a cos(x) - 6a)sin(x) +--R 4 +--R + +--R 3 2 2x + %pi 2 +--R (4a cos(x) + 4a cos(x) - 14a cos(x) - 14a)sin(--------) +--R 4 +--R + +--R 3 2 +--R - 4a cos(x) - 4a cos(x) + 14a cos(x) + 14a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (8a cos(x) + 34a cos(x) + 38a cos(x) + 6a cos(x) - 6a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R - 8a cos(x) - 34a cos(x) - 38a cos(x) - 6a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (24a cos(x) + 62a cos(x) + 62a cos(x) + 34a cos(x) + 10a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R - 24a cos(x) - 62a cos(x) - 62a cos(x) - 34a cos(x) - 10a +--R * +--R sin(x) +--R + +--R 5 4 2 2x + %pi 2 +--R (4a cos(x) + 8a cos(x) - 8a cos(x) - 4a cos(x))sin(--------) +--R 4 +--R + +--R 5 4 2 +--R - 4a cos(x) - 8a cos(x) + 8a cos(x) + 4a cos(x) +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 3 2 2x + %pi 3 +--R (- 2a cos(x) - 14a cos(x) - 22a cos(x) - 10a)sin(--------) +--R 4 +--R + +--R 3 2 2x + %pi +--R (2a cos(x) + 14a cos(x) + 22a cos(x) + 10a)sin(--------) +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2x + %pi 3 +--R (- 26a cos(x) - 70a cos(x) - 62a cos(x) - 18a)sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R - 2a cos(--------)cos(x) - 14a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R - 22a cos(--------)cos(x) - 10a cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 3 2 2x + %pi +--R (26a cos(x) + 70a cos(x) + 62a cos(x) + 18a)sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R 2a cos(--------)cos(x) + 14a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R 22a cos(--------)cos(x) + 10a cos(--------)cos(x) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 22a cos(x) - 18a cos(x) - 2a cos(x) + 2a) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R - 28a cos(--------)cos(x) - 84a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R - 84a cos(--------)cos(x) - 28a cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R (8a cos(x) + 22a cos(x) + 18a cos(x) + 2a cos(x) - 2a) +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R 28a cos(--------)cos(x) + 84a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R 84a cos(--------)cos(x) + 28a cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (8a cos(x) + 50a cos(x) + 102a cos(x) + 86a cos(x) + 26a) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 5 2x + %pi 4 +--R - 8a cos(--------)cos(x) - 50a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - 102a cos(--------)cos(x) - 86a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R - 26a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R (- 8a cos(x) - 50a cos(x) - 102a cos(x) - 86a cos(x) - 26a) +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 5 2x + %pi 4 +--R 8a cos(--------)cos(x) + 50a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R 102a cos(--------)cos(x) + 86a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R 26a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi +--R atanh(sin(--------)) +--R 4 +--R + +--R 3 2 2x + %pi 2 +--R (4a cos(x) + 28a cos(x) + 44a cos(x) + 20a)sin(--------) +--R 4 +--R + +--R 3 2 +--R - 4a cos(x) - 28a cos(x) - 44a cos(x) - 20a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (52a cos(x) + 140a cos(x) + 124a cos(x) + 36a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 2a cos(--------) - 52a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 14a cos(--------) - 140a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 22a cos(--------) - 124a)cos(x) - 10a cos(--------) - 36a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 2a cos(x) + 30a cos(x) + 66a cos(x) + 46a cos(x) + 4a cos(x) +--R + +--R - 4a +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 5 4 2x + %pi 2 3 +--R - 2a cos(x) - 30a cos(x) + (- 26a cos(--------) - 66a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 70a cos(--------) - 46a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 62a cos(--------) - 4a)cos(x) - 18a cos(--------) + 4a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R 28a cos(x) + 68a cos(x) - 16a cos(x) - 176a cos(x) +--R + +--R - 172a cos(x) - 52a +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 5 2x + %pi 2 4 +--R - 28a cos(x) + (- 8a cos(--------) - 68a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 22a cos(--------) + 16a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 18a cos(--------) + 176a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 2a cos(--------) + 172a)cos(x) + 2a cos(--------) + 52a +--R 4 4 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (8a cos(x) + 50a cos(x) + 102a cos(x) + 86a cos(x) + 26a cos(x) ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 6 5 2x + %pi 2 4 +--R - 8a cos(x) - 50a cos(x) + (8a cos(--------) - 102a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (50a cos(--------) - 86a)cos(x) + (102a cos(--------) - 26a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R 86a cos(--------) cos(x) + 26a cos(--------) +--R 4 4 +--R / +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R - 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (4a\|2 cos(x) + 20a\|2 cos(x) + 28a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 4a\|2 cos(x) - 20a\|2 cos(x) - 28a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi 2 +--R (8a\|2 cos(x) + 12a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 12a\|2 cos(x) + 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) - 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 12a\|2 cos(x) + 36a\|2 cos(x) + 36a\|2 cos(x) + 12a\|2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 3 2 2x + %pi 2 +--R (- 2a cos(x) - 14a cos(x) - 22a cos(x) - 10a)sin(--------) +--R 4 +--R + +--R 3 2 +--R 2a cos(x) + 14a cos(x) + 22a cos(x) + 10a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (- 26a cos(x) - 70a cos(x) - 62a cos(x) - 18a)sin(--------) +--R 4 +--R + +--R 3 2 +--R 26a cos(x) + 70a cos(x) + 62a cos(x) + 18a +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 22a cos(x) - 18a cos(x) - 2a cos(x) + 2a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R 8a cos(x) + 22a cos(x) + 18a cos(x) + 2a cos(x) - 2a +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (8a cos(x) + 50a cos(x) + 102a cos(x) + 86a cos(x) + 26a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R - 8a cos(x) - 50a cos(x) - 102a cos(x) - 86a cos(x) - 26a +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 419 + +--S 420 of 534 +t0681:= sin(x)/(a+b*sin(x))^(1/2) +--R +--R +--R sin(x) +--R (360) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression Integer +--E 420 + +--S 421 of 534 +r0681:= 2*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*(a+b*sin(x))^(1/2)/b/((a+b*sin(x))/(a+b))^(1/2)-2*a*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*((a+b*sin(x))/(a+b))^(1/2)/b/(a+b*sin(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 421 + +--S 422 of 534 +a0681:= integrate(t0681,x) +--R +--R +--R x +--R ++ sin(%L) +--R (361) | ---------------- d%L +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Union(Expression Integer,...) +--E 422 + +--S 423 of 534 +m0681:= a0681-r0681 +--R +--R +--R x +--R ++ sin(%L) +--R (362) | ---------------- d%L - r0681 +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Expression Integer +--E 423 + +--S 424 of 534 +d0681:= D(m0681,x) +--R +--R +--R sin(x) +--R (363) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression Integer +--E 424 + +--S 425 of 534 +t0682:= (A+B*sin(x))/(a+a*sin(x))^(1/2) +--R +--R +--R B sin(x) + A +--R (364) --------------- +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 425 + +--S 426 of 534 +r0682:= -2*B*cos(x)/(a+a*sin(x))^(1/2)-2*(A-B)*atanh(cos(1/4*%pi+1/2*x))*cos(-1/4*%pi+1/2*x)/(a+a*sin(x))^(1/2) +--R +--R +--R 2x - %pi 2x + %pi +--R (2B - 2A)cos(--------)atanh(cos(--------)) - 2B cos(x) +--R 4 4 +--R (365) ------------------------------------------------------ +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 426 + +--S 427 of 534 +a0682:= integrate(t0682,x) +--R +--R +--R (366) +--R [ +--R +-+ +--R |2 +--R ((B - A)a cos(x) + (B - A)a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R ((- B + A)a cos(x) + (- B + A)a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 427 + +--S 428 of 534 +m0682a:= a0682.1-r0682 +--R +--R +--R (367) +--R +-+ +--R |2 +------------+ +--R ((B - A)a cos(x) + (B - A)a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x - %pi 2x - %pi +--R ((- 4B + 4A)a cos(--------)cos(x) + (- 4B + 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression Integer +--E 428 + +--S 429 of 534 +d0682a:= D(m0682a,x) +--R +--R +--R (368) +--R +-+ 2x + %pi 2 +-+ 4 +--R (B\|2 cos(--------) - B\|2 )sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) - A\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R A\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2B\|2 cos(--------) - 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((B - A)\|2 cos(--------) + (- B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 3B - 2A)\|2 cos(--------) + (3B + 2A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 4B\|2 cos(--------) + 4B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 6B - A)\|2 cos(--------) + (6B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2B - A)\|2 cos(--------) + (2B + A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((2B - 2A)\|2 cos(--------) + (- 2B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 6A\|2 cos(--------) + 6A\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 2B - 4A)\|2 cos(--------) + (2B + 4A)\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 4 +--R (2B a cos(--------) - 2B a)sin(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (2B a cos(--------) - 2B a)sin(x) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (2B a cos(--------) - 2B a)cos(x) - 2B a cos(--------) +--R 4 4 +--R + +--R 2B a +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 6B a cos(--------) + 6B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4B a cos(--------) + 4B a)cos(x) - 2B a cos(--------) +--R 4 4 +--R + +--R 2B a +--R * +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 4A a cos(--------) + 4A a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 8A a cos(--------) + 8A a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 4A a cos(--------) + 4A a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((2B - 2A)a\|2 cos(--------) + (- 2B + 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (2B - 2A)a\|2 cos(--------) + (- 2B + 2A)a\|2 +--R 4 +--R * +--R 2x - %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 )cos(x) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 4B + 4A)a\|2 cos(--------) + (4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 2B + 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (2B - 2A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 4B + 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 2B + 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (2B - 2A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 4B a\|2 cos(--------) + 4B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (8B a\|2 cos(--------) - 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 4B a\|2 cos(--------) - 4B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------)cos(x) + (2B - 2A)a\|2 cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 2 +--R ((2B - 2A)a cos(--------) + (- 2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((4B - 4A)a cos(--------) + (- 4B + 4A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (2B - 2A)a cos(--------) + (- 2B + 2A)a +--R 4 +--R * +--R 2x - %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((- 4B + 4A)a cos(--------) + (4B - 4A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 8B + 8A)a cos(--------) + (8B - 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 4B + 4A)a cos(--------) + (4B - 4A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (2B - 2A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 2B + 2A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (4B - 4A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 4B + 4A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (2B - 2A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 2B + 2A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R 2x + %pi 2 2 +--R ((- 6B + 6A)a cos(--------) + (6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 12B + 12A)a cos(--------) + (12B - 12A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 6B + 6A)a cos(--------) + (6B - 6A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 6B + 6A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (6B - 6A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 12B + 12A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (12B - 12A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 6B + 6A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (6B - 6A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8B a cos(--------) + 8B a)cos(x) - 4B a cos(--------) + 4B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 2 +--R (- 2B + 2A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 4B + 4A)a cos(--------)cos(x) + (- 2B + 2A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (16B a cos(--------) - 16B a)cos(x) + 8B a cos(--------) - 8B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 2x - %pi +--R (4B - 4A)a cos(--------)cos(x) + (8B - 8A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi +--R (4B - 4A)a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 2B a cos(--------) + 2B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (10B a cos(--------) - 10B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (24B a cos(--------) - 24B a)cos(x) + 12B a cos(--------) - 12B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 2x - %pi +--R (6B - 6A)a cos(--------)cos(x) + (12B - 12A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi +--R (6B - 6A)a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (6B a cos(--------) - 6B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (12B a cos(--------) - 12B a)cos(x) + (6B a cos(--------) - 6B a)cos(x) +--R 4 4 +--R / +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) + 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 2a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) - 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 2a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (2a cos(--------) - 2a)cos(x) + (4a cos(--------) - 4a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 2a cos(--------) - 2a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 2 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8a cos(--------) + 8a)cos(x) - 4a cos(--------) + 4a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) + (- 12a cos(--------) + 12a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 6a cos(--------) + 6a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 429 + +--S 430 of 534 +m0682b:= a0682.2-r0682 +--R +--R +--R (369) +--R +-+ +--R |2 +------------+ +--R ((- B + A)a cos(x) + (- B + A)a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x - %pi 2x - %pi +--R ((- 4B + 4A)a cos(--------)cos(x) + (- 4B + 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression Integer +--E 430 + +--S 431 of 534 +d0682b:= D(m0682b,x) +--R +--R +--R (370) +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) + 5B\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 5B\|2 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 6B - A)\|2 cos(--------) + (6B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 3B - A)\|2 cos(--------) + (3B + A)\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (2B\|2 cos(--------) - 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((4B - A)\|2 cos(--------) + (- 4B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 9B\|2 cos(--------) + 9B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 11B + A)\|2 cos(--------) + (11B - A)\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 22B\|2 cos(--------) + 22B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((- 35B + 2A)\|2 cos(--------) + (35B - 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 6B + 7A)\|2 cos(--------) + (6B - 7A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (7B + 5A)\|2 cos(--------) + (- 7B - 5A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R ((10B - 2A)\|2 cos(--------) + (- 10B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((34B - 16A)\|2 cos(--------) + (- 34B + 16A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((48B - 23A)\|2 cos(--------) + (- 48B + 23A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((34B - 6A)\|2 cos(--------) + (- 34B + 6A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (10B + 3A)\|2 cos(--------) + (- 10B - 3A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R ((- 6B + 14A)\|2 cos(--------) + (6B - 14A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((- 6B + 48A)\|2 cos(--------) + (6B - 48A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((6B + 54A)\|2 cos(--------) + (- 6B - 54A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((6B + 20A)\|2 cos(--------) + (- 6B - 20A)\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (4B a cos(--------) - 4B a)cos(x) + 4B a cos(--------) +--R 4 4 +--R + +--R - 4B a +--R * +--R 5 +--R sin(x) +--R + +--R 2x + %pi 2 +--R ((- 6B - 2A)a cos(--------) + (6B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 6B - 2A)a cos(--------) + (6B + 2A)a +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 14B - 2A)a cos(--------) + (14B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 14B - 2A)a cos(--------) + (14B + 2A)a +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (- 8B a cos(--------) + 8B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((- 34B + 2A)a cos(--------) + (34B - 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((- 38B + 6A)a cos(--------) + (38B - 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 6B + 6A)a cos(--------) + (6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (6B + 2A)a cos(--------) + (- 6B - 2A)a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R ((24B - 8A)a cos(--------) + (- 24B + 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((62B - 26A)a cos(--------) + (- 62B + 26A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((62B - 26A)a cos(--------) + (- 62B + 26A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((34B - 6A)a cos(--------) + (- 34B + 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (10B + 2A)a cos(--------) + (- 10B - 2A)a +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 5 +--R ((- 4B + 4A)a cos(--------) + (4B - 4A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R ((- 8B + 32A)a cos(--------) + (8B - 32A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (72A a cos(--------) - 72A a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((8B + 64A)a cos(--------) + (- 8B - 64A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((4B + 20A)a cos(--------) + (- 4B - 20A)a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((4B - 4A)a\|2 cos(--------) + (- 4B + 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((8B - 8A)a\|2 cos(--------) + (- 8B + 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4B - 4A)a\|2 cos(--------) + (- 4B + 4A)a\|2 +--R 4 +--R * +--R 2x - %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((- 4B + 4A)a\|2 cos(--------) + (4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 20B + 20A)a\|2 cos(--------) + (20B - 20A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 28B + 28A)a\|2 cos(--------) + (28B - 28A)a\|2 ) +--R 4 +--R * +--R cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 12B + 12A)a\|2 cos(--------) + (12B - 12A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (4B - 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (8B - 8A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 8B + 8A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (4B - 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((8B - 8A)a\|2 cos(--------) + (- 8B + 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((12B - 12A)a\|2 cos(--------) + (- 12B + 12A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 4B + 4A)a\|2 cos(--------) + (4B - 4A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 4B + 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 24B + 24A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (24B - 24A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 36B + 36A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (36B - 36A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 16B + 16A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (16B - 16A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((12B - 12A)a\|2 cos(--------) + (- 12B + 12A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((36B - 36A)a\|2 cos(--------) + (- 36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((36B - 36A)a\|2 cos(--------) + (- 36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (12B - 12A)a\|2 cos(--------) + (- 12B + 12A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (12B - 12A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (36B - 36A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 36B + 36A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (36B - 36A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 36B + 36A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (12B - 12A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 8B a\|2 cos(--------) + 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 16B a\|2 cos(--------) + 16B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 8B a\|2 cos(--------) + 8B a\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +--R (- 4B + 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 8B + 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8B a\|2 cos(--------) - 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (40B a\|2 cos(--------) - 40B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (56B a\|2 cos(--------) - 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 24B a\|2 cos(--------) - 24B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 3 +--R (4B - 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +--R (20B - 20A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (28B - 28A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (12B - 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 24B a\|2 cos(--------) + 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 28B a\|2 cos(--------) + 28B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 8B a\|2 cos(--------) - 8B a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 3 +--R (- 8B + 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +--R (- 12B + 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (24B a\|2 cos(--------) - 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12B a\|2 cos(--------) - 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 56B a\|2 cos(--------) + 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 72B a\|2 cos(--------) + 72B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 24B a\|2 cos(--------) + 24B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 3 +--R (- 12B + 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +--R (- 36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 3 +--R ((2B - 2A)a cos(--------) + (- 2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((14B - 14A)a cos(--------) + (- 14B + 14A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((22B - 22A)a cos(--------) + (- 22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (10B - 10A)a cos(--------) + (- 10B + 10A)a +--R 4 +--R * +--R 2x - %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((- 26B + 26A)a cos(--------) + (26B - 26A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((- 70B + 70A)a cos(--------) + (70B - 70A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 62B + 62A)a cos(--------) + (62B - 62A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 18B + 18A)a cos(--------) + (18B - 18A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (2B - 2A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 2B + 2A)a cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (14B - 14A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 14B + 14A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (22B - 22A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 22B + 22A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (10B - 10A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 10B + 10A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R ((8B - 8A)a cos(--------) + (- 8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((22B - 22A)a cos(--------) + (- 22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((18B - 18A)a cos(--------) + (- 18B + 18A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((2B - 2A)a cos(--------) + (- 2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 2B + 2A)a cos(--------) + (2B - 2A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 28B + 28A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (28B - 28A)a cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 84B + 84A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (84B - 84A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 84B + 84A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (84B - 84A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 28B + 28A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (28B - 28A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R ((8B - 8A)a cos(--------) + (- 8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((50B - 50A)a cos(--------) + (- 50B + 50A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((102B - 102A)a cos(--------) + (- 102B + 102A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((86B - 86A)a cos(--------) + (- 86B + 86A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (26B - 26A)a cos(--------) + (- 26B + 26A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (8B - 8A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 8B + 8A)a cos(--------) +--R 4 +--R * +--R 5 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (50B - 50A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 50B + 50A)a cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (102B - 102A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 102B + 102A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (86B - 86A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 86B + 86A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (26B - 26A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 26B + 26A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 28B a cos(--------) + 28B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 44B a cos(--------) + 44B a)cos(x) - 20B a cos(--------) + 20B a +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x - %pi 3 +--R (- 2B + 2A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 14B + 14A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 22B + 22A)a cos(--------)cos(x) + (- 10B + 10A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (52B a cos(--------) - 52B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (140B a cos(--------) - 140B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (124B a cos(--------) - 124B a)cos(x) + 36B a cos(--------) - 36B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 3 +--R (26B - 26A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (70B - 70A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (62B - 62A)a cos(--------)cos(x) + (18B - 18A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (- 2B a cos(--------) + 2B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 30B a cos(--------) + 30B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 66B a cos(--------) + 66B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 46B a cos(--------) + 46B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4B a cos(--------) + 4B a)cos(x) + 4B a cos(--------) - 4B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 4 +--R (- 8B + 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 3 +--R (- 22B + 22A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 18B + 18A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 2B + 2A)a cos(--------)cos(x) + (2B - 2A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (28B a cos(--------) - 28B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (68B a cos(--------) - 68B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 16B a cos(--------) + 16B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 176B a cos(--------) + 176B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 172B a cos(--------) + 172B a)cos(x) - 52B a cos(--------) + 52B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 4 +--R (- 8B + 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 3 +--R (- 50B + 50A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 102B + 102A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 86B + 86A)a cos(--------)cos(x) + (- 26B + 26A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 6 +--R (- 8B a cos(--------) + 8B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (- 50B a cos(--------) + 50B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 102B a cos(--------) + 102B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 86B a cos(--------) + 86B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 26B a cos(--------) + 26B a)cos(x) +--R 4 +--R / +--R +-+ 2x + %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 20a\|2 cos(--------) + 20a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 28a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 12a\|2 cos(--------) + 12a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +-+ 2x + %pi 2 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) - 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) + 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 12a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (2a cos(--------) - 2a)cos(x) + (14a cos(--------) - 14a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (22a cos(--------) - 22a)cos(x) + 10a cos(--------) - 10a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 26a cos(--------) + 26a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 70a cos(--------) + 70a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 62a cos(--------) + 62a)cos(x) - 18a cos(--------) + 18a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (22a cos(--------) - 22a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (18a cos(--------) - 18a)cos(x) + (2a cos(--------) - 2a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 2a cos(--------) + 2a +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (50a cos(--------) - 50a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (102a cos(--------) - 102a)cos(x) + (86a cos(--------) - 86a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 26a cos(--------) - 26a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression Integer +--E 431 + +--S 432 of 534 +t0683:= (A+B*sin(x))/(a-a*sin(x))^(1/2) +--R +--R +--R B sin(x) + A +--R (371) ----------------- +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 432 + +--S 433 of 534 +r0683:= -2*B*cos(x)/(a-a*sin(x))^(1/2)+2*(A+B)*atanh(cos(-1/4*%pi+1/2*x))*cos(1/4*%pi+1/2*x)/(a-a*sin(x))^(1/2) +--R +--R +--R 2x + %pi 2x - %pi +--R (2B + 2A)cos(--------)atanh(cos(--------)) - 2B cos(x) +--R 4 4 +--R (372) ------------------------------------------------------ +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 433 + +--S 434 of 534 +a0683:= integrate(t0683,x) +--R +--R +--R (373) +--R [ +--R +-+ +--R |2 +--R ((B + A)a cos(x) + (B + A)a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R ((- B - A)a cos(x) + (- B - A)a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 434 + +--S 435 of 534 +m0683a:= a0683.1-r0683 +--R +--R +--R (374) +--R +-+ +--R |2 +--------------+ +--R ((B + A)a cos(x) + (B + A)a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi +--R ((- 4B - 4A)a cos(--------)cos(x) + (- 4B - 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression Integer +--E 435 + +--S 436 of 534 +d0683a:= D(m0683a,x) +--R +--R +--R (375) +--R +-+ 2x - %pi 2 +-+ 4 +--R (- B\|2 cos(--------) + B\|2 )sin(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) + A\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - A\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 2B\|2 cos(--------) + 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- B - A)\|2 cos(--------) + (B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (3B - 2A)\|2 cos(--------) + (- 3B + 2A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 4B\|2 cos(--------) + 4B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 6B + A)\|2 cos(--------) + (6B - A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 2B + A)\|2 cos(--------) + (2B - A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 2B - 2A)\|2 cos(--------) + (2B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 6A\|2 cos(--------) + 6A\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B - 4A)\|2 cos(--------) + (- 2B + 4A)\|2 )cos(x) +--R 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 2B - 2A)a\|2 cos(--------) + (2B + 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 4B - 4A)a\|2 cos(--------) + (4B + 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 2B - 2A)a\|2 cos(--------) + (2B + 2A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2x + %pi +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2x + %pi +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 )cos(--------) +--R 4 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2x + %pi +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(--------) +--R 4 4 +--R * +--R cos(x) +--R * +--R +-+ +--R |2 2x - %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R - 4B a\|2 cos(--------) + 4B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi +--R (- 2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 2B - 2A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +--R (- 2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (8B a\|2 cos(--------) - 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R 4B a\|2 cos(--------) - 4B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +--R (2B + 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +-+ 2x + %pi +--R (4B + 4A)a\|2 cos(--------)cos(x) + (2B + 2A)a\|2 cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x - %pi 2 4 +--R (2B a cos(--------) - 2B a)sin(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (- 2B a cos(--------) + 2B a)sin(x) +--R 4 +--R + +--R 2x - %pi 2 2 2x - %pi 2 +--R ((2B a cos(--------) - 2B a)cos(x) - 2B a cos(--------) + 2B a) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (6B a cos(--------) - 6B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (4B a cos(--------) - 4B a)cos(x) + 2B a cos(--------) - 2B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (4A a cos(--------) - 4A a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (8A a cos(--------) - 8A a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (4A a cos(--------) - 4A a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 2x - %pi 2 2 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 4B - 4A)a cos(--------) + (4B + 4A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 2B - 2A)a cos(--------) + (2B + 2A)a +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 4B - 4A)a cos(--------) + (4B + 4A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 8B - 8A)a cos(--------) + (8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 4B - 4A)a cos(--------) + (4B + 4A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 3 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi 2 +--R ((- 4B - 4A)a cos(--------) + (4B + 4A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 2 +--R ((6B + 6A)a cos(--------) + (- 6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((12B + 12A)a cos(--------) + (- 12B - 12A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (6B + 6A)a cos(--------) + (- 6B - 6A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 3 +--R ((- 6B - 6A)a cos(--------) + (6B + 6A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi 2 +--R ((- 12B - 12A)a cos(--------) + (12B + 12A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 6B - 6A)a cos(--------) + (6B + 6A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (8B a cos(--------) - 8B a)cos(x) + 4B a cos(--------) - 4B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 2x + %pi +--R (2B + 2A)a cos(--------)cos(x) + (4B + 4A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R (2B + 2A)a cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (16B a cos(--------) - 16B a)cos(x) + 8B a cos(--------) - 8B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 2x + %pi +--R (4B + 4A)a cos(--------)cos(x) + (8B + 8A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R (4B + 4A)a cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (2B a cos(--------) - 2B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 10B a cos(--------) + 10B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 24B a cos(--------) + 24B a)cos(x) - 12B a cos(--------) + 12B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 +--R (- 6B - 6A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (- 12B - 12A)a cos(--------)cos(x) + (- 6B - 6A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (6B a cos(--------) - 6B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 2x - %pi 2 2 +--R (12B a cos(--------) - 12B a)cos(x) + (6B a cos(--------) - 6B a)cos(x) +--R 4 4 +--R / +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) + 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 2a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +-+ +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) - 2a\|2 cos(--------) + 2a\|2 +--R 4 4 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 2x - %pi 2 2 +--R (- 2a cos(--------) + 2a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) - 2a cos(--------) + 2a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 2 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 8a cos(--------) + 8a)cos(x) - 4a cos(--------) + 4a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 2 2x - %pi 2 +--R (6a cos(--------) - 6a)cos(x) + (12a cos(--------) - 12a)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 +--R 6a cos(--------) - 6a +--R 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 436 + +--S 437 of 534 +m0683b:= a0683.2-r0683 +--R +--R +--R (376) +--R +-+ +--R |2 +--------------+ +--R ((- B - A)a cos(x) + (- B - A)a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi +--R ((- 4B - 4A)a cos(--------)cos(x) + (- 4B - 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression Integer +--E 437 + +--S 438 of 534 +d0683b:= D(m0683b,x) +--R +--R +--R (377) +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (- B\|2 cos(--------) + B\|2 )cos(x) - 5B\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 5B\|2 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 6B + A)\|2 cos(--------) + (6B - A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 3B + A)\|2 cos(--------) + (3B - A)\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 2B\|2 cos(--------) + 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 4B - A)\|2 cos(--------) + (4B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (9B\|2 cos(--------) - 9B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (11B + A)\|2 cos(--------) + (- 11B - A)\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 22B\|2 cos(--------) + 22B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 35B - 2A)\|2 cos(--------) + (35B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 6B - 7A)\|2 cos(--------) + (6B + 7A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (7B - 5A)\|2 cos(--------) + (- 7B + 5A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R ((- 10B - 2A)\|2 cos(--------) + (10B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 34B - 16A)\|2 cos(--------) + (34B + 16A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 48B - 23A)\|2 cos(--------) + (48B + 23A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 34B - 6A)\|2 cos(--------) + (34B + 6A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 10B + 3A)\|2 cos(--------) + (10B - 3A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R ((- 6B - 14A)\|2 cos(--------) + (6B + 14A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 6B - 48A)\|2 cos(--------) + (6B + 48A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((6B - 54A)\|2 cos(--------) + (- 6B + 54A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((6B - 20A)\|2 cos(--------) + (- 6B + 20A)\|2 )cos(x) +--R 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((8B + 8A)a\|2 cos(--------) + (- 8B - 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 +--R 4 +--R * +--R 2x + %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((20B + 20A)a\|2 cos(--------) + (- 20B - 20A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((28B + 28A)a\|2 cos(--------) + (- 28B - 28A)a\|2 ) +--R 4 +--R * +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ +--R (12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 3 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((8B + 8A)a\|2 cos(--------) + (- 8B - 8A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((8B + 8A)a\|2 cos(--------) + (- 8B - 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 4B - 4A)a\|2 cos(--------) + (4B + 4A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 4 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((24B + 24A)a\|2 cos(--------) + (- 24B - 24A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 3 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((36B + 36A)a\|2 cos(--------) + (- 36B - 36A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((16B + 16A)a\|2 cos(--------) + (- 16B - 16A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 12B - 12A)a\|2 cos(--------) + (12B + 12A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 36B - 36A)a\|2 cos(--------) + (36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 36B - 36A)a\|2 cos(--------) + (36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 12B - 12A)a\|2 cos(--------) + (12B + 12A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 4 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((36B + 36A)a\|2 cos(--------) + (- 36B - 36A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 3 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((36B + 36A)a\|2 cos(--------) + (- 36B - 36A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R +-+ +--R |2 2x - %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 8B a\|2 cos(--------) + 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 16B a\|2 cos(--------) + 16B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R - 8B a\|2 cos(--------) + 8B a\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +--R (- 4B - 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 8B - 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 8B a\|2 cos(--------) + 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 40B a\|2 cos(--------) + 40B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 56B a\|2 cos(--------) + 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R - 24B a\|2 cos(--------) + 24B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 3 +--R (- 4B - 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R (- 20B - 20A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 28B - 28A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 12B - 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 24B a\|2 cos(--------) + 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 28B a\|2 cos(--------) + 28B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R 8B a\|2 cos(--------) - 8B a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 3 +--R (- 8B - 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R (- 12B - 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 5 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 24B a\|2 cos(--------) + 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (56B a\|2 cos(--------) - 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (72B a\|2 cos(--------) - 72B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R 24B a\|2 cos(--------) - 24B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 3 +--R (12B + 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R (36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 5 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x - %pi 2 2x - %pi 2 +--R ((4B a cos(--------) - 4B a)cos(x) + 4B a cos(--------) - 4B a) +--R 4 4 +--R * +--R 5 +--R sin(x) +--R + +--R 2x - %pi 2 +--R ((6B - 2A)a cos(--------) + (- 6B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (6B - 2A)a cos(--------) + (- 6B + 2A)a +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 14B + 2A)a cos(--------) + (14B - 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 14B + 2A)a cos(--------) + (14B - 2A)a +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((34B + 2A)a cos(--------) + (- 34B - 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((38B + 6A)a cos(--------) + (- 38B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((6B + 6A)a cos(--------) + (- 6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 6B + 2A)a cos(--------) + (6B - 2A)a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R ((24B + 8A)a cos(--------) + (- 24B - 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((62B + 26A)a cos(--------) + (- 62B - 26A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((62B + 26A)a cos(--------) + (- 62B - 26A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((34B + 6A)a cos(--------) + (- 34B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (10B - 2A)a cos(--------) + (- 10B + 2A)a +--R 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 5 +--R ((4B + 4A)a cos(--------) + (- 4B - 4A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R ((8B + 32A)a cos(--------) + (- 8B - 32A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (72A a cos(--------) - 72A a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 8B + 64A)a cos(--------) + (8B - 64A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 4B + 20A)a cos(--------) + (4B - 20A)a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 2x - %pi 2 3 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 14B - 14A)a cos(--------) + (14B + 14A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 22B - 22A)a cos(--------) + (22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 10B - 10A)a cos(--------) + (10B + 10A)a +--R 4 +--R * +--R 2x + %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((- 26B - 26A)a cos(--------) + (26B + 26A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 70B - 70A)a cos(--------) + (70B + 70A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 62B - 62A)a cos(--------) + (62B + 62A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 18B - 18A)a cos(--------) + (18B + 18A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 4 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 14B - 14A)a cos(--------) + (14B + 14A)a)cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 22B - 22A)a cos(--------) + (22B + 22A)a)cos(--------) +--R 4 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 10B - 10A)a cos(--------) + (10B + 10A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R ((- 8B - 8A)a cos(--------) + (8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((- 22B - 22A)a cos(--------) + (22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 18B - 18A)a cos(--------) + (18B + 18A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (2B + 2A)a cos(--------) + (- 2B - 2A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 28B - 28A)a cos(--------) + (28B + 28A)a)cos(--------) +--R 4 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 84B - 84A)a cos(--------) + (84B + 84A)a)cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 84B - 84A)a cos(--------) + (84B + 84A)a)cos(--------) +--R 4 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 28B - 28A)a cos(--------) + (28B + 28A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R ((8B + 8A)a cos(--------) + (- 8B - 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((50B + 50A)a cos(--------) + (- 50B - 50A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((102B + 102A)a cos(--------) + (- 102B - 102A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((86B + 86A)a cos(--------) + (- 86B - 86A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (26B + 26A)a cos(--------) + (- 26B - 26A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 5 +--R ((- 8B - 8A)a cos(--------) + (8B + 8A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi 4 +--R ((- 50B - 50A)a cos(--------) + (50B + 50A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 102B - 102A)a cos(--------) + (102B + 102A)a)cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi 2 +--R ((- 86B - 86A)a cos(--------) + (86B + 86A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 26B - 26A)a cos(--------) + (26B + 26A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (28B a cos(--------) - 28B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (44B a cos(--------) - 44B a)cos(x) + 20B a cos(--------) - 20B a +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x + %pi 3 +--R (2B + 2A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (14B + 14A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (22B + 22A)a cos(--------)cos(x) + (10B + 10A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (52B a cos(--------) - 52B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (140B a cos(--------) - 140B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (124B a cos(--------) - 124B a)cos(x) + 36B a cos(--------) - 36B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 3 +--R (26B + 26A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (70B + 70A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (62B + 62A)a cos(--------)cos(x) + (18B + 18A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 5 +--R (2B a cos(--------) - 2B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (30B a cos(--------) - 30B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (66B a cos(--------) - 66B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (46B a cos(--------) - 46B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (4B a cos(--------) - 4B a)cos(x) - 4B a cos(--------) + 4B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 4 +--R (8B + 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 3 +--R (22B + 22A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (18B + 18A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (2B + 2A)a cos(--------)cos(x) + (- 2B - 2A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 5 +--R (28B a cos(--------) - 28B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (68B a cos(--------) - 68B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (- 16B a cos(--------) + 16B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 176B a cos(--------) + 176B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 172B a cos(--------) + 172B a)cos(x) - 52B a cos(--------) + 52B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 4 +--R (- 8B - 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 3 +--R (- 50B - 50A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 102B - 102A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (- 86B - 86A)a cos(--------)cos(x) + (- 26B - 26A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 6 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 5 +--R (50B a cos(--------) - 50B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (102B a cos(--------) - 102B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (86B a cos(--------) - 86B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (26B a cos(--------) - 26B a)cos(x) +--R 4 +--R / +--R +-+ 2x - %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (20a\|2 cos(--------) - 20a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (28a\|2 cos(--------) - 28a\|2 )cos(x) + 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +-+ 2x - %pi 2 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) - 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 12a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) - 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 12a\|2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 2x - %pi 2 3 +--R (- 2a cos(--------) + 2a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 14a cos(--------) + 14a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 22a cos(--------) + 22a)cos(x) - 10a cos(--------) + 10a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (- 26a cos(--------) + 26a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 70a cos(--------) + 70a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 62a cos(--------) + 62a)cos(x) - 18a cos(--------) + 18a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R (- 8a cos(--------) + 8a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (- 22a cos(--------) + 22a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 18a cos(--------) + 18a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 2a cos(--------) + 2a)cos(x) + 2a cos(--------) - 2a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 4 2x - %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (50a cos(--------) - 50a)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2 +--R (102a cos(--------) - 102a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (86a cos(--------) - 86a)cos(x) + 26a cos(--------) - 26a +--R 4 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression Integer +--E 438 + +--S 439 of 534 +t0684:= (A+B*sin(x))/(a+b*sin(x))^(1/2) +--R +--R +--R B sin(x) + A +--R (378) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression Integer +--E 439 + +--S 440 of 534 +r0684:= 2*B*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*(a+b*sin(x))^(1/2)/b/((a+b*sin(x))/(a+b))^(1/2)+2*(A*b-a*B)*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*((a+b*sin(x))/(a+b))^(1/2)/b/(a+b*sin(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 440 + +--S 441 of 534 +a0684:= integrate(t0684,x) +--R +--R +--R x +--R ++ B sin(%L) + A +--R (379) | ---------------- d%L +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Union(Expression Integer,...) +--E 441 + +--S 442 of 534 +m0684:= a0684-r0684 +--R +--R +--R x +--R ++ B sin(%L) + A +--R (380) | ---------------- d%L - r0684 +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Expression Integer +--E 442 + +--S 443 of 534 +d0684:= D(m0684,x) +--R +--R +--R B sin(x) + A +--R (381) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression Integer +--E 443 + +--S 444 of 534 +t0685:= cos(x)/(a+a*cos(x))^(1/2) +--R +--R +--R cos(x) +--R (382) --------------- +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression Integer +--E 444 + +--S 445 of 534 +r0685:= -2*(atanh(sin(1/2*x))*cos(1/2*x)-sin(x))/(a*(cos(x)+1))^(1/2) +--R +--R +--R x x +--R - 2cos(-)atanh(sin(-)) + 2sin(x) +--R 2 2 +--R (383) -------------------------------- +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression Integer +--E 445 + +--S 446 of 534 +a0685:= integrate(t0685,x) +--R +--R +--R (384) +--R [ +--R +-+ +--R |2 +--R (a cos(x) + a) |- +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +------------+ +--R 4sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R (- a cos(x) - a) |- +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R +------------+ +--R 4sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 446 + +--S 447 of 534 +m0685a:= a0685.1-r0685 +--R +--R +--R (385) +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R x x +--R 4cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression Integer +--E 447 + +--S 448 of 534 +d0685a:= D(m0685a,x) +--R +--R +--R (386) +--R x x 2 x 2 +--R (2cos(-)sin(-) - 2cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 x +--R ((- 2cos(x) - 2)sin(-) + (2cos(x) + 2)sin(-))sin(x) +--R 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 x 2 x 2 +--R ((- 2cos(x) - 2)sin(-) + (- 2cos(-) + 2)cos(x) - 2cos(-) + 2) +--R 2 2 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 x x x 2 x 2 +--R (cos(-)cos(x) - 2cos(-)cos(x) - 3cos(-))sin(-) - cos(-)cos(x) +--R 2 2 2 2 2 +--R + +--R x x +--R 2cos(-)cos(x) + 3cos(-) +--R 2 2 +--R * +--R sin(x) +--R + +--R 3 2 x 3 +--R (- cos(x) + cos(x) + 5cos(x) + 3)sin(-) +--R 2 +--R + +--R 3 2 x +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R x 2 2 +--R ((3cos(x) + 3)sin(-) - 3cos(x) - 3)sin(x) +--R 2 +--R + +--R 3 2 x 2 x 2 3 +--R (2cos(x) + 4cos(x) + 2cos(x))sin(-) + (- cos(-) - 2)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 x 2 +--R (cos(-) - 4)cos(x) + (5cos(-) - 2)cos(x) + 3cos(-) +--R 2 2 2 +--R / +--R 3 2 x 2 3 2 +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) - cos(x) + cos(x) +--R 2 +--R + +--R 5cos(x) + 3 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2 x 2 2 +--R ((2a cos(x) + 4a cos(x) + 2a)sin(-) - 2a cos(x) - 4a cos(x) - 2a) +--R 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression Integer +--E 448 + +--S 449 of 534 +m0685b:= a0685.2-r0685 +--R +--R +--R (387) +--R - +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R x x +--R 4cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression Integer +--E 449 + +--S 450 of 534 +d0685b:= D(m0685b,x) +--R +--R +--R (388) +--R x x x 2 x x +--R ((4cos(-)cos(x) - 12cos(-))sin(-) - 4cos(-)cos(x) + 12cos(-)) +--R 2 2 2 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 x 3 +--R (- 4cos(x) + 8cos(x) + 12)sin(-) +--R 2 +--R + +--R 2 x +--R (4cos(x) - 8cos(x) - 12)sin(-) +--R 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 3 +--R (6sin(-) - 6)sin(x) +--R 2 +--R + +--R 2 x 2 x 2 2 +--R (2cos(x) + 8cos(x) + 6)sin(-) + (- 4cos(-) - 2)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (8cos(-) - 8)cos(x) + 12cos(-) - 6 +--R 2 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x x 2 x 3 +--R (8cos(-)sin(-) - 8cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 x 2 +--R ((- 8cos(x) - 8)sin(-) + (8cos(x) + 8)sin(-))sin(x) +--R 2 2 +--R + +--R x 3 x 2 x x x 2 +--R (cos(-)cos(x) - 5cos(-)cos(x) + 3cos(-)cos(x) + 9cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 3 x 2 x x +--R - cos(-)cos(x) + 5cos(-)cos(x) - 3cos(-)cos(x) - 9cos(-) +--R 2 2 2 2 +--R * +--R sin(x) +--R + +--R 4 3 2 x 3 +--R (- cos(x) + 4cos(x) + 2cos(x) - 12cos(x) - 9)sin(-) +--R 2 +--R + +--R 4 3 2 x +--R (cos(x) - 4cos(x) - 2cos(x) + 12cos(x) + 9)sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R 2 x 2 2 +--R (3cos(x) - 14cos(x) - 17)sin(-) - 3cos(x) +--R 2 +--R + +--R x 2 x 2 +--R (- 8cos(-) + 14)cos(x) - 8cos(-) + 17 +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 x 2 +--R (2cos(x) - 2cos(x) - 10cos(x) - 6cos(x))sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 x 2 2 +--R (- cos(-) - 2)cos(x) + (4cos(-) + 2)cos(x) + (2cos(-) + 10)cos(x) +--R 2 2 2 +--R + +--R x 2 x 2 +--R (- 12cos(-) + 6)cos(x) - 9cos(-) +--R 2 2 +--R / +--R x 2 2 +--R ((8cos(x) + 8)sin(-) - 8cos(x) - 8)sin(x) +--R 2 +--R + +--R 4 3 2 x 2 4 +--R (cos(x) - 4cos(x) - 2cos(x) + 12cos(x) + 9)sin(-) - cos(x) +--R 2 +--R + +--R 3 2 +--R 4cos(x) + 2cos(x) - 12cos(x) - 9 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 3 2 x 2 3 +--R (4a cos(x) - 4a cos(x) - 20a cos(x) - 12a)sin(-) - 4a cos(x) +--R 2 +--R + +--R 2 +--R 4a cos(x) + 20a cos(x) + 12a +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression Integer +--E 450 + +--S 451 of 534 +t0686:= cos(x)/(a-a*cos(x))^(1/2) +--R +--R +--R cos(x) +--R (389) ----------------- +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 451 + +--S 452 of 534 +r0686:= -2*(atanh(cos(1/2*x))*sin(1/2*x)-sin(x))/(-(-1+cos(x))*a)^(1/2) +--R +--R +--R x x +--R - 2sin(-)atanh(cos(-)) + 2sin(x) +--R 2 2 +--R (390) -------------------------------- +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 452 + +--S 453 of 534 +a0686:= integrate(t0686,x) +--R +--R +--R (391) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 \|a +------------+ +--R a |- log(---------------------------------) + 4\|a cos(x) + a +--R \|a cos(x) - 1 +--R [--------------------------------------------------------------, +--R 2a +--R +-+ +--R |2 cos(x) - 1 +------------+ +--R - a |- log(---------------------------------) + 4\|a cos(x) + a +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R ----------------------------------------------------------------] +--R 2a +--R Type: Union(List Expression Integer,...) +--E 453 + +--S 454 of 534 +m0686a:= a0686.1-r0686 +--R +--R +--R (392) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 +--------------+ \|a +--R a |- \|- a cos(x) + a log(---------------------------------) +--R \|a cos(x) - 1 +--R + +--R +--------------+ +------------+ x x +--R 4\|- a cos(x) + a \|a cos(x) + a + 4a sin(-)atanh(cos(-)) - 4a sin(x) +--R 2 2 +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression Integer +--E 454 + +--S 455 of 534 +d0686a:= D(m0686a,x) +--R +--R +--R (393) +--R x 2 2 x 2 +--------------+ +--R ((cos(-) - 1)cos(x) + (3cos(-) - 3)cos(x))sin(x)\|- a cos(x) + a +--R 2 2 +--R + +--R x 2 x 2 x +--R ((2a cos(-) - 2a)cos(x) + 2a cos(-) - 2a)sin(-)sin(x) +--R 2 2 2 +--R + +--R x 3 x 2 x 3 x +--R (2a cos(-) - 2a cos(-))cos(x) - 2a cos(-) + 2a cos(-) +--R 2 2 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 x 2 2 +--R ((- 2a cos(-) + 2a)cos(x) - 2a cos(-) + 2a)sin(x) +--R 2 2 +--R + +--R 2 x 2 x 2 3 +--R (2a cos(x) - 2a)sin(-) + (- 4a cos(-) + 4a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (4a cos(-) - 4a)cos(x) +--R 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R +-+ +--R x 2 2 x 2 |2 +--R ((- 2a cos(-) + 2a)cos(x) + (- 2a cos(-) + 2a)cos(x))sin(x) |- +--R 2 2 \|a +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R + +--R x 2 2 x 2 x 2 +--R (- a cos(-) + a)cos(x) + (- 4a cos(-) + 4a)cos(x) - 3a cos(-) +--R 2 2 2 +--R + +--R 3a +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 x 3 x 2 +--R (- a cos(-) + a cos(-))cos(x) + (- 3a cos(-) + 3a cos(-))cos(x) +--R 2 2 2 2 +--R + +--R x 3 x x 3 x +--R (a cos(-) - a cos(-))cos(x) + 3a cos(-) - 3a cos(-) +--R 2 2 2 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 2 x 2 x 2 +--R ((a cos(-) - a)cos(x) + (4a cos(-) - 4a)cos(x) + 3a cos(-) - 3a) +--R 2 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 x 2 +--R (- a cos(x) - 3a cos(x) + a cos(x) + 3a)sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (2a cos(-) - 2a)cos(x) + (6a cos(-) - 6a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 2a cos(-) + 2a)cos(x) + (- 6a cos(-) + 6a)cos(x) +--R 2 2 +--R / +--R +-+ +--R x 2 2 x 2 |2 +--------------+ +--R ((2a cos(-) - 2a)cos(x) - 2a cos(-) + 2a) |- \|- a cos(x) + a +--R 2 2 \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 x 2 2 +--R (- a cos(-) + a)cos(x) + (- 3a cos(-) + 3a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (a cos(-) - a)cos(x) + 3a cos(-) - 3a +--R 2 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 455 + +--S 456 of 534 +m0686b:= a0686.2-r0686 +--R +--R +--R (394) +--R +-+ +--R |2 +--------------+ cos(x) - 1 +--R - a |- \|- a cos(x) + a log(---------------------------------) +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R + +--R +--------------+ +------------+ x x +--R 4\|- a cos(x) + a \|a cos(x) + a + 4a sin(-)atanh(cos(-)) - 4a sin(x) +--R 2 2 +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression Integer +--E 456 + +--S 457 of 534 +d0686b:= D(m0686b,x) +--R +--R +--R (395) +--R x 2 3 x 2 2 +--R (cos(-) - 1)cos(x) + (14cos(-) - 14)cos(x) +--R 2 2 +--R + +--R x 2 +--R (17cos(-) - 17)cos(x) +--R 2 +--R * +--R +--------------+ +--R sin(x)\|- a cos(x) + a +--R + +--R x 2 2 x 2 +--R (4a cos(-) - 4a)cos(x) + (16a cos(-) - 16a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 12a cos(-) - 12a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 +--R (4a cos(-) - 4a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R (12a cos(-) - 12a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x x 3 x +--R (- 4a cos(-) + 4a cos(-))cos(x) - 12a cos(-) + 12a cos(-) +--R 2 2 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 2 x 2 +--R (- 4a cos(-) + 4a)cos(x) + (- 16a cos(-) + 16a)cos(x) +--R 2 2 +--R + +--R x 2 +--R - 12a cos(-) + 12a +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 x 2 +--R (4a cos(x) + 12a cos(x) - 4a cos(x) - 12a)sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 8a cos(-) + 8a)cos(x) + (- 24a cos(-) + 24a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (8a cos(-) - 8a)cos(x) + (24a cos(-) - 24a)cos(x) +--R 2 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 x 2 2 +--R (- 4a cos(-) + 4a)cos(x) + (- 16a cos(-) + 16a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (- 12a cos(-) + 12a)cos(x) +--R 2 +--R * +--R +-+ +--R |2 +--------------+ +--R sin(x) |- \|- a cos(x) + a +--R \|a +--R + +--R x 2 3 x 2 2 +--R (- a cos(-) + a)cos(x) + (- 15a cos(-) + 15a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (- 31a cos(-) + 31a)cos(x) - 17a cos(-) + 17a +--R 2 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 4 x 3 x 3 +--R (- a cos(-) + a cos(-))cos(x) + (- 14a cos(-) + 14a cos(-))cos(x) +--R 2 2 2 2 +--R + +--R x 3 x 2 +--R (- 16a cos(-) + 16a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x x 3 x +--R (14a cos(-) - 14a cos(-))cos(x) + 17a cos(-) - 17a cos(-) +--R 2 2 2 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 3 x 2 2 +--R (a cos(-) - a)cos(x) + (15a cos(-) - 15a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (31a cos(-) - 31a)cos(x) + 17a cos(-) - 17a +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 x 2 +--R (- a cos(x) - 14a cos(x) - 16a cos(x) + 14a cos(x) + 17a)sin(-) +--R 2 +--R + +--R x 2 5 x 2 4 +--R (2a cos(-) - 2a)cos(x) + (28a cos(-) - 28a)cos(x) +--R 2 2 +--R + +--R x 2 3 x 2 2 +--R (32a cos(-) - 32a)cos(x) + (- 28a cos(-) + 28a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (- 34a cos(-) + 34a)cos(x) +--R 2 +--R / +--R x 2 3 x 2 2 +--R (4a cos(-) - 4a)cos(x) + (12a cos(-) - 12a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (- 4a cos(-) + 4a)cos(x) - 12a cos(-) + 12a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a cos(x) + a \|a cos(x) + a +--R \|a +--R + +--R x 2 4 x 2 3 +--R (- a cos(-) + a)cos(x) + (- 14a cos(-) + 14a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 16a cos(-) + 16a)cos(x) + (14a cos(-) - 14a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 17a cos(-) - 17a +--R 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 457 + +--S 458 of 534 +t0687:= cos(x)/(a+b*cos(x))^(1/2) +--R +--R +--R cos(x) +--R (396) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression Integer +--E 458 + +--S 459 of 534 +r0687:= 2*(a+b*cos(x))^(1/2)*(EllipticE(1/2*x,2*b/(a+b))*a+EllipticE(1/2*x,2*b/(a+b))*b-a*EllipticF(1/2*x,2*b/(a+b)))/(a+b)/b/((a+b*cos(x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 459 + +--S 460 of 534 +a0687:= integrate(t0687,x) +--R +--R +--R x +--R ++ cos(%L) +--R (397) | ---------------- d%L +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Union(Expression Integer,...) +--E 460 + +--S 461 of 534 +m0687:= a0687-r0687 +--R +--R +--R x +--R ++ cos(%L) +--R (398) | ---------------- d%L - r0687 +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Expression Integer +--E 461 + +--S 462 of 534 +d0687:= D(m0687,x) +--R +--R +--R cos(x) +--R (399) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression Integer +--E 462 + +--S 463 of 534 +t0688:= (A+B*cos(x))/(a+a*cos(x))^(1/2) +--R +--R +--R B cos(x) + A +--R (400) --------------- +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression Integer +--E 463 + +--S 464 of 534 +r0688:= 2*(A-B)*atanh(sin(1/2*x))*cos(1/2*x)/(a+a*cos(x))^(1/2)+2*B*sin(x)/(a+a*cos(x))^(1/2) +--R +--R +--R x x +--R (- 2B + 2A)cos(-)atanh(sin(-)) + 2B sin(x) +--R 2 2 +--R (401) ------------------------------------------ +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression Integer +--E 464 + +--S 465 of 534 +a0688:= integrate(t0688,x) +--R +--R +--R (402) +--R [ +--R +-+ +--R |2 +--R ((B - A)a cos(x) + (B - A)a) |- +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +------------+ +--R 4B sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R ((- B + A)a cos(x) + (- B + A)a) |- +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R +------------+ +--R 4B sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 465 + +--S 466 of 534 +m0688a:= a0688.1-r0688 +--R +--R +--R (403) +--R +-+ +--R |2 +------------+ +--R (B - A) |- \|a cos(x) + a +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R x x +--R (4B - 4A)cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression Integer +--E 466 + +--S 467 of 534 +d0688a:= D(m0688a,x) +--R +--R +--R (404) +--R x x 2 x 2 +--R ((2B - 2A)cos(-)sin(-) + (- 2B + 2A)cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 +--R ((- 2B + 2A)cos(x) - 2B + 2A)sin(-) +--R 2 +--R + +--R x +--R ((2B - 2A)cos(x) + 2B - 2A)sin(-) +--R 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 +--R ((- 2B + 2A)cos(x) - 2B + 2A)sin(-) +--R 2 +--R + +--R x 2 x 2 +--R ((- 2B + 2A)cos(-) + 2B - 2A)cos(x) + (- 2B + 2A)cos(-) + 2B - 2A +--R 2 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 x +--R (B - A)cos(-)cos(x) + (- 2B + 2A)cos(-)cos(x) +--R 2 2 +--R + +--R x +--R (- 3B + 3A)cos(-) +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 x x +--R (- B + A)cos(-)cos(x) + (2B - 2A)cos(-)cos(x) + (3B - 3A)cos(-) +--R 2 2 2 +--R * +--R sin(x) +--R + +--R 3 2 +--R ((- B + A)cos(x) + (B - A)cos(x) + (5B - 5A)cos(x) + 3B - 3A) +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R 3 2 x +--R ((B - A)cos(x) + (- B + A)cos(x) + (- 5B + 5A)cos(x) - 3B + 3A)sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R x 2 2 +--R (((3B - 3A)cos(x) + 3B - 3A)sin(-) + (- 3B + 3A)cos(x) - 3B + 3A)sin(x) +--R 2 +--R + +--R 3 2 x 2 +--R ((2B - 2A)cos(x) + (4B - 4A)cos(x) + (2B - 2A)cos(x))sin(-) +--R 2 +--R + +--R x 2 3 x 2 2 +--R ((- B + A)cos(-) - 2B + 2A)cos(x) + ((B - A)cos(-) - 4B + 4A)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R ((5B - 5A)cos(-) - 2B + 2A)cos(x) + (3B - 3A)cos(-) +--R 2 2 +--R / +--R 3 2 x 2 3 2 +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) - cos(x) + cos(x) +--R 2 +--R + +--R 5cos(x) + 3 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2 x 2 2 +--R ((2a cos(x) + 4a cos(x) + 2a)sin(-) - 2a cos(x) - 4a cos(x) - 2a) +--R 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression Integer +--E 467 + +--S 468 of 534 +m0688b:= a0688.2-r0688 +--R +--R +--R (405) +--R +-+ +--R |2 +------------+ +--R (- B + A) |- \|a cos(x) + a +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R x x +--R (4B - 4A)cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression Integer +--E 468 + +--S 469 of 534 +d0688b:= D(m0688b,x) +--R +--R +--R (406) +--R x x x 2 +--R ((4B - 4A)cos(-)cos(x) + (- 12B + 12A)cos(-))sin(-) +--R 2 2 2 +--R + +--R x x +--R (- 4B + 4A)cos(-)cos(x) + (12B - 12A)cos(-) +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 x 3 +--R ((- 4B + 4A)cos(x) + (8B - 8A)cos(x) + 12B - 12A)sin(-) +--R 2 +--R + +--R 2 x +--R ((4B - 4A)cos(x) + (- 8B + 8A)cos(x) - 12B + 12A)sin(-) +--R 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 3 +--R ((6B - 6A)sin(-) - 6B + 6A)sin(x) +--R 2 +--R + +--R 2 x 2 +--R ((2B - 2A)cos(x) + (8B - 8A)cos(x) + 6B - 6A)sin(-) +--R 2 +--R + +--R x 2 2 +--R ((- 4B + 4A)cos(-) - 2B + 2A)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((8B - 8A)cos(-) - 8B + 8A)cos(x) + (12B - 12A)cos(-) - 6B +--R 2 2 +--R + +--R 6A +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x x 2 x 3 +--R ((8B - 8A)cos(-)sin(-) + (- 8B + 8A)cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 +--R ((- 8B + 8A)cos(x) - 8B + 8A)sin(-) +--R 2 +--R + +--R x +--R ((8B - 8A)cos(x) + 8B - 8A)sin(-) +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R x 3 x 2 +--R (B - A)cos(-)cos(x) + (- 5B + 5A)cos(-)cos(x) +--R 2 2 +--R + +--R x x +--R (3B - 3A)cos(-)cos(x) + (9B - 9A)cos(-) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 3 x 2 +--R (- B + A)cos(-)cos(x) + (5B - 5A)cos(-)cos(x) +--R 2 2 +--R + +--R x x +--R (- 3B + 3A)cos(-)cos(x) + (- 9B + 9A)cos(-) +--R 2 2 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- B + A)cos(x) + (4B - 4A)cos(x) + (2B - 2A)cos(x) +--R + +--R (- 12B + 12A)cos(x) - 9B + 9A +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R 4 3 2 +--R (B - A)cos(x) + (- 4B + 4A)cos(x) + (- 2B + 2A)cos(x) +--R + +--R (12B - 12A)cos(x) + 9B - 9A +--R * +--R x +--R sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R 2 x 2 +--R ((3B - 3A)cos(x) + (- 14B + 14A)cos(x) - 17B + 17A)sin(-) +--R 2 +--R + +--R 2 x 2 +--R (- 3B + 3A)cos(x) + ((- 8B + 8A)cos(-) + 14B - 14A)cos(x) +--R 2 +--R + +--R x 2 +--R (- 8B + 8A)cos(-) + 17B - 17A +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (2B - 2A)cos(x) + (- 2B + 2A)cos(x) + (- 10B + 10A)cos(x) +--R + +--R (- 6B + 6A)cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R ((- B + A)cos(-) - 2B + 2A)cos(x) + ((4B - 4A)cos(-) + 2B - 2A)cos(x) +--R 2 2 +--R + +--R x 2 2 +--R ((2B - 2A)cos(-) + 10B - 10A)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 12B + 12A)cos(-) + 6B - 6A)cos(x) + (- 9B + 9A)cos(-) +--R 2 2 +--R / +--R x 2 2 +--R ((8cos(x) + 8)sin(-) - 8cos(x) - 8)sin(x) +--R 2 +--R + +--R 4 3 2 x 2 4 +--R (cos(x) - 4cos(x) - 2cos(x) + 12cos(x) + 9)sin(-) - cos(x) +--R 2 +--R + +--R 3 2 +--R 4cos(x) + 2cos(x) - 12cos(x) - 9 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 3 2 x 2 3 +--R (4a cos(x) - 4a cos(x) - 20a cos(x) - 12a)sin(-) - 4a cos(x) +--R 2 +--R + +--R 2 +--R 4a cos(x) + 20a cos(x) + 12a +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression Integer +--E 469 + +--S 470 of 534 +t0689:= (A+B*cos(x))/(a-a*cos(x))^(1/2) +--R +--R +--R B cos(x) + A +--R (407) ----------------- +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 470 + +--S 471 of 534 +r0689:= -2*(A+B)*atanh(cos(1/2*x))*sin(1/2*x)/(a-a*cos(x))^(1/2)+2*B*sin(x)/(a-a*cos(x))^(1/2) +--R +--R +--R x x +--R (- 2B - 2A)sin(-)atanh(cos(-)) + 2B sin(x) +--R 2 2 +--R (408) ------------------------------------------ +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 471 + +--S 472 of 534 +a0689:= integrate(t0689,x) +--R +--R +--R (409) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 \|a +------------+ +--R (B + A)a |- log(---------------------------------) + 4B\|a cos(x) + a +--R \|a cos(x) - 1 +--R [----------------------------------------------------------------------, +--R 2a +--R +-+ +--R |2 cos(x) - 1 +------------+ +--R (- B - A)a |- log(---------------------------------) + 4B\|a cos(x) + a +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R ------------------------------------------------------------------------] +--R 2a +--R Type: Union(List Expression Integer,...) +--E 472 + +--S 473 of 534 +m0689a:= a0689.1-r0689 +--R +--R +--R (410) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 +--------------+ \|a +--R (B + A)a |- \|- a cos(x) + a log(---------------------------------) +--R \|a cos(x) - 1 +--R + +--R +--------------+ +------------+ x x +--R 4B\|- a cos(x) + a \|a cos(x) + a + (4B + 4A)a sin(-)atanh(cos(-)) +--R 2 2 +--R + +--R - 4B a sin(x) +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression Integer +--E 473 + +--S 474 of 534 +d0689a:= D(m0689a,x) +--R +--R +--R (411) +--R x 2 2 x 2 +--R (B cos(-) - B)cos(x) + ((3B + A)cos(-) - 3B - A)cos(x) +--R 2 2 +--R + +--R x 2 +--R 3A cos(-) - 3A +--R 2 +--R * +--R +--------------+ +--R sin(x)\|- a cos(x) + a +--R + +--R x 2 +--R ((2B + 2A)a cos(-) + (- 2B - 2A)a)cos(x) +--R 2 +--R + +--R x 2 +--R (2B + 2A)a cos(-) + (- 2B - 2A)a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 2 +--R ((2B + 2A)a cos(-) + (- 2B - 2A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R (- 2B - 2A)a cos(-) + (2B + 2A)a cos(-) +--R 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 x 2 2 +--R ((- 2B a cos(-) + 2B a)cos(x) - 2B a cos(-) + 2B a)sin(x) +--R 2 2 +--R + +--R 2 x 2 +--R ((2B + 2A)a cos(x) + (- 2B - 2A)a)sin(-) +--R 2 +--R + +--R x 2 3 x 2 +--R (- 4B a cos(-) + 4B a)cos(x) + (4B a cos(-) - 4B a)cos(x) +--R 2 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 2 +--R (- 2B a cos(-) + 2B a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 2B - 2A)a cos(-) + (2B + 2A)a)cos(x) - 2A a cos(-) + 2A a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +--R sin(x) |- \|- a cos(x) + a +--R \|a +--R + +--R x 2 2 +--R ((- B - A)a cos(-) + (B + A)a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 4B - 4A)a cos(-) + (4B + 4A)a)cos(x) + (- 3B - 3A)a cos(-) +--R 2 2 +--R + +--R (3B + 3A)a +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 +--R ((- B - A)a cos(-) + (B + A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((- 3B - 3A)a cos(-) + (3B + 3A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x x 3 +--R ((B + A)a cos(-) + (- B - A)a cos(-))cos(x) + (3B + 3A)a cos(-) +--R 2 2 2 +--R + +--R x +--R (- 3B - 3A)a cos(-) +--R 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 2 x 2 +--R (B a cos(-) - B a)cos(x) + (4B a cos(-) - 4B a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 3B a cos(-) - 3B a +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (- B - A)a cos(x) + (- 3B - 3A)a cos(x) + (B + A)a cos(x) +--R + +--R (3B + 3A)a +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (2B a cos(-) - 2B a)cos(x) + (6B a cos(-) - 6B a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 2B a cos(-) + 2B a)cos(x) + (- 6B a cos(-) + 6B a)cos(x) +--R 2 2 +--R / +--R +-+ +--R x 2 2 x 2 |2 +--------------+ +--R ((2a cos(-) - 2a)cos(x) - 2a cos(-) + 2a) |- \|- a cos(x) + a +--R 2 2 \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 x 2 2 +--R (- a cos(-) + a)cos(x) + (- 3a cos(-) + 3a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (a cos(-) - a)cos(x) + 3a cos(-) - 3a +--R 2 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 474 + +--S 475 of 534 +m0689b:= a0689.2-r0689 +--R +--R +--R (412) +--R +-+ +--R |2 +--------------+ cos(x) - 1 +--R (- B - A)a |- \|- a cos(x) + a log(---------------------------------) +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R + +--R +--------------+ +------------+ x x +--R 4B\|- a cos(x) + a \|a cos(x) + a + (4B + 4A)a sin(-)atanh(cos(-)) +--R 2 2 +--R + +--R - 4B a sin(x) +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression Integer +--E 475 + +--S 476 of 534 +d0689b:= D(m0689b,x) +--R +--R +--R (413) +--R x 2 3 x 2 2 +--R (B cos(-) - B)cos(x) + ((14B + A)cos(-) - 14B - A)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R ((17B + 14A)cos(-) - 17B - 14A)cos(x) + 17A cos(-) - 17A +--R 2 2 +--R * +--R +--------------+ +--R sin(x)\|- a cos(x) + a +--R + +--R x 2 2 +--R ((4B + 4A)a cos(-) + (- 4B - 4A)a)cos(x) +--R 2 +--R + +--R x 2 +--R ((16B + 16A)a cos(-) + (- 16B - 16A)a)cos(x) +--R 2 +--R + +--R x 2 +--R (12B + 12A)a cos(-) + (- 12B - 12A)a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 +--R ((4B + 4A)a cos(-) + (- 4B - 4A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((12B + 12A)a cos(-) + (- 12B - 12A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R ((- 4B - 4A)a cos(-) + (4B + 4A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R (- 12B - 12A)a cos(-) + (12B + 12A)a cos(-) +--R 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 2 +--R (- 4B a cos(-) + 4B a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R (- 16B a cos(-) + 16B a)cos(x) - 12B a cos(-) + 12B a +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (4B + 4A)a cos(x) + (12B + 12A)a cos(x) +--R + +--R (- 4B - 4A)a cos(x) + (- 12B - 12A)a +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 8B a cos(-) + 8B a)cos(x) + (- 24B a cos(-) + 24B a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (8B a cos(-) - 8B a)cos(x) + (24B a cos(-) - 24B a)cos(x) +--R 2 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 +--R (- 4B a cos(-) + 4B a)cos(x) +--R 2 +--R + +--R x 2 2 +--R ((- 16B - 4A)a cos(-) + (16B + 4A)a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 12B - 16A)a cos(-) + (12B + 16A)a)cos(x) - 12A a cos(-) + 12A a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +--R sin(x) |- \|- a cos(x) + a +--R \|a +--R + +--R x 2 3 +--R ((- B - A)a cos(-) + (B + A)a)cos(x) +--R 2 +--R + +--R x 2 2 +--R ((- 15B - 15A)a cos(-) + (15B + 15A)a)cos(x) +--R 2 +--R + +--R x 2 +--R ((- 31B - 31A)a cos(-) + (31B + 31A)a)cos(x) +--R 2 +--R + +--R x 2 +--R (- 17B - 17A)a cos(-) + (17B + 17A)a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 4 +--R ((- B - A)a cos(-) + (B + A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 3 +--R ((- 14B - 14A)a cos(-) + (14B + 14A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((- 16B - 16A)a cos(-) + (16B + 16A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R ((14B + 14A)a cos(-) + (- 14B - 14A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R (17B + 17A)a cos(-) + (- 17B - 17A)a cos(-) +--R 2 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 3 x 2 2 +--R (B a cos(-) - B a)cos(x) + (15B a cos(-) - 15B a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (31B a cos(-) - 31B a)cos(x) + 17B a cos(-) - 17B a +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- B - A)a cos(x) + (- 14B - 14A)a cos(x) + (- 16B - 16A)a cos(x) +--R + +--R (14B + 14A)a cos(x) + (17B + 17A)a +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 5 x 2 4 +--R (2B a cos(-) - 2B a)cos(x) + (28B a cos(-) - 28B a)cos(x) +--R 2 2 +--R + +--R x 2 3 x 2 2 +--R (32B a cos(-) - 32B a)cos(x) + (- 28B a cos(-) + 28B a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (- 34B a cos(-) + 34B a)cos(x) +--R 2 +--R / +--R x 2 3 x 2 2 +--R (4a cos(-) - 4a)cos(x) + (12a cos(-) - 12a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (- 4a cos(-) + 4a)cos(x) - 12a cos(-) + 12a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a cos(x) + a \|a cos(x) + a +--R \|a +--R + +--R x 2 4 x 2 3 +--R (- a cos(-) + a)cos(x) + (- 14a cos(-) + 14a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 16a cos(-) + 16a)cos(x) + (14a cos(-) - 14a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 17a cos(-) - 17a +--R 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression Integer +--E 476 + +--S 477 of 534 +t0690:= (A+B*cos(x))/(a+b*cos(x))^(1/2) +--R +--R +--R B cos(x) + A +--R (414) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression Integer +--E 477 + +--S 478 of 534 +r0690:= 2*B*(a+b*cos(x))^(1/2)*EllipticE(1/2*x,2*b/(a+b))/b/((a+b*cos(x))/(a+b))^(1/2)+2*(A*b-a*B)*((a+b*cos(x))/(a+b))^(1/2)*EllipticF(1/2*x,2*b/(a+b))/b/(a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial Fraction Integer +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 478 + +--S 479 of 534 +a0690:= integrate(t0690,x) +--R +--R +--R x +--R ++ B cos(%L) + A +--R (415) | ---------------- d%L +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Union(Expression Integer,...) +--E 479 + +--S 480 of 534 +m0690:= a0690-r0690 +--R +--R +--R x +--R ++ B cos(%L) + A +--R (416) | ---------------- d%L - r0690 +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Expression Integer +--E 480 + +--S 481 of 534 +d0690:= D(m0690,x) +--R +--R +--R B cos(x) + A +--R (417) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression Integer +--E 481 + +--S 482 of 534 +t0691:= (-1+1/d^2*c^2+sin(x)^2)/(c+d*cos(x)) +--R +--R +--R 2 2 2 2 +--R d sin(x) - d + c +--R (418) ------------------- +--R 3 2 +--R d cos(x) + c d +--R Type: Expression Integer +--E 482 + +--S 483 of 534 +r0691:= c*x/d^2-sin(x)/d +--R +--R +--R - d sin(x) + c x +--R (419) ---------------- +--R 2 +--R d +--R Type: Expression Integer +--E 483 + +--S 484 of 534 +a0691:= integrate(t0691,x) +--R +--R +--R - d sin(x) + c x +--R (420) ---------------- +--R 2 +--R d +--R Type: Union(Expression Integer,...) +--E 484 + +--S 485 of 534 +m0691:= a0691-r0691 +--R +--R +--R (421) 0 +--R Type: Expression Integer +--E 485 + +--S 486 of 534 +d0691:= D(m0691,x) +--R +--R +--R (422) 0 +--R Type: Expression Integer +--E 486 + +--S 487 of 534 +t0692:= (a+b*sin(x)^2)/(c+d*cos(x)) +--R +--R +--R 2 +--R b sin(x) + a +--R (423) ------------- +--R d cos(x) + c +--R Type: Expression Integer +--E 487 + +--S 488 of 534 +r0692:= b*c*x/d^2+2*(a*d^2-b*(c^2-d^2))*atan((c-d)*tan(1/2*x)/(c^2-d^2)^(1/2))/d^2/(c^2-d^2)^(1/2)-b*sin(x)/d +--R +--R +--R (424) +--R x +--R (d - c)tan(-) +--R 2 2 2 +--R ((- 2b - 2a)d + 2b c )atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +--R | 2 2 +--R (- b d sin(x) + b c x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression Integer +--E 488 + +--S 489 of 534 +a0692:= integrate(t0692,x) +--R +--R +--R (425) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 2 2 (- c cos(x) - d)\|d - c + (- d + c )sin(x) +--R ((b + a)d - b c )log(----------------------------------------------) +--R d cos(x) + c +--R + +--R +-------+ +--R | 2 2 +--R (- b d sin(x) + b c x)\|d - c +--R / +--R +-------+ +--R 2 | 2 2 +--R d \|d - c +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 sin(x)\|- d + c +--R ((2b + 2a)d - 2b c )atan(---------------------) +--R (d + c)cos(x) + d + c +--R + +--R +---------+ +--R | 2 2 +--R (- b d sin(x) + b c x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R ] +--R Type: Union(List Expression Integer,...) +--E 489 + +--S 490 of 534 +m0692a:= a0692.1-r0692 +--R +--R +--R (426) +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)d - b c )\|- d + c +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- c cos(x) - d)\|d - c + (- d + c )sin(x) +--R log(----------------------------------------------) +--R d cos(x) + c +--R + +--R x +--R +-------+ (d - c)tan(-) +--R 2 2 | 2 2 2 +--R ((2b + 2a)d - 2b c )\|d - c atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R d \|- d + c \|d - c +--R Type: Expression Integer +--E 490 + +--S 491 of 534 +d0692a:= D(m0692a,x) +--R +--R +--R (427) +--R 3 2 2 3 2 +--R ((b + a)d + (- b - a)c d - b c d + b c )sin(x) +--R + +--R 3 2 2 +--R ((b + a)d - b c d)cos(x) +--R + +--R 3 2 2 3 2 3 +--R ((b + a)d + (b + a)c d - b c d - b c )cos(x) + (b + a)c d - b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R ((- b - a)d + (- b - a)c d + b c d + b c )sin(x) +--R + +--R 3 2 2 +--R ((- b - a)d + b c d)cos(x) +--R + +--R 3 2 2 3 2 3 +--R ((b + a)d + (- b - a)c d - b c d + b c )cos(x) + (b + a)c d - b c +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 4 2 2 4 4 +--R ((b + a)d + (- 2b - a)c d + b c )cos(x) + (b + a)d +--R + +--R 2 2 4 +--R (- 2b - a)c d + b c +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 4 2 2 4 4 +--R ((b + a)d + (- 2b - a)c d + b c )cos(x) + (- b - a)d +--R + +--R 2 2 4 +--R (2b + a)c d - b c +--R * +--R sin(x) +--R / +--R 3 2 2 2 4 3 2 2 3 3 +--R (c d - c d )cos(x) + (d - c d + c d - c d)cos(x) + c d +--R + +--R 2 2 +--R - c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 4 3 2 2 3 3 2 2 +--R (- c d - c d )cos(x) + (- d - c d - c d - c d)cos(x) - c d - c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 x 2 +--R ((d - c d - c d + c d )cos(x) + c d - c d - c d + c d)sin(x)tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 +--R ((- d - c d + c d + c d )cos(x) - c d - c d + c d + c d)sin(x) +--R Type: Expression Integer +--E 491 + +--S 492 of 534 +m0692b:= a0692.2-r0692 +--R +--R +--R (428) +--R +---------+ +--R | 2 2 +--R 2 2 sin(x)\|- d + c +--R ((2b + 2a)d - 2b c )atan(---------------------) +--R (d + c)cos(x) + d + c +--R + +--R x +--R (d - c)tan(-) +--R 2 2 2 +--R ((2b + 2a)d - 2b c )atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression Integer +--E 492 + +--S 493 of 534 +d0692b:= D(m0692b,x) +--R +--R +--R (429) +--R 3 2 2 3 2 +--R ((- b - a)d + (b + a)c d + b c d - b c )sin(x) +--R + +--R 3 2 2 3 2 +--R ((- 3b - 3a)d + (b + a)c d + 3b c d - b c )cos(x) +--R + +--R 3 2 3 2 2 +--R ((- 4b - 4a)d + 4b c d)cos(x) + (- b - a)d + (- b - a)c d + b c d +--R + +--R 3 +--R b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R ((3b + 3a)d + (b + a)c d - 3b c d - b c )sin(x) +--R + +--R 3 2 2 3 2 3 +--R ((b + a)d + (b + a)c d - b c d - b c )cos(x) + (- b - a)d +--R + +--R 2 2 3 +--R (- b - a)c d + b c d + b c +--R / +--R 4 3 2 2 2 4 2 2 2 +--R (d - 2c d + c d )sin(x) + (- d + c d )cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2d + 2c d )cos(x) - d + c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 4 3 2 2 2 +--R (- d + c d )sin(x) + (d + 2c d + c d )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R (2d + 4c d + 2c d )cos(x) + d + 2c d + c d +--R Type: Expression Integer +--E 493 + +--S 494 of 534 +t0693:= (a+b*sin(x)^2)/(c+c*cos(x)^2) +--R +--R +--R 2 +--R b sin(x) + a +--R (430) ------------- +--R 2 +--R c cos(x) + c +--R Type: Expression Integer +--E 494 + +--S 495 of 534 +r0693:= -b*x/c+1/2*(a+2*b)*atan(1/2*2^(1/2)*tan(x))*2^(1/2)/c +--R +--R +--R +-+ +--R +-+ \|2 tan(x) +--R (2b + a)\|2 atan(----------) - 2b x +--R 2 +--R (431) ----------------------------------- +--R 2c +--R Type: Expression Integer +--E 495 + +--S 496 of 534 +a0693:= integrate(t0693,x) +--R +--R +--R (432) +--R +-+ +--R \|2 sin(x) +--R (2b + a)atan(-----------) +--R 2cos(x) + 2 +--R + +--R 2sin(x) +-+ +--R (2b + a)atan(--------------------------------) - b x\|2 +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Union(Expression Integer,...) +--E 496 + +--S 497 of 534 +m0693:= a0693-r0693 +--R +--R +--R (433) +--R +-+ +-+ +--R \|2 tan(x) \|2 sin(x) +--R (- 2b - a)atan(----------) + (2b + a)atan(-----------) +--R 2 2cos(x) + 2 +--R + +--R 2sin(x) +--R (2b + a)atan(--------------------------------) +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Expression Integer +--E 497 + +--S 498 of 534 +d0693:= D(m0693,x) +--R +--R +--R (434) +--R 4 +--R ((4b + 2a)cos(x) + 4b + 2a)sin(x) +--R + +--R 3 2 2 +--R ((10b + 5a)cos(x) + (24b + 12a)cos(x) + (14b + 7a)cos(x))sin(x) +--R + +--R 6 5 4 +--R (- 2b - a)cos(x) + (- 10b - 5a)cos(x) + (- 24b - 12a)cos(x) +--R + +--R 3 2 +--R (- 36b - 18a)cos(x) + (- 34b - 17a)cos(x) + (- 18b - 9a)cos(x) - 4b +--R + +--R - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 4 +--R ((8b + 4a)cos(x) + 12b + 6a)sin(x) +--R + +--R 4 3 2 +--R (2b + a)cos(x) + (28b + 14a)cos(x) + (68b + 34a)cos(x) +--R + +--R (52b + 26a)cos(x) + 10b + 5a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 +--R (4b + 2a)cos(x) + (12b + 6a)cos(x) + (8b + 4a)cos(x) +--R + +--R 2 +--R (- 8b - 4a)cos(x) + (- 12b - 6a)cos(x) - 4b - 2a +--R / +--R 4 +--R 2c sin(x) +--R + +--R 4 3 2 2 +--R (c cos(x) + 4c cos(x) + 10c cos(x) + 12c cos(x) + 5c)sin(x) +--R + +--R 6 5 4 3 2 +--R 2c cos(x) + 12c cos(x) + 30c cos(x) + 40c cos(x) + 30c cos(x) +--R + +--R 12c cos(x) + 2c +--R * +--R 2 +--R tan(x) +--R + +--R 4 +--R 4c sin(x) +--R + +--R 4 3 2 2 +--R (2c cos(x) + 8c cos(x) + 20c cos(x) + 24c cos(x) + 10c)sin(x) +--R + +--R 6 5 4 3 2 +--R 4c cos(x) + 24c cos(x) + 60c cos(x) + 80c cos(x) + 60c cos(x) +--R + +--R 24c cos(x) + 4c +--R Type: Expression Integer +--E 498 + +--S 499 of 534 +t0694:= (a+b*sin(x)^2)/(c-c*cos(x)^2) +--R +--R +--R 2 +--R - b sin(x) - a +--R (435) --------------- +--R 2 +--R c cos(x) - c +--R Type: Expression Integer +--E 499 + +--S 500 of 534 +r0694:= -(-b*x+a*cot(x))/c +--R +--R +--R - a cot(x) + b x +--R (436) ---------------- +--R c +--R Type: Expression Integer +--E 500 + +--S 501 of 534 +a0694:= integrate(t0694,x) +--R +--R +--R b x sin(x) - a cos(x) +--R (437) --------------------- +--R c sin(x) +--R Type: Union(Expression Integer,...) +--E 501 + +--S 502 of 534 +m0694:= a0694-r0694 +--R +--R +--R a cot(x)sin(x) - a cos(x) +--R (438) ------------------------- +--R c sin(x) +--R Type: Expression Integer +--E 502 + +--S 503 of 534 +d0694:= D(m0694,x) +--R +--R +--R 2 2 2 +--R - a cot(x) sin(x) + a cos(x) +--R (439) ------------------------------ +--R 2 +--R c sin(x) +--R Type: Expression Integer +--E 503 + +--S 504 of 534 +t0695:= (a+b*sin(x)^2)/(c+d*cos(x)^2) +--R +--R +--R 2 +--R b sin(x) + a +--R (440) ------------- +--R 2 +--R d cos(x) + c +--R Type: Expression Integer +--E 504 + +--S 505 of 534 +r0695:= -b*x/d+(b*c+(a+b)*d)*atan(c^(1/2)*tan(x)/(c+d)^(1/2))/c^(1/2)/d/(c+d)^(1/2) +--R +--R +--R +-+ +--R tan(x)\|c +-+ +-----+ +--R ((b + a)d + b c)atan(----------) - b x\|c \|d + c +--R +-----+ +--R \|d + c +--R (441) -------------------------------------------------- +--R +-+ +-----+ +--R d\|c \|d + c +--R Type: Expression Integer +--E 505 + +--S 506 of 534 +a0695:= integrate(t0695,x) +--R +--R +--R (442) +--R [ +--R ((b + a)d + b c) +--R * +--R +----------+ +--R 2 | 2 2 +--R ((d + 2c)cos(x) - c)\|- c d - c + (- 2c d - 2c )cos(x)sin(x) +--R log(---------------------------------------------------------------) +--R 2 +--R d cos(x) + c +--R + +--R +----------+ +--R | 2 +--R - 2b x\|- c d - c +--R / +--R +----------+ +--R | 2 +--R 2d\|- c d - c +--R , +--R +--R +--------+ +--R | 2 +--R sin(x)\|c d + c +--R ((b + a)d + b c)atan(-----------------) +--R 2c cos(x) + 2c +--R + +--R ((d - c)cos(x) - 2c)sin(x) +--R ((- b - a)d - b c)atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R + +--R +--------+ +--R | 2 +--R - b x\|c d + c +--R / +--R +--------+ +--R | 2 +--R d\|c d + c +--R ] +--R Type: Union(List Expression Integer,...) +--E 506 + +--S 507 of 534 +m0695a:= a0695.1-r0695 +--R +--R +--R (443) +--R +-+ +-----+ +--R ((b + a)d + b c)\|c \|d + c +--R * +--R +----------+ +--R 2 | 2 2 +--R ((d + 2c)cos(x) - c)\|- c d - c + (- 2c d - 2c )cos(x)sin(x) +--R log(---------------------------------------------------------------) +--R 2 +--R d cos(x) + c +--R + +--R +----------+ +-+ +--R | 2 tan(x)\|c +--R ((- 2b - 2a)d - 2b c)\|- c d - c atan(----------) +--R +-----+ +--R \|d + c +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R 2d\|- c d - c \|c \|d + c +--R Type: Expression Integer +--E 507 + +--S 508 of 534 +d0695a:= D(m0695a,x) +--R +--R +--R (444) +--R 2 2 2 2 3 2 +--R (((b + a)c d + b c d)cos(x) + (- b - a)c d - b c )sin(x) +--R + +--R 3 2 2 4 +--R ((- b - a)d + (- 2b - a)c d - b c d)cos(x) +--R + +--R 2 3 2 2 3 +--R ((- b - a)c d - b c )cos(x) + (b + a)c d + b c +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 2 2 +--R ((b + a)d + (2b + a)c d + b c d)cos(x) + (- b - a)c d +--R + +--R 2 3 +--R (- 2b - a)c d - b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 2 2 3 2 +--R ((- b - a)c d - b c d)cos(x) + ((b + a)c d - a c d - b c )cos(x) +--R + +--R 2 3 +--R (b + a)c d + b c +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 3 2 2 3 3 2 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) sin(x)tan(x) +--R + +--R 3 2 2 3 3 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) +--R + +--R 3 2 2 3 +--R ((- 2b - 2a)c d + (- 4b - 2a)c d - 2b c d)cos(x) +--R * +--R sin(x) +--R / +--R 3 2 2 4 3 2 3 2 +--R ((c d + 2c d )cos(x) + 2c d cos(x) - c d)tan(x) +--R + +--R 4 3 2 2 4 2 2 3 2 2 2 3 +--R (d + 3c d + 2c d )cos(x) + (2c d + 2c d)cos(x) - c d - c d +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 2 3 3 2 3 3 2 4 2 +--R ((- 2c d - 2c d )cos(x) + (- 2c d - 2c d)cos(x))sin(x)tan(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 4 +--R ((- 2c d - 4c d - 2c d )cos(x) + (- 2c d - 4c d - 2c d)cos(x))sin(x) +--R Type: Expression Integer +--E 508 + +--S 509 of 534 +m0695b:= a0695.2-r0695 +--R +--R +--R (445) +--R +--------+ +--R | 2 +--R +-+ +-----+ sin(x)\|c d + c +--R ((b + a)d + b c)\|c \|d + c atan(-----------------) +--R 2c cos(x) + 2c +--R + +--R +--------+ +-+ +--R | 2 tan(x)\|c +--R ((- b - a)d - b c)\|c d + c atan(----------) +--R +-----+ +--R \|d + c +--R + +--R +-+ +-----+ ((d - c)cos(x) - 2c)sin(x) +--R ((- b - a)d - b c)\|c \|d + c atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R d\|c \|d + c \|c d + c +--R Type: Expression Integer +--E 509 + +--S 510 of 534 +d0695b:= D(m0695b,x) +--R +--R +--R (446) +--R 4 3 2 2 3 +--R (- b - a)d + (b + 2a)c d + (- b - 3a)c d + (- b + 2a)c d +--R + +--R 4 +--R 2b c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((4b + 4a)c d - 4a c d + (4b + 8a)c d + 8b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (b + a)c d + b c d + (7b + 7a)c d + 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R ((- 4b - 4a)c d - 4b c d + (4b + 4a)c d + 4b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 12b - 12a)c d + (2b + 14a)c d + (32b + 18a)c d + 18b c ) +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 11b - 11a)c d + (25b + 36a)c d + (59b + 23a)c d + 23b c ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 4b - 4a)c d + (22b + 26a)c d + (32b + 6a)c d + 6b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (- b - a)c d + (3b + 4a)c d + (b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 6 +--R ((- 6b - 6a)c d + (- 4b + 2a)c d + 2b c )cos(x) +--R + +--R 2 2 3 4 5 +--R ((- 30b - 30a)c d + (- 20b + 10a)c d + 10b c )cos(x) +--R + +--R 2 2 3 4 4 +--R ((- 64b - 64a)c d + (- 48b + 16a)c d + 16b c )cos(x) +--R + +--R 2 2 3 4 3 +--R ((- 76b - 76a)c d + (- 72b + 4a)c d + 4b c )cos(x) +--R + +--R 2 2 3 4 2 +--R ((- 54b - 54a)c d + (- 68b - 14a)c d - 14b c )cos(x) +--R + +--R 2 2 3 4 +--R ((- 22b - 22a)c d + (- 36b - 14a)c d - 14b c )cos(x) +--R + +--R 2 2 3 4 +--R (- 4b - 4a)c d + (- 8b - 4a)c d - 4b c +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 2 +--R ((- 2b - 2a)c d - 2b c d + (2b + 2a)c d + 2b c )cos(x) +--R + +--R 2 2 3 4 4 +--R ((8b + 8a)c d + (16b + 8a)c d + 8b c )cos(x) + (b + a)d +--R + +--R 3 2 2 3 4 +--R (6b + 5a)c d + (16b + 11a)c d + (18b + 7a)c d + 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 3 +--R (b + a)d + (- 9b - 10a)c d + (- b + 9a)c d + (13b + 4a)c d +--R + +--R 4 +--R 4b c +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 22b - 22a)c d + (38b + 60a)c d + (78b + 18a)c d + 18b c ) +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- b - a)d + (- 4b - 3a)c d + (114b + 117a)c d +--R + +--R 3 4 +--R (140b + 23a)c d + 23b c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((14b + 14a)c d + (98b + 84a)c d + (90b + 6a)c d + 6b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (5b + 5a)c d + (23b + 18a)c d + (15b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 6 +--R ((- 2b - 2a)c d - 2b c d + (2b + 2a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 5 +--R ((- 6b - 6a)c d + (- 2b + 4a)c d + (14b + 10a)c d + 10b c )cos(x) +--R + +--R 3 2 2 3 4 4 +--R ((- 4b - 4a)c d + (8b + 12a)c d + (28b + 16a)c d + 16b c )cos(x) +--R + +--R 3 2 2 3 4 3 +--R ((4b + 4a)c d + (12b + 8a)c d + (12b + 4a)c d + 4b c )cos(x) +--R + +--R 3 2 2 3 4 2 +--R ((6b + 6a)c d + (- 2b - 8a)c d + (- 22b - 14a)c d - 14b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((2b + 2a)c d + (- 10b - 12a)c d + (- 26b - 14a)c d - 14b c )cos(x) +--R + +--R 2 2 3 4 +--R (- 4b - 4a)c d + (- 8b - 4a)c d - 4b c +--R / +--R 4 2 3 3 2 4 2 2 3 4 +--R (c d - c d - c d + c d)cos(x) + (- 4c d + 4c d)cos(x) +--R + +--R 3 2 4 +--R 4c d + 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (5c d - 6c d + 5c d)cos(x) + (12c d - 24c d + 28c d)cos(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (10c d - 28c d + 58c d)cos(x) + (4c d - 8c d + 52c d)cos(x) +--R + +--R 2 3 3 2 4 +--R c d + 2c d + 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (4c d + 4c d)cos(x) + (24c d + 24c d)cos(x) +--R + +--R 3 2 4 4 3 2 4 3 +--R (60c d + 60c d)cos(x) + (80c d + 80c d)cos(x) +--R + +--R 3 2 4 2 3 2 4 3 2 4 +--R (60c d + 60c d)cos(x) + (24c d + 24c d)cos(x) + 4c d + 4c d +--R * +--R 2 +--R tan(x) +--R + +--R 5 2 3 4 2 4 2 3 3 2 4 +--R (d - 2c d + c d)cos(x) + (- 4c d - 4c d + 4c d + 4c d)cos(x) +--R + +--R 2 3 3 2 4 +--R 4c d + 8c d + 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 4 4 +--R (5c d - c d - c d + 5c d)cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (12c d - 12c d + 4c d + 28c d)cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (10c d - 18c d + 30c d + 58c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 4 +--R (4c d - 4c d + 44c d + 52c d)cos(x) + c d + 3c d + 19c d + 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (4c d + 8c d + 4c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (60c d + 120c d + 60c d)cos(x) + (80c d + 160c d + 80c d)cos(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (60c d + 120c d + 60c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 +--R 4c d + 8c d + 4c d +--R Type: Expression Integer +--E 510 + +--S 511 of 534 +t0696:= (-1+1/d^2*c^2+cos(x)^2)/(c+d*sin(x)) +--R +--R +--R 2 2 2 2 +--R d cos(x) - d + c +--R (447) ------------------- +--R 3 2 +--R d sin(x) + c d +--R Type: Expression Integer +--E 511 + +--S 512 of 534 +r0696:= (c*x+d*cos(x))/d^2 +--R +--R +--R d cos(x) + c x +--R (448) -------------- +--R 2 +--R d +--R Type: Expression Integer +--E 512 + +--S 513 of 534 +a0696:= integrate(t0696,x) +--R +--R +--R d cos(x) + c x +--R (449) -------------- +--R 2 +--R d +--R Type: Union(Expression Integer,...) +--E 513 + +--S 514 of 534 +m0696:= a0696-r0696 +--R +--R +--R (450) 0 +--R Type: Expression Integer +--E 514 + +--S 515 of 534 +d0696:= D(m0696,x) +--R +--R +--R (451) 0 +--R Type: Expression Integer +--E 515 + +--S 516 of 534 +t0697:= (a+b*cos(x)^2)/(c+d*sin(x)) +--R +--R +--R 2 +--R b cos(x) + a +--R (452) ------------- +--R d sin(x) + c +--R Type: Expression Integer +--E 516 + +--S 517 of 534 +r0697:= b*c*x/d^2+2*(a*d^2-b*(c^2-d^2))*atan((d+c*tan(1/2*x))/(c^2-d^2)^(1/2))/d^2/(c^2-d^2)^(1/2)+b*cos(x)/d +--R +--R +--R (453) +--R x +--R c tan(-) + d +---------+ +--R 2 2 2 | 2 2 +--R ((2b + 2a)d - 2b c )atan(------------) + (b d cos(x) + b c x)\|- d + c +--R +---------+ +--R | 2 2 +--R \|- d + c +--R -------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression Integer +--E 517 + +--S 518 of 534 +a0697:= integrate(t0697,x) +--R +--R +--R (454) +--R [ +--R 2 2 +--R ((b + a)d - b c ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (- c d + c )sin(x) + (- d + c d)cos(x) - d + c d +--R / +--R d sin(x) + c +--R + +--R +-------+ +--R | 2 2 +--R (b d cos(x) + b c x)\|d - c +--R / +--R +-------+ +--R 2 | 2 2 +--R d \|d - c +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 (c sin(x) + d cos(x) + d)\|- d + c +--R ((- 2b - 2a)d + 2b c )atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R + +--R +---------+ +--R | 2 2 +--R (b d cos(x) + b c x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R ] +--R Type: Union(List Expression Integer,...) +--E 518 + +--S 519 of 534 +m0697a:= a0697.1-r0697 +--R +--R +--R (455) +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)d - b c )\|- d + c +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (- c d + c )sin(x) + (- d + c d)cos(x) - d + c d +--R / +--R d sin(x) + c +--R + +--R x +--R +-------+ c tan(-) + d +--R 2 2 | 2 2 2 +--R ((- 2b - 2a)d + 2b c )\|d - c atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R d \|- d + c \|d - c +--R Type: Expression Integer +--E 519 + +--S 520 of 534 +d0697a:= D(m0697a,x) +--R +--R +--R (456) +--R 4 2 2 4 4 +--R ((- b - a)d + (2b + a)c d - b c )cos(x) + (- b - a)d +--R + +--R 2 2 +--R b c d +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 +--R ((b + a)c d - b c d)cos(x) + (- b - a)c d + b c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 3 3 +--R ((2b + 2a)d - 2b c d )sin(x) + ((2b + 2a)c d - 2b c d)sin(x) +--R + +--R 4 2 2 2 +--R ((2b + 2a)d - 2b c d )cos(x) +--R + +--R 4 2 2 4 +--R ((2b + 2a)d + (- 4b - 2a)c d + 2b c )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 4 2 2 +--R (((- b - a)d + (2b + a)c d - b c )cos(x) + (- b - a)d + b c d ) +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 +--R ((b + a)c d - b c d)cos(x) + (- b - a)c d + b c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 5 2 3 4 5 +--R ((b + a)d + (- 2b - a)c d + b c d)cos(x) + (b + a)d +--R + +--R 2 3 4 +--R (- 2b - a)c d + b c d +--R * +--R sin(x) +--R + +--R 4 3 2 5 2 4 +--R ((- b - a)c d + (2b + a)c d - b c )cos(x) + (b + a)c d +--R + +--R 3 2 5 +--R (- 2b - a)c d + b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 +--R ((- 2b - 2a)d + (4b + 2a)c d - 2b c d)sin(x) +--R + +--R 4 3 2 5 +--R ((- 2b - 2a)c d + (4b + 2a)c d - 2b c )sin(x) +--R + +--R 5 2 3 4 2 +--R ((- 2b - 2a)d + (4b + 2a)c d - 2b c d)cos(x) +--R + +--R 5 2 3 4 +--R ((- 2b - 2a)d + (4b + 2a)c d - 2b c d)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 5 +--R ((b + a)d + (- 2b - a)c d + b c d)cos(x) + (b + a)d +--R + +--R 2 3 4 +--R (- 2b - a)c d + b c d +--R * +--R sin(x) +--R + +--R 4 3 2 5 2 4 +--R ((- b - a)c d + (2b + a)c d - b c )cos(x) + (b + a)c d +--R + +--R 3 2 5 +--R (- 2b - a)c d + b c +--R / +--R 2 3 2 4 3 2 4 3 2 +--R c d sin(x) + ((c d - c d )cos(x) + c d + c d )sin(x) +--R + +--R 2 3 4 2 3 +--R (c d - c d)cos(x) + c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R 2c d sin(x) + ((2d - 2c d )cos(x) + 2d + 2c d )sin(x) +--R + +--R 4 3 2 4 +--R (2c d - 2c d )cos(x) + 2c d +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R c d sin(x) + ((c d - c d )cos(x) + c d + c d )sin(x) +--R + +--R 2 3 4 2 3 +--R (c d - c d)cos(x) + c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- c d + c d )sin(x) + ((- c d + c d )cos(x) - c d + c d)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- c d + c d )cos(x) - c d + c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (- 2c d + 2c d )sin(x) +--R + +--R 6 2 4 6 4 2 5 3 3 +--R ((- 2d + 2c d )cos(x) - 2d + 2c d )sin(x) + (- 2c d + 2c d )cos(x) +--R + +--R 5 3 3 +--R - 2c d + 2c d +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- c d + c d )sin(x) + ((- c d + c d )cos(x) - c d + c d)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- c d + c d )cos(x) - c d + c d +--R Type: Expression Integer +--E 520 + +--S 521 of 534 +m0697b:= a0697.2-r0697 +--R +--R +--R (457) +--R +---------+ +--R | 2 2 +--R 2 2 (c sin(x) + d cos(x) + d)\|- d + c +--R ((- 2b - 2a)d + 2b c )atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R + +--R x +--R c tan(-) + d +--R 2 2 2 +--R ((- 2b - 2a)d + 2b c )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression Integer +--E 521 + +--S 522 of 534 +d0697b:= D(m0697b,x) +--R +--R +--R (458) +--R 2 3 2 +--R ((b + a)c d - b c )sin(x) +--R + +--R 3 2 3 2 +--R (((- 2b - 2a)d + 2b c d)cos(x) + (- 2b - 2a)d + 2b c d)sin(x) +--R + +--R 2 3 2 2 3 +--R ((b + a)c d - b c )cos(x) + (- b - a)c d + b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R ((4b + 4a)d - 4b c d)sin(x) + ((4b + 4a)d - 4b c d)cos(x) +--R + +--R 3 2 +--R ((4b + 4a)d - 4b c d)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 +--R ((b + a)c d - b c )sin(x) +--R + +--R 3 2 3 2 +--R (((- 2b - 2a)d + 2b c d)cos(x) + (- 2b - 2a)d + 2b c d)sin(x) +--R + +--R 2 3 2 2 3 +--R ((b + a)c d - b c )cos(x) + (- b - a)c d + b c +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R c d sin(x) + (2c d cos(x) + 2c d )sin(x) + c d cos(x) + 2c d cos(x) +--R + +--R 2 2 +--R c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2c d sin(x) + (4d cos(x) + 4d )sin(x) + 2c d cos(x) + 4c d cos(x) +--R + +--R 3 +--R 2c d +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R c d sin(x) + (2c d cos(x) + 2c d )sin(x) + c d cos(x) + 2c d cos(x) +--R + +--R 2 2 +--R c d +--R Type: Expression Integer +--E 522 + +--S 523 of 534 +t0698:= (a+b*cos(x)^2)/(c+c*sin(x)^2) +--R +--R +--R 2 +--R b cos(x) + a +--R (459) ------------- +--R 2 +--R c sin(x) + c +--R Type: Expression Integer +--E 523 + +--S 524 of 534 +r0698:= -b*x/c+1/2*(a+2*b)*atan(2^(1/2)*tan(x))*2^(1/2)/c +--R +--R +--R +-+ +-+ +--R (2b + a)\|2 atan(\|2 tan(x)) - 2b x +--R (460) ----------------------------------- +--R 2c +--R Type: Expression Integer +--E 524 + +--S 525 of 534 +a0698:= integrate(t0698,x) +--R +--R +--R (461) +--R +-+ +--R \|2 sin(x) +--R (2b + a)atan(-----------) +--R 4cos(x) + 4 +--R + +--R (3cos(x) + 4)sin(x) +-+ +--R (2b + a)atan(--------------------------------) - b x\|2 +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Union(Expression Integer,...) +--E 525 + +--S 526 of 534 +m0698:= a0698-r0698 +--R +--R +--R (462) +--R +-+ +--R +-+ \|2 sin(x) +--R (- 2b - a)atan(\|2 tan(x)) + (2b + a)atan(-----------) +--R 4cos(x) + 4 +--R + +--R (3cos(x) + 4)sin(x) +--R (2b + a)atan(--------------------------------) +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Expression Integer +--E 526 + +--S 527 of 534 +d0698:= D(m0698,x) +--R +--R +--R (463) +--R 2 4 +--R ((66b + 33a)cos(x) + (176b + 88a)cos(x) + 116b + 58a)sin(x) +--R + +--R 4 3 2 +--R (48b + 24a)cos(x) + (128b + 64a)cos(x) + (36b + 18a)cos(x) +--R + +--R (- 128b - 64a)cos(x) - 84b - 42a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R (80b + 40a)cos(x) + (400b + 200a)cos(x) + (768b + 384a)cos(x) +--R + +--R 3 2 +--R (672b + 336a)cos(x) + (208b + 104a)cos(x) + (- 48b - 24a)cos(x) +--R + +--R - 32b - 16a +--R * +--R 2 +--R tan(x) +--R + +--R 2 4 +--R ((24b + 12a)cos(x) + (64b + 32a)cos(x) + 42b + 21a)sin(x) +--R + +--R 4 3 +--R (- 50b - 25a)cos(x) + (- 280b - 140a)cos(x) +--R + +--R 2 +--R (- 578b - 289a)cos(x) + (- 520b - 260a)cos(x) - 172b - 86a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R (24b + 12a)cos(x) + (104b + 52a)cos(x) + (144b + 72a)cos(x) +--R + +--R 3 2 +--R (16b + 8a)cos(x) + (- 136b - 68a)cos(x) + (- 120b - 60a)cos(x) - 32b +--R + +--R - 16a +--R / +--R 2 4 +--R (18c cos(x) + 48c cos(x) + 32c)sin(x) +--R + +--R 4 3 2 +--R (148c cos(x) + 688c cos(x) + 1192c cos(x) + 912c cos(x) + 260c) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R 32c cos(x) + 192c cos(x) + 480c cos(x) + 640c cos(x) +--R + +--R 2 +--R 480c cos(x) + 192c cos(x) + 32c +--R * +--R 2 +--R tan(x) +--R + +--R 2 4 +--R (9c cos(x) + 24c cos(x) + 16c)sin(x) +--R + +--R 4 3 2 2 +--R (74c cos(x) + 344c cos(x) + 596c cos(x) + 456c cos(x) + 130c)sin(x) +--R + +--R 6 5 4 3 2 +--R 16c cos(x) + 96c cos(x) + 240c cos(x) + 320c cos(x) + 240c cos(x) +--R + +--R 96c cos(x) + 16c +--R Type: Expression Integer +--E 527 + +--S 528 of 534 +t0699:= (a+b*cos(x)^2)/(c+d*sin(x)^2) +--R +--R +--R 2 +--R b cos(x) + a +--R (464) ------------- +--R 2 +--R d sin(x) + c +--R Type: Expression Integer +--E 528 + +--S 529 of 534 +r0699:= -b*x/d+(b*c+(a+b)*d)*atan((c+d)^(1/2)*tan(x)/c^(1/2))/c^(1/2)/d/(c+d)^(1/2) +--R +--R +--R +-----+ +--R tan(x)\|d + c +-+ +-----+ +--R ((b + a)d + b c)atan(--------------) - b x\|c \|d + c +--R +-+ +--R \|c +--R (465) ------------------------------------------------------ +--R +-+ +-----+ +--R d\|c \|d + c +--R Type: Expression Integer +--E 529 + +--S 530 of 534 +a0699:= integrate(t0699,x) +--R +--R +--R (466) +--R [ +--R ((b + a)d + b c) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R ((- d - 2c)cos(x) + d + c)\|- c d - c +--R + +--R 2 +--R (2c d + 2c )cos(x)sin(x) +--R / +--R 2 +--R d cos(x) - d - c +--R + +--R +----------+ +--R | 2 +--R - 2b x\|- c d - c +--R / +--R +----------+ +--R | 2 +--R 2d\|- c d - c +--R , +--R +--R +--------+ +--R | 2 +--R sin(x)\|c d + c +--R ((b + a)d + b c)atan(-------------------------) +--R (2d + 2c)cos(x) + 2d + 2c +--R + +--R +--------+ +--R ((2d + c)cos(x) + 2d + 2c)sin(x) | 2 +--R ((b + a)d + b c)atan(----------------------------------) - b x\|c d + c +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R / +--R +--------+ +--R | 2 +--R d\|c d + c +--R ] +--R Type: Union(List Expression Integer,...) +--E 530 + +--S 531 of 534 +m0699a:= a0699.1-r0699 +--R +--R +--R (467) +--R +-+ +-----+ +--R ((b + a)d + b c)\|c \|d + c +--R * +--R +----------+ +--R 2 | 2 2 +--R ((- d - 2c)cos(x) + d + c)\|- c d - c + (2c d + 2c )cos(x)sin(x) +--R log(-------------------------------------------------------------------) +--R 2 +--R d cos(x) - d - c +--R + +--R +----------+ +-----+ +--R | 2 tan(x)\|d + c +--R ((- 2b - 2a)d - 2b c)\|- c d - c atan(--------------) +--R +-+ +--R \|c +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R 2d\|- c d - c \|c \|d + c +--R Type: Expression Integer +--E 531 + +--S 532 of 534 +d0699a:= D(m0699a,x) +--R +--R +--R (468) +--R 3 2 2 2 3 +--R ((b + a)d + (2b + a)c d + b c d)cos(x) + (b + a)d +--R + +--R 2 2 3 +--R (3b + 2a)c d + (3b + a)c d + b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R ((- b - a)c d - b c d)cos(x) +--R + +--R 3 2 2 3 2 +--R ((b + a)d + (3b + 2a)c d + (3b + a)c d + b c )cos(x) +--R + +--R 3 2 2 3 +--R (- b - a)d + (- 3b - 2a)c d + (- 3b - a)c d - b c +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 2 2 3 +--R (((b + a)c d + b c d)cos(x) + (b + a)c d + (2b + a)c d + b c ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 +--R ((- b - a)d + (- 2b - a)c d - b c d)cos(x) +--R + +--R 3 2 2 3 2 +--R ((2b + 2a)d + (5b + 3a)c d + (4b + a)c d + b c )cos(x) +--R + +--R 3 2 2 3 +--R (- b - a)d + (- 3b - 2a)c d + (- 3b - a)c d - b c +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 3 2 2 3 3 2 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) sin(x)tan(x) +--R + +--R 3 2 2 3 3 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) +--R + +--R 3 2 2 3 +--R ((- 2b - 2a)c d + (- 4b - 2a)c d - 2b c d)cos(x) +--R * +--R sin(x) +--R / +--R 4 3 2 2 4 +--R (d + 3c d + 2c d )cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- 2d - 6c d - 6c d - 2c d)cos(x) + d + 3c d + 3c d + c d +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 4 3 2 2 3 2 3 +--R (c d + 2c d )cos(x) + (- 2c d - 4c d - 2c d)cos(x) + c d +--R + +--R 2 2 3 +--R 2c d + c d +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 4 2 3 3 2 3 +--R (- 2c d - 4c d - 2c d )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (2c d + 6c d + 6c d + 2c d)cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 2 3 3 2 3 2 3 3 2 4 +--R ((- 2c d - 2c d )cos(x) + (2c d + 4c d + 2c d)cos(x))sin(x) +--R Type: Expression Integer +--E 532 + +--S 533 of 534 +m0699b:= a0699.2-r0699 +--R +--R +--R (469) +--R +--------+ +--R | 2 +--R +-+ +-----+ sin(x)\|c d + c +--R ((b + a)d + b c)\|c \|d + c atan(-------------------------) +--R (2d + 2c)cos(x) + 2d + 2c +--R + +--R +--------+ +-----+ +--R | 2 tan(x)\|d + c +--R ((- b - a)d - b c)\|c d + c atan(--------------) +--R +-+ +--R \|c +--R + +--R +-+ +-----+ ((2d + c)cos(x) + 2d + 2c)sin(x) +--R ((b + a)d + b c)\|c \|d + c atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R d\|c \|d + c \|c d + c +--R Type: Expression Integer +--E 533 + +--S 534 of 534 +d0699b:= D(m0699b,x) +--R +--R +--R (470) +--R 4 3 2 2 +--R (8b + 8a)d + (22b + 14a)c d + (23b + 9a)c d +--R + +--R 3 4 +--R (11b + 2a)c d + 2b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (16b + 16a)d + (52b + 36a)c d + (64b + 28a)c d +--R + +--R 3 4 +--R (36b + 8a)c d + 8b c +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 +--R (8b + 8a)d + (30b + 22a)c d + (43b + 21a)c d + (28b + 7a)c d +--R + +--R 4 +--R 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R ((8b + 8a)c d + (20b + 12a)c d + (16b + 4a)c d + 4b c )cos(x) +--R + +--R 4 3 2 2 +--R (- 8b - 8a)d + (6b + 14a)c d + (54b + 40a)c d +--R + +--R 3 4 +--R (58b + 18a)c d + 18b c +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 24b - 24a)d + (- 38b - 14a)c d + (19b + 33a)c d +--R + +--R 3 4 +--R (56b + 23a)c d + 23b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 24b - 24a)d + (- 62b - 38a)c d + (- 46b - 8a)c d +--R + +--R 3 4 +--R (- 2b + 6a)c d + 6b c +--R * +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 8b - 8a)d + (- 26b - 18a)c d + (- 31b - 13a)c d +--R + +--R 3 4 +--R (- 16b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 3 +--R (8b + 8a)d + (26b + 18a)c d + (30b + 12a)c d + (14b + 2a)c d +--R + +--R 4 +--R 2b c +--R * +--R 6 +--R cos(x) +--R + +--R 4 3 2 2 +--R (40b + 40a)d + (130b + 90a)c d + (150b + 60a)c d +--R + +--R 3 4 +--R (70b + 10a)c d + 10b c +--R * +--R 5 +--R cos(x) +--R + +--R 4 3 2 2 +--R (80b + 80a)d + (256b + 176a)c d + (288b + 112a)c d +--R + +--R 3 4 +--R (128b + 16a)c d + 16b c +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 2 2 +--R (80b + 80a)d + (244b + 164a)c d + (252b + 88a)c d +--R + +--R 3 4 +--R (92b + 4a)c d + 4b c +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (40b + 40a)d + (106b + 66a)c d + (78b + 12a)c d +--R + +--R 3 4 +--R (- 2b - 14a)c d - 14b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (8b + 8a)d + (10b + 2a)c d + (- 18b - 20a)c d +--R + +--R 3 4 +--R (- 34b - 14a)c d - 14b c +--R * +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 4a)c d + (- 12b - 8a)c d + (- 12b - 4a)c d - 4b c +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 2 +--R ((4b + 4a)c d + (10b + 6a)c d + (8b + 2a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((8b + 8a)c d + (24b + 16a)c d + (24b + 8a)c d + 8b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (4b + 4a)c d + (14b + 10a)c d + (17b + 7a)c d + 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 16b - 16a)d + (- 32b - 16a)c d + (- 13b + 3a)c d +--R + +--R 3 4 +--R (7b + 4a)c d + 4b c +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 64b - 64a)d + (- 152b - 88a)c d + (- 94b - 6a)c d +--R + +--R 3 4 +--R (12b + 18a)c d + 18b c +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 96b - 96a)d + (- 264b - 168a)c d + (- 216b - 48a)c d +--R + +--R 3 4 +--R (- 25b + 23a)c d + 23b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 64b - 64a)d + (- 200b - 136a)c d + (- 202b - 66a)c d +--R + +--R 3 4 +--R (- 60b + 6a)c d + 6b c +--R * +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 16b - 16a)d + (- 56b - 40a)c d + (- 67b - 27a)c d +--R + +--R 3 4 +--R (- 30b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 6 +--R ((4b + 4a)c d + (10b + 6a)c d + (8b + 2a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 5 +--R ((16b + 16a)c d + (42b + 26a)c d + (36b + 10a)c d + 10b c )cos(x) +--R + +--R 3 2 2 3 4 4 +--R ((20b + 20a)c d + (56b + 36a)c d + (52b + 16a)c d + 16b c )cos(x) +--R + +--R 2 2 3 4 3 +--R ((4b + 4a)c d + (8b + 4a)c d + 4b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 20b - 20a)c d + (- 54b - 34a)c d + (- 48b - 14a)c d - 14b c ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 16b - 16a)c d + (- 46b - 30a)c d + (- 44b - 14a)c d - 14b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 4a)c d + (- 12b - 8a)c d + (- 12b - 4a)c d - 4b c +--R / +--R 4 2 3 3 2 4 2 +--R (4c d + 8c d + 5c d + c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (8c d + 20c d + 16c d + 4c d)cos(x) + 4c d + 12c d + 12c d +--R + +--R 4 +--R 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (16d + 48c d + 53c d + 26c d + 5c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (64d + 208c d + 252c d + 136c d + 28c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (96d + 336c d + 442c d + 260c d + 58c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (64d + 240c d + 340c d + 216c d + 52c d)cos(x) + 16d +--R + +--R 4 2 3 3 2 4 +--R 64c d + 97c d + 66c d + 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 4 6 +--R (4c d + 12c d + 12c d + 4c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (24c d + 72c d + 72c d + 24c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (60c d + 180c d + 180c d + 60c d)cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (80c d + 240c d + 240c d + 80c d)cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (60c d + 180c d + 180c d + 60c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (24c d + 72c d + 72c d + 24c d)cos(x) + 4c d + 12c d + 12c d +--R + +--R 4 +--R 4c d +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 2 3 +--R (4c d + 4c d + c d)cos(x) + (8c d + 12c d + 4c d)cos(x) + 4c d +--R + +--R 3 2 4 +--R 8c d + 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 4 4 +--R (16c d + 32c d + 21c d + 5c d)cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (64c d + 144c d + 108c d + 28c d)cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (96c d + 240c d + 202c d + 58c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (64c d + 176c d + 164c d + 52c d)cos(x) + 16c d + 48c d + 49c d +--R + +--R 4 +--R 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (4c d + 8c d + 4c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (60c d + 120c d + 60c d)cos(x) + (80c d + 160c d + 80c d)cos(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (60c d + 120c d + 60c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 +--R 4c d + 8c d + 4c d +--R Type: Expression Integer +--E 534 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}