diff --git a/changelog b/changelog index 0e19c20..b8fd57d 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100612 tpd src/axiom-website/patches.html 20100612.01.tpd.patch +20100612 tpd src/input/Makefile rule-based trig integration +20100612 tpd src/input/richtrig800-899.input rule-based trig integration 20100611 tpd src/axiom-website/patches.html 20100611.01.tpd.patch 20100611 tpd src/input/Makefile rule-based trig integration 20100611 tpd src/input/richtrig700-799.input rule-based trig integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 0770418..a62f79c 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2882,6 +2882,8 @@ src/input/richtrig500-599.input rule-based trig integration
src/input/richtrig600-699.input rule-based trig integration
20100611.01.tpd.patch src/input/richtrig700-799.input rule-based trig integration
+20100612.01.tpd.patch +src/input/richtrig800-899.input rule-based trig integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 56e6e36..a9dab57 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -384,6 +384,7 @@ REGRES= ackermann.regress \ richtrig500-599.regress \ richtrig600-699.regress \ richtrig700-799.regress \ + richtrig800-899.regress \ robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -711,6 +712,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richtrig500-599.input \ ${OUT}/richtrig600-699.input \ ${OUT}/richtrig700-799.input \ + ${OUT}/richtrig800-899.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1067,6 +1069,7 @@ DOCFILES= \ ${DOC}/richtrig500-599.input.dvi \ ${DOC}/richtrig600-699.input.dvi \ ${DOC}/richtrig700-799.input.dvi \ + ${DOC}/richtrig800-899.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/richtrig800-899.input.pamphlet b/src/input/richtrig800-899.input.pamphlet new file mode 100644 index 0000000..1adf663 --- /dev/null +++ b/src/input/richtrig800-899.input.pamphlet @@ -0,0 +1,45927 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richtrig800-899.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig800-899.output +)spool richtrig800-899.output +)set message auto off +)clear all + +--S 1 of 526 +t0800:= cos(a+b*x)*csc(c+b*x)^2 +--R +--R +--R 2 +--R (1) cos(b x + a)csc(b x + c) +--R Type: Expression Integer +--E 1 + +--S 2 of 526 +r0800:= -cos(a-c)*csc(c+b*x)/b+atanh(cos(c+b*x))*sin(a-c)/b +--R +--R +--R - sin(c - a)atanh(cos(b x + c)) - cos(c - a)csc(b x + c) +--R (2) -------------------------------------------------------- +--R b +--R Type: Expression Integer +--E 2 + +--S 3 of 526 +a0800:= integrate(t0800,x) +--R +--R +--R c - a sin(b x + c) c - a 2 +--R 2sin(b x + c)tan(-----)log(----------------) + tan(-----) - 1 +--R 2 cos(b x + c) + 1 2 +--R (3) -------------------------------------------------------------- +--R c - a 2 +--R b sin(b x + c)tan(-----) + b sin(b x + c) +--R 2 +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 526 +m0800:= a0800-r0800 +--R +--R +--R (4) +--R c - a sin(b x + c) +--R 2sin(b x + c)tan(-----)log(----------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R (sin(c - a)sin(b x + c)tan(-----) + sin(c - a)sin(b x + c)) +--R 2 +--R * +--R atanh(cos(b x + c)) +--R + +--R c - a 2 +--R (cos(c - a)csc(b x + c)sin(b x + c) + 1)tan(-----) +--R 2 +--R + +--R cos(c - a)csc(b x + c)sin(b x + c) - 1 +--R / +--R c - a 2 +--R b sin(b x + c)tan(-----) + b sin(b x + c) +--R 2 +--R Type: Expression Integer +--E 4 + +--S 5 of 526 +d0800:= D(m0800,x) +--R +--R +--R (5) +--R 3 +--R sin(c - a)sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + c) + cos(c - a))cot(b x + c)csc(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R - cos(b x + c) + cos(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 3 +--R (2cos(b x + c) - 2)sin(b x + c) +--R + +--R 3 +--R (2cos(b x + c) - 2cos(b x + c))sin(b x + c) +--R * +--R c - a +--R tan(-----) +--R 2 +--R + +--R 3 +--R sin(c - a)sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + c) + cos(c - a))cot(b x + c)csc(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R cos(b x + c) - cos(b x + c) +--R / +--R 2 2 c - a 2 +--R (cos(b x + c) - 1)sin(b x + c) tan(-----) +--R 2 +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + c) +--R Type: Expression Integer +--E 5 + +--S 6 of 526 +t0801:= cos(a+b*x)*csc(c+b*x)^3 +--R +--R +--R 3 +--R (6) cos(b x + a)csc(b x + c) +--R Type: Expression Integer +--E 6 + +--S 7 of 526 +r0801:= -1/2*cos(a-c)*csc(c+b*x)^2/b+cot(c+b*x)*sin(a-c)/b +--R +--R +--R 2 +--R - 2cot(b x + c)sin(c - a) - cos(c - a)csc(b x + c) +--R (7) --------------------------------------------------- +--R 2b +--R Type: Expression Integer +--E 7 + +--S 8 of 526 +a0801:= integrate(t0801,x) +--R +--R +--R (8) +--R 2 c - a 2 c - a +--R (- cos(b x + c) - 1)tan(-----) + 8cos(b x + c)sin(b x + c)tan(-----) +--R 2 2 +--R + +--R 2 +--R cos(b x + c) + 1 +--R / +--R 2 c - a 2 2 +--R (4b cos(b x + c) - 4b)tan(-----) + 4b cos(b x + c) - 4b +--R 2 +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 526 +m0801:= a0801-r0801 +--R +--R +--R (9) +--R 2 +--R (4cos(b x + c) - 4)cot(b x + c)sin(c - a) +--R + +--R 2 2 2 +--R (2cos(c - a)cos(b x + c) - 2cos(c - a))csc(b x + c) - cos(b x + c) +--R + +--R - 1 +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R c - a +--R 8cos(b x + c)sin(b x + c)tan(-----) +--R 2 +--R + +--R 2 +--R (4cos(b x + c) - 4)cot(b x + c)sin(c - a) +--R + +--R 2 2 2 +--R (2cos(c - a)cos(b x + c) - 2cos(c - a))csc(b x + c) + cos(b x + c) + 1 +--R / +--R 2 c - a 2 2 +--R (4b cos(b x + c) - 4b)tan(-----) + 4b cos(b x + c) - 4b +--R 2 +--R Type: Expression Integer +--E 9 + +--S 10 of 526 +d0801:= D(m0801,x) +--R +--R +--R (10) +--R - cos(b x + c)sin(b x + c) +--R + +--R 4 2 2 +--R (- cos(b x + c) + 2cos(b x + c) - 1)cot(b x + c) +--R + +--R 4 2 +--R - cos(b x + c) + 2cos(b x + c) - 1 +--R * +--R sin(c - a) +--R + +--R 4 2 +--R (- cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) - cos(c - a)) +--R * +--R 2 +--R cot(b x + c)csc(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 2 4 2 +--R ((2cos(b x + c) + 2)sin(b x + c) + 2cos(b x + c) - 2cos(b x + c) ) +--R * +--R c - a +--R tan(-----) +--R 2 +--R + +--R cos(b x + c)sin(b x + c) +--R + +--R 4 2 2 4 +--R (- cos(b x + c) + 2cos(b x + c) - 1)cot(b x + c) - cos(b x + c) +--R + +--R 2 +--R 2cos(b x + c) - 1 +--R * +--R sin(c - a) +--R + +--R 4 2 +--R (- cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) - cos(c - a)) +--R * +--R 2 +--R cot(b x + c)csc(b x + c) +--R / +--R 4 2 c - a 2 4 +--R (cos(b x + c) - 2cos(b x + c) + 1)tan(-----) + cos(b x + c) +--R 2 +--R + +--R 2 +--R - 2cos(b x + c) + 1 +--R Type: Expression Integer +--E 10 + +--S 11 of 526 +t0802:= sin(x)^2/(a+b*sin(2*x)) +--R +--R +--R 2 +--R sin(x) +--R (11) ------------- +--R b sin(2x) + a +--R Type: Expression Integer +--E 11 + +--S 12 of 526 +r0802:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)-1/4*log(a+b*sin(2*x))/b +--R +--R +--R +---------+ +--R | 2 2 a tan(x) + b +--R - \|- b + a log(b sin(2x) + a) + 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (12) -------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression Integer +--E 12 + +--S 13 of 526 +a0802:= integrate(t0802,x) +--R +--R +--R (13) +--R [ +--R b +--R * +--R log +--R 2 2 2 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a ) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +-------+ +-------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R - \|b - a log(---------------------) + 2\|b - a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b - a +--R , +--R +--R +---------+ +---------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R - \|- b + a log(---------------------) + 2\|- b + a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 13 + +--S 14 of 526 +m0802a:= a0802.1-r0802 +--R +--R +--R (14) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a )\|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a log(b sin(2x) + a) +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R - \|- b + a \|b - a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +-------+ +-------+ +--R | 2 2 | 2 2 2 | 2 2 a tan(x) + b +--R 2\|- b + a \|b - a log(----------) - 2b\|b - a atan(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R 4b\|- b + a \|b - a +--R Type: Expression Integer +--E 14 + +--S 15 of 526 +d0802a:= D(m0802a,x) +--R +--R +--R (15) +--R 2 2 3 +--R 2a b cos(x)sin(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 4a b + 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 6a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 3 4 3 2 3 3 +--R (4a b - 2a b)cos(x) - 2a b cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 +--R 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 4 2 2 2 4 +--R (4a b cos(x) cos(2x) + (- 4a b + 2a )cos(x) + 4a b - 2a ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 +--R ((- 4a b + 4a b)cos(x) + 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 6a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 +--R ((- 2a b + 2a )cos(x) + 2a b - a )cos(2x) +--R + +--R 2 2 4 4 2 2 2 2 2 4 +--R (4a b - 2a )cos(x) - 2a b cos(x) - 2a b + a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 2 2 2 4 2 2 2 +--R 4a b cos(x)sin(x) + (4a b cos(x) + 8b - 4a b )sin(x) +--R + +--R 3 3 3 4 2 2 4 +--R (- 4a b cos(x) + 4a b cos(x))sin(x) + (8b - 4a b )cos(x) +--R + +--R 4 2 2 2 +--R (- 8b + 4a b )cos(x) +--R * +--R sin(2x) +--R + +--R 2 2 3 +--R 4a b cos(x)sin(x) +--R + +--R 3 2 3 2 3 3 2 +--R (8a b cos(x) cos(2x) + 4a b cos(x) + 8a b - 4a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 3 +--R ((- 8b + 8a b )cos(x) + 8b cos(x))cos(2x) - 4a b cos(x) +--R + +--R 2 2 +--R 4a b cos(x) +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 +--R ((- 4a b + 4a b)cos(x) + 4a b - 2a b)cos(2x) +--R + +--R 3 3 4 3 3 2 +--R (8a b - 4a b)cos(x) + (- 8a b + 4a b)cos(x) +--R * +--R tan(x) +--R + +--R 2 2 3 +--R 2a b cos(x)sin(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 4a b + 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 6a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 3 4 3 2 3 3 +--R (4a b - 2a b)cos(x) - 2a b cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 +--R 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 4 2 2 2 4 2 +--R (4a b cos(x) cos(2x) + (- 4a b + 2a )cos(x) + 4a b - 2a )sin(x) +--R + +--R 3 3 3 3 +--R ((- 4a b + 4a b)cos(x) + 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 6a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 4 +--R ((- 2a b + 2a )cos(x) + 2a b - a )cos(2x) + (4a b - 2a )cos(x) +--R + +--R 2 2 2 2 2 4 +--R - 2a b cos(x) - 2a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 4 3 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 6a b + 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 4 4 3 2 2 4 3 2 +--R (4a b - 4a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 +--R (2a b - 2a )cos(x)sin(x) +--R + +--R 2 3 4 2 2 3 4 2 2 3 +--R (4a b - 4a b)cos(x) cos(2x) + (- 4a b + 4a b)cos(x) + 4a b +--R + +--R 4 +--R - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((- 4a b + 4a b )cos(x) + (4a b - 2a b - 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 6a b + 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R ((- 2a b + 2a b)cos(x) + 2a b - 2a b)cos(2x) +--R + +--R 2 3 4 4 2 3 4 2 2 3 4 +--R (4a b - 4a b)cos(x) + (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 3 5 2 3 2 +--R (4a b - 4a b )cos(x)sin(x) + (8b - 8a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 +--R ((- 4a b + 4a b )cos(x) + (4a b - 4a b )cos(x))sin(x) +--R + +--R 5 2 3 4 5 2 3 2 +--R (8b - 8a b )cos(x) + (- 8b + 8a b )cos(x) +--R * +--R sin(2x) +--R + +--R 2 3 4 3 +--R (4a b - 4a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R ((8a b - 8a b )cos(x) cos(2x) + 8a b - 8a b )sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R ((- 8b + 8a b )cos(x) + (8b - 4a b - 4a b)cos(x))cos(2x) +--R + +--R 2 3 4 3 2 3 4 +--R (- 4a b + 4a b)cos(x) + (4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )cos(2x) +--R + +--R 4 3 2 4 4 3 2 2 +--R (8a b - 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R * +--R tan(x) +--R + +--R 2 3 4 3 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 6a b + 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 4 4 3 2 2 4 3 2 +--R (4a b - 4a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 +--R (2a b - 2a )cos(x)sin(x) +--R + +--R 2 3 4 2 2 3 4 2 2 3 4 +--R ((4a b - 4a b)cos(x) cos(2x) + (- 4a b + 4a b)cos(x) + 4a b - 4a b) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((- 4a b + 4a b )cos(x) + (4a b - 2a b - 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 6a b + 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 4 +--R ((- 2a b + 2a b)cos(x) + 2a b - 2a b)cos(2x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R / +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 5 2 3 3 5 +--R ((- 16b + 16a b )cos(x) + 16b cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 4a b +--R * +--R sin(2x) +--R + +--R 2 3 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 16a b + 16a b )cos(x) + 16a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 8a b + 8a b)cos(x) + 8a b - 4a b +--R * +--R tan(x) +--R + +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 2 3 4 3 2 3 +--R 8a b cos(x) sin(x) + ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R * +--R 2 +--R tan(x) +--R + +--R 5 3 3 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 6 2 4 3 6 2 4 4 2 +--R ((- 16b + 16a b )cos(x) + (16b - 8a b - 8a b )cos(x))sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R sin(2x) +--R + +--R 2 4 4 2 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 16a b + 16a b )cos(x) + (16a b - 8a b - 8a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R tan(x) +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R Type: Expression Integer +--E 15 + +--S 16 of 526 +m0802b:= a0802.2-r0802 +--R +--R +--R (16) +--R +---------+ +---------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R \|- b + a log(b sin(2x) + a) - \|- b + a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 +--R 2\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R a tan(x) + b +--R - 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression Integer +--E 16 + +--S 17 of 526 +d0802b:= D(m0802b,x) +--R +--R +--R (17) +--R 4 2 4 4 6 +--R (a b cos(x) + 4a b cos(x) + 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (6a b cos(x) + 12a b cos(x) - 12a b cos(x) - 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + (- 56a b + 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 92a b + 56a b)cos(x) + (- 24a b + 60a b)cos(x) + 16a b +--R + +--R 4 +--R 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (32a b + 26a b )cos(x) + (160a b + 132a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b + 214a b )cos(x) + (160a b + 100a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (32a b - 32a b )cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (64b + 24a b - a b)cos(x) + (128b + 8a b - 4a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 192a b + 6a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 128b - 288a b + 46a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 4 +--R (- 64b - 88a b + 66a b)cos(x) + (24a b + 30a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 4 3 2 6 +--R - 16a b cos(x) + (- 64a b - 72a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b - 116a b )cos(x) + (64a b - 132a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (128a b - 192a b )cos(x) - 184a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 32a b - 4a b)cos(x) + (- 96a b - 24a b)cos(x) +--R + +--R 2 3 4 6 4 5 +--R (- 80a b - 58a b)cos(x) - 70a b cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (32a b - 44a b)cos(x) + (64a b - 20a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (80a b - 18a b)cos(x) + (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 4 3 4 2 4 4 3 +--R (2a b cos(x) + 8a b cos(x) + 8a b cos(x))cos(2x) + 6a b cos(x) +--R + +--R 4 2 4 4 +--R 12a b cos(x) - 12a b cos(x) - 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R 4a b cos(x) - 8a b cos(x) + (- 52a b + a )cos(x) +--R + +--R 3 2 5 5 +--R (- 40a b + 4a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 4a b + 4a )cos(x) + (- 56a b + 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (- 92a b + 56a )cos(x) + (- 24a b + 60a )cos(x) + 16a b + 24a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 32a b + 10a b)cos(x) + (- 160a b + 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 192a b + 118a b)cos(x) + (- 32a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b + 8a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b + 26a b)cos(x) + (160a b + 132a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b + 214a b)cos(x) + (160a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 32a b)cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 64a b + 40a b )cos(x) + (- 128a b + 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (256a b + 5a )cos(x) + (128a b + 32a b + 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (64a b - 152a b + 58a )cos(x) + (- 56a b + 52a )cos(x) +--R + +--R 3 2 5 +--R 16a b + 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b + 24a b - a )cos(x) + (128a b + 8a b - 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 192a b + 6a )cos(x) + (- 128a b - 288a b + 46a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b - 88a b + 66a )cos(x) + (24a b + 30a )cos(x) + a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b + 140a b)cos(x) + (- 192a b + 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (- 192a b + 256a b)cos(x) + 104a b cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 20a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 4 7 2 3 4 6 +--R - 16a b cos(x) + (- 64a b - 72a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 116a b)cos(x) + (64a b - 132a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (128a b - 192a b)cos(x) - 184a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 60a b)cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (64a b + 60a )cos(x) + (- 64a b + 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (- 96a b + 60a )cos(x) + (- 32a b + 24a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 6 5 5 3 2 5 4 +--R (- 80a b - 58a )cos(x) - 70a cos(x) + (32a b - 44a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (64a b - 20a )cos(x) + (80a b - 18a )cos(x) +--R + +--R 3 2 5 5 +--R (32a b - 14a )cos(x) - 4a +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 2 3 2 6 +--R (2a b cos(x) + 8a b cos(x) + 8a b )sin(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 5 +--R (16a b cos(x) + 40a b cos(x) - 8a b cos(x) - 40a b )sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R 8a b cos(x) + (- 128a b + 48a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 288a b + 114a b )cos(x) + (- 128a b + 128a b )cos(x) +--R + +--R 4 3 2 +--R 32a b + 56a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 5 2 3 4 5 2 3 3 +--R 72a b cos(x) + 376a b cos(x) + (128b + 664a b )cos(x) +--R + +--R 5 2 3 2 5 2 3 2 3 +--R (256b + 400a b )cos(x) + (128b - 48a b )cos(x) - 88a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (128a b - 2a b )cos(x) + (384a b - 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (128a b + 22a b )cos(x) + (- 512a b + 148a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 480a b + 248a b )cos(x) + (- 64a b + 164a b )cos(x) +--R + +--R 4 3 2 +--R 32a b + 36a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 7 5 2 3 6 +--R (128b - 16a b )cos(x) + (256b - 48a b )cos(x) +--R + +--R 2 3 5 5 2 3 4 +--R 48a b cos(x) + (- 256b + 240a b )cos(x) +--R + +--R 5 2 3 3 2 3 2 2 3 +--R (- 128b + 128a b )cos(x) - 160a b cos(x) - 160a b cos(x) +--R + +--R 2 3 +--R - 32a b +--R * +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 64a b - 8a b )cos(x) + (- 192a b - 48a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 96a b - 108a b )cos(x) + (192a b - 92a b )cos(x) +--R + +--R 4 3 2 4 3 2 3 +--R (192a b + 32a b )cos(x) + 120a b cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 32a b + 84a b )cos(x) + 20a b cos(x) +--R * +--R sin(2x) +--R + +--R 4 2 4 4 6 +--R (2a b cos(x) + 8a b cos(x) + 8a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))cos(2x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R 16a b cos(x) + 40a b cos(x) - 8a b cos(x) - 40a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R cos(2x) +--R + +--R 4 4 2 3 4 3 +--R 8a b cos(x) + (- 128a b + 48a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 288a b + 114a b)cos(x) + (- 128a b + 128a b)cos(x) + 32a b +--R + +--R 4 +--R 56a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R cos(2x) +--R + +--R 3 2 5 3 2 4 4 3 2 3 +--R 72a b cos(x) + 376a b cos(x) + (128a b + 664a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 3 2 +--R (256a b + 400a b )cos(x) + (128a b - 48a b )cos(x) - 88a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 6 5 2 3 5 +--R (- 128b + 80a b )cos(x) + (- 256b + 368a b )cos(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (512a b + 10a b)cos(x) + (256b + 64a b + 56a b)cos(x) +--R + +--R 5 2 3 4 2 +--R (128b - 304a b + 116a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 112a b + 104a b)cos(x) + 32a b + 34a b +--R * +--R cos(2x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (128a b - 2a b)cos(x) + (384a b - 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (128a b + 22a b)cos(x) + (- 512a b + 148a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 480a b + 248a b)cos(x) + (- 64a b + 164a b)cos(x) + 32a b +--R + +--R 4 +--R 36a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 4 3 2 3 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R cos(2x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (128a b - 16a b )cos(x) + (256a b - 48a b )cos(x) +--R + +--R 3 2 5 4 3 2 4 +--R 48a b cos(x) + (- 256a b + 240a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 3 2 +--R (- 128a b + 128a b )cos(x) - 160a b cos(x) - 160a b cos(x) +--R + +--R 3 2 +--R - 32a b +--R * +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R cos(2x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 96a b - 108a b)cos(x) + (192a b - 92a b)cos(x) +--R + +--R 2 3 4 4 4 3 2 3 4 2 +--R (192a b + 32a b)cos(x) + 120a b cos(x) + (- 32a b + 84a b)cos(x) +--R + +--R 4 +--R 20a b cos(x) +--R * +--R tan(x) +--R + +--R 4 2 4 4 6 +--R (a b cos(x) + 4a b cos(x) + 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (6a b cos(x) + 12a b cos(x) - 12a b cos(x) - 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + (- 56a b + 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 92a b + 56a b)cos(x) + (- 24a b + 60a b)cos(x) + 16a b +--R + +--R 4 +--R 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (32a b + 26a b )cos(x) + (160a b + 132a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b + 214a b )cos(x) + (160a b + 100a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (32a b - 32a b )cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (64b + 24a b - a b)cos(x) + (128b + 8a b - 4a b)cos(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 192a b + 6a b)cos(x) + (- 128b - 288a b + 46a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 4 +--R (- 64b - 88a b + 66a b)cos(x) + (24a b + 30a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 4 3 2 6 +--R - 16a b cos(x) + (- 64a b - 72a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b - 116a b )cos(x) + (64a b - 132a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (128a b - 192a b )cos(x) - 184a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 32a b - 4a b)cos(x) + (- 96a b - 24a b)cos(x) +--R + +--R 2 3 4 6 4 5 2 3 4 4 +--R (- 80a b - 58a b)cos(x) - 70a b cos(x) + (32a b - 44a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (64a b - 20a b)cos(x) + (80a b - 18a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 4 3 4 2 4 4 3 +--R (2a b cos(x) + 8a b cos(x) + 8a b cos(x))cos(2x) + 6a b cos(x) +--R + +--R 4 2 4 4 +--R 12a b cos(x) - 12a b cos(x) - 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R 4a b cos(x) - 8a b cos(x) + (- 52a b + a )cos(x) +--R + +--R 3 2 5 5 +--R (- 40a b + 4a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 4a b + 4a )cos(x) + (- 56a b + 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (- 92a b + 56a )cos(x) + (- 24a b + 60a )cos(x) + 16a b + 24a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 32a b + 10a b)cos(x) + (- 160a b + 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 192a b + 118a b)cos(x) + (- 32a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b + 8a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b + 26a b)cos(x) + (160a b + 132a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b + 214a b)cos(x) + (160a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 32a b)cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 64a b + 40a b )cos(x) + (- 128a b + 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (256a b + 5a )cos(x) + (128a b + 32a b + 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (64a b - 152a b + 58a )cos(x) + (- 56a b + 52a )cos(x) +--R + +--R 3 2 5 +--R 16a b + 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b + 24a b - a )cos(x) + (128a b + 8a b - 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 192a b + 6a )cos(x) + (- 128a b - 288a b + 46a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b - 88a b + 66a )cos(x) + (24a b + 30a )cos(x) + a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b + 140a b)cos(x) + (- 192a b + 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (- 192a b + 256a b)cos(x) + 104a b cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 20a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 4 7 2 3 4 6 +--R - 16a b cos(x) + (- 64a b - 72a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 116a b)cos(x) + (64a b - 132a b)cos(x) +--R + +--R 2 3 4 3 4 2 2 3 4 +--R (128a b - 192a b)cos(x) - 184a b cos(x) + (- 32a b - 60a b)cos(x) +--R + +--R 4 +--R 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (64a b + 60a )cos(x) + (- 64a b + 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (- 96a b + 60a )cos(x) + (- 32a b + 24a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 6 5 5 3 2 5 4 +--R (- 80a b - 58a )cos(x) - 70a cos(x) + (32a b - 44a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 3 2 5 +--R (64a b - 20a )cos(x) + (80a b - 18a )cos(x) + (32a b - 14a )cos(x) +--R + +--R 5 +--R - 4a +--R / +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (128a b - 304a b + 116a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 112a b + 104a b)cos(x) + 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) +--R + +--R 3 3 5 5 +--R (64a b - 40a b)cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 3 3 3 2 3 3 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (- 160a b + 16a b )cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 6 6 2 4 5 +--R (- 256b + 160a b )cos(x) + (- 512b + 736a b )cos(x) +--R + +--R 2 4 4 2 4 +--R (1024a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (512b + 128a b + 112a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (256b - 608a b + 232a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 224a b + 208a b )cos(x) + 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (256a b + 240a b )cos(x) + (- 256a b + 320a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 4 2 +--R (- 384a b + 240a b )cos(x) + (- 128a b + 96a b )cos(x) + 16a b +--R * +--R sin(2x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 160a b + 16a b)cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 256a b + 160a b )cos(x) + (- 512a b + 736a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (1024a b + 20a b)cos(x) + (512a b + 128a b + 112a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (256a b - 608a b + 232a b)cos(x) + (- 224a b + 208a b)cos(x) +--R + +--R 3 3 5 +--R 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (256a b + 240a b)cos(x) + (- 256a b + 320a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 384a b + 240a b)cos(x) + (- 128a b + 96a b)cos(x) + 16a b +--R * +--R tan(x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (128a b - 304a b + 116a b)cos(x) + (- 112a b + 104a b)cos(x) +--R + +--R 3 3 5 +--R 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 3 3 5 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) + (64a b - 40a b)cos(x) +--R + +--R 5 +--R - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R Type: Expression Integer +--E 17 + +--S 18 of 526 +t0803:= cos(x)^2/(a+b*sin(2*x)) +--R +--R +--R 2 +--R cos(x) +--R (18) ------------- +--R b sin(2x) + a +--R Type: Expression Integer +--E 18 + +--S 19 of 526 +r0803:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)+1/4*log(a+b*sin(2*x))/b +--R +--R +--R +---------+ +--R | 2 2 a tan(x) + b +--R \|- b + a log(b sin(2x) + a) + 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (19) ------------------------------------------------------ +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression Integer +--E 19 + +--S 20 of 526 +a0803:= integrate(t0803,x) +--R +--R +--R (20) +--R [ +--R b +--R * +--R log +--R 2 2 2 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a ) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +-------+ +-------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R \|b - a log(---------------------) - 2\|b - a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b - a +--R , +--R +--R +---------+ +---------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R \|- b + a log(---------------------) - 2\|- b + a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 20 + +--S 21 of 526 +m0803a:= a0803.1-r0803 +--R +--R +--R (21) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a )\|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - \|- b + a \|b - a log(b sin(2x) + a) +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R \|- b + a \|b - a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +-------+ +-------+ +--R | 2 2 | 2 2 2 | 2 2 a tan(x) + b +--R - 2\|- b + a \|b - a log(----------) - 2b\|b - a atan(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R 4b\|- b + a \|b - a +--R Type: Expression Integer +--E 21 + +--S 22 of 526 +d0803a:= D(m0803a,x) +--R +--R +--R (22) +--R 2 2 3 3 2 2 +--R - 2a b cos(x)sin(x) - 2a b cos(x) sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 2a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 4 3 3 2 3 3 +--R 2a b cos(x) + (2a b - 2a b)cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 4 2 2 +--R (- 4a b cos(x) cos(2x) - 2a cos(x) )sin(x) +--R + +--R 3 3 3 3 +--R ((4a b - 4a b)cos(x) - 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 2a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 4 4 +--R ((2a b - 2a )cos(x) - 2a b + a )cos(2x) + 2a cos(x) +--R + +--R 2 2 4 2 2 2 4 +--R (2a b - 2a )cos(x) - 2a b + a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 4 2 2 2 2 +--R - 4a b cos(x)sin(x) + (8b - 4a b )cos(x) sin(x) +--R + +--R 3 3 3 2 2 4 +--R (4a b cos(x) + 4a b cos(x))sin(x) + 4a b cos(x) +--R * +--R sin(2x) +--R + +--R 2 2 3 +--R - 4a b cos(x)sin(x) +--R + +--R 3 2 3 3 2 2 +--R (- 8a b cos(x) cos(2x) + (8a b - 4a b)cos(x) )sin(x) +--R + +--R 4 2 2 3 4 2 2 3 +--R ((8b - 8a b )cos(x) - 8b cos(x))cos(2x) + 4a b cos(x) +--R + +--R 2 2 +--R 4a b cos(x) +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 3 4 +--R ((4a b - 4a b)cos(x) - 4a b + 2a b)cos(2x) + 4a b cos(x) +--R * +--R tan(x) +--R + +--R 2 2 3 3 2 2 +--R - 2a b cos(x)sin(x) - 2a b cos(x) sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 2a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 4 3 3 2 3 3 +--R 2a b cos(x) + (2a b - 2a b)cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 2 2 2 4 2 2 +--R - 2a b cos(x)sin(x) + (- 4a b cos(x) cos(2x) - 2a cos(x) )sin(x) +--R + +--R 3 3 3 3 +--R ((4a b - 4a b)cos(x) - 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 2a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 4 4 +--R ((2a b - 2a )cos(x) - 2a b + a )cos(2x) + 2a cos(x) +--R + +--R 2 2 4 2 2 2 4 +--R (2a b - 2a )cos(x) - 2a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 4 3 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 2a b - 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 2 3 4 2 2 +--R (- 2a b + 2a )cos(x)sin(x) + (- 4a b + 4a b)cos(x) cos(2x)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((4a b - 4a b )cos(x) + (- 4a b + 2a b + 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 2a b - 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)cos(2x) + (2a b - 2a b)cos(x) +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 3 5 2 3 2 2 +--R (- 4a b + 4a b )cos(x)sin(x) + (8b - 8a b )cos(x) sin(x) +--R + +--R 4 3 2 3 4 3 2 +--R ((4a b - 4a b )cos(x) + (4a b - 4a b )cos(x))sin(x) +--R * +--R sin(2x) +--R + +--R 2 3 4 3 +--R (- 4a b + 4a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 2 +--R ((- 8a b + 8a b )cos(x) cos(2x) + (8a b - 8a b )cos(x) )sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R ((8b - 8a b )cos(x) + (- 8b + 4a b + 4a b)cos(x))cos(2x) +--R + +--R 2 3 4 3 2 3 4 +--R (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R ((4a b - 4a b )cos(x) - 4a b + 4a b )cos(2x) +--R * +--R tan(x) +--R + +--R 2 3 4 3 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 2a b - 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 2 3 4 2 2 +--R (- 2a b + 2a )cos(x)sin(x) + (- 4a b + 4a b)cos(x) cos(2x)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((4a b - 4a b )cos(x) + (- 4a b + 2a b + 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 2a b - 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)cos(2x) + (2a b - 2a b)cos(x) +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R / +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 5 2 3 3 5 +--R ((- 16b + 16a b )cos(x) + 16b cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 4a b +--R * +--R sin(2x) +--R + +--R 2 3 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 16a b + 16a b )cos(x) + 16a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 8a b + 8a b)cos(x) + 8a b - 4a b +--R * +--R tan(x) +--R + +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 2 3 4 3 2 3 +--R 8a b cos(x) sin(x) + ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R * +--R 2 +--R tan(x) +--R + +--R 5 3 3 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 6 2 4 3 6 2 4 4 2 +--R ((- 16b + 16a b )cos(x) + (16b - 8a b - 8a b )cos(x))sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R sin(2x) +--R + +--R 2 4 4 2 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 16a b + 16a b )cos(x) + (16a b - 8a b - 8a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R tan(x) +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R Type: Expression Integer +--E 22 + +--S 23 of 526 +m0803b:= a0803.2-r0803 +--R +--R +--R (23) +--R +---------+ +---------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R - \|- b + a log(b sin(2x) + a) + \|- b + a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 +--R - 2\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R a tan(x) + b +--R - 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression Integer +--E 23 + +--S 24 of 526 +d0803b:= D(m0803b,x) +--R +--R +--R (24) +--R 4 2 4 4 6 +--R (- a b cos(x) - 4a b cos(x) - 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (2a b cos(x) + 20a b cos(x) + 40a b cos(x) + 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (28a b - 4a b)cos(x) + (104a b - 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (100a b - 52a b)cos(x) + (8a b - 44a b)cos(x) - 16a b +--R + +--R 4 +--R - 10a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (96a b - 10a b )cos(x) + (288a b - 60a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b - 110a b )cos(x) + (32a b - 52a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b + 24a b )cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 +--R (64b - 72a b + a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (128b - 344a b + 4a b)cos(x) + (- 512a b + 2a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 128b - 192a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (- 64b + 136a b - 20a b)cos(x) + (88a b - 18a b)cos(x) +--R + +--R 4 +--R - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 64a b + 24a b )cos(x) + (- 192a b + 112a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b + 156a b )cos(x) + (192a b - 20a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (192a b - 248a b )cos(x) - 224a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (32a b + 4a b)cos(x) + (96a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (48a b + 62a b)cos(x) + (- 128a b + 90a b)cos(x) +--R + +--R 2 3 4 4 4 3 +--R (- 160a b + 76a b)cos(x) + 28a b cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (80a b - 10a b)cos(x) + (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (- a cos(x) - 4a cos(x) - 4a )sin(x) +--R + +--R 4 3 4 2 4 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b cos(x))cos(2x) +--R + +--R 4 3 4 2 4 4 +--R 2a b cos(x) + 20a b cos(x) + 40a b cos(x) + 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R - 4a b cos(x) + 8a b cos(x) + (52a b - a )cos(x) +--R + +--R 3 2 5 5 +--R (40a b - 4a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (28a b - 4a )cos(x) + (104a b - 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (100a b - 52a )cos(x) + (8a b - 44a )cos(x) - 16a b - 10a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b - 10a b)cos(x) + (160a b - 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (192a b - 118a b)cos(x) + (32a b - 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 8a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b - 10a b)cos(x) + (288a b - 60a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b - 110a b)cos(x) + (32a b - 52a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 24a b)cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (64a b - 40a b )cos(x) + (128a b - 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 256a b - 5a )cos(x) + (- 128a b - 32a b - 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (- 64a b + 152a b - 58a )cos(x) + (56a b - 52a )cos(x) +--R + +--R 3 2 5 +--R - 16a b - 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b - 72a b + a )cos(x) + (128a b - 344a b + 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 512a b + 2a )cos(x) + (- 128a b - 192a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b + 136a b - 20a )cos(x) + (88a b - 18a )cos(x) - 7a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 140a b)cos(x) + (192a b - 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (192a b - 256a b)cos(x) - 104a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 20a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b + 24a b)cos(x) + (- 192a b + 112a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b + 156a b)cos(x) + (192a b - 20a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (192a b - 248a b)cos(x) - 224a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 60a b)cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 64a b - 60a )cos(x) + (64a b - 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (96a b - 60a )cos(x) + (32a b - 24a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (48a b + 62a )cos(x) + (- 128a b + 90a )cos(x) +--R + +--R 3 2 5 4 5 3 3 2 5 2 +--R (- 160a b + 76a )cos(x) + 28a cos(x) + (80a b - 10a )cos(x) +--R + +--R 3 2 5 5 +--R (32a b - 14a )cos(x) - 4a +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 2 3 2 6 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b )sin(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 5 +--R (8a b cos(x) + 56a b cos(x) + 96a b cos(x) + 40a b )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (64a b - 8a b )cos(x) + (192a b - 48a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (96a b - 102a b )cos(x) + (- 64a b - 80a b )cos(x) +--R + +--R 4 3 2 +--R - 32a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 5 5 2 3 4 +--R 128b cos(x) + (256b - 8a b )cos(x) +--R + +--R 5 2 3 3 2 3 2 2 3 2 3 +--R (128b + 16a b )cos(x) + 96a b cos(x) + 64a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 64a b + 2a b )cos(x) + (- 320a b + 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 512a b + 14a b )cos(x) + (- 320a b + 36a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- 32a b + 76a b )cos(x) + (64a b + 68a b )cos(x) + 32a b +--R + +--R 3 2 +--R 20a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 7 2 3 6 2 3 5 +--R 64a b cos(x) + 320a b cos(x) + 592a b cos(x) +--R + +--R 2 3 4 2 3 3 2 3 2 +--R 464a b cos(x) + 16a b cos(x) - 240a b cos(x) +--R + +--R 2 3 2 3 +--R - 160a b cos(x) - 32a b +--R * +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (64a b + 8a b )cos(x) + (192a b + 48a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (160a b + 132a b )cos(x) + (- 64a b + 228a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 192a b + 272a b )cos(x) + (- 128a b + 216a b )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 32a b + 100a b )cos(x) + 20a b cos(x) +--R * +--R sin(2x) +--R + +--R 4 2 4 4 6 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 4a b cos(x) - 16a b cos(x) - 16a b cos(x))cos(2x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R 8a b cos(x) + 56a b cos(x) + 96a b cos(x) + 40a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R - 8a b cos(x) + 16a b cos(x) + (104a b - 2a b)cos(x) +--R + +--R 2 3 4 4 +--R (80a b - 8a b)cos(x) - 8a b +--R * +--R cos(2x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (64a b - 8a b)cos(x) + (192a b - 48a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (96a b - 102a b)cos(x) + (- 64a b - 80a b)cos(x) - 32a b +--R + +--R 4 +--R - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (64a b - 20a b )cos(x) + (320a b - 112a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (384a b - 236a b )cos(x) + (64a b - 200a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 64a b - 16a b )cos(x) + 40a b +--R * +--R cos(2x) +--R + +--R 4 5 4 3 2 4 +--R 128a b cos(x) + (256a b - 8a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 3 2 3 2 +--R (128a b + 16a b )cos(x) + 96a b cos(x) + 64a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 6 5 2 3 5 +--R (128b - 80a b )cos(x) + (256b - 368a b )cos(x) +--R + +--R 2 3 4 4 +--R (- 512a b - 10a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 256b - 64a b - 56a b)cos(x) +--R + +--R 5 2 3 4 2 +--R (- 128b + 304a b - 116a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (112a b - 104a b)cos(x) - 32a b - 34a b +--R * +--R cos(2x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 64a b + 2a b)cos(x) + (- 320a b + 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 512a b + 14a b)cos(x) + (- 320a b + 36a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 32a b + 76a b)cos(x) + (64a b + 68a b)cos(x) + 32a b + 20a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 128a b - 16a b )cos(x) + (- 384a b - 96a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 192a b - 280a b )cos(x) + (384a b - 504a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (384a b - 512a b )cos(x) - 208a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 64a b + 40a b )cos(x) + 40a b +--R * +--R cos(2x) +--R + +--R 3 2 7 3 2 6 3 2 5 3 2 4 +--R 64a b cos(x) + 320a b cos(x) + 592a b cos(x) + 464a b cos(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R 16a b cos(x) - 240a b cos(x) - 160a b cos(x) - 32a b +--R * +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 128a b - 120a b)cos(x) + (128a b - 160a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (192a b - 120a b)cos(x) + (64a b - 48a b)cos(x) - 8a b +--R * +--R cos(2x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (160a b + 132a b)cos(x) + (- 64a b + 228a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 192a b + 272a b)cos(x) + (- 128a b + 216a b)cos(x) +--R + +--R 2 3 4 2 4 +--R (- 32a b + 100a b)cos(x) + 20a b cos(x) +--R * +--R tan(x) +--R + +--R 4 2 4 4 6 +--R (- a b cos(x) - 4a b cos(x) - 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (2a b cos(x) + 20a b cos(x) + 40a b cos(x) + 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (28a b - 4a b)cos(x) + (104a b - 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (100a b - 52a b)cos(x) + (8a b - 44a b)cos(x) - 16a b - 10a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (96a b - 10a b )cos(x) + (288a b - 60a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b - 110a b )cos(x) + (32a b - 52a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b + 24a b )cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (64b - 72a b + a b)cos(x) + (128b - 344a b + 4a b)cos(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 512a b + 2a b)cos(x) + (- 128b - 192a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 4 +--R (- 64b + 136a b - 20a b)cos(x) + (88a b - 18a b)cos(x) - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 64a b + 24a b )cos(x) + (- 192a b + 112a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b + 156a b )cos(x) + (192a b - 20a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (192a b - 248a b )cos(x) - 224a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (32a b + 4a b)cos(x) + (96a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (48a b + 62a b)cos(x) + (- 128a b + 90a b)cos(x) +--R + +--R 2 3 4 4 4 3 2 3 4 2 +--R (- 160a b + 76a b)cos(x) + 28a b cos(x) + (80a b - 10a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (- a cos(x) - 4a cos(x) - 4a )sin(x) +--R + +--R 4 3 4 2 4 4 3 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b cos(x))cos(2x) + 2a b cos(x) +--R + +--R 4 2 4 4 +--R 20a b cos(x) + 40a b cos(x) + 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R - 4a b cos(x) + 8a b cos(x) + (52a b - a )cos(x) +--R + +--R 3 2 5 5 +--R (40a b - 4a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (28a b - 4a )cos(x) + (104a b - 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (100a b - 52a )cos(x) + (8a b - 44a )cos(x) - 16a b - 10a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b - 10a b)cos(x) + (160a b - 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (192a b - 118a b)cos(x) + (32a b - 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 8a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b - 10a b)cos(x) + (288a b - 60a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b - 110a b)cos(x) + (32a b - 52a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 24a b)cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (64a b - 40a b )cos(x) + (128a b - 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 256a b - 5a )cos(x) + (- 128a b - 32a b - 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (- 64a b + 152a b - 58a )cos(x) + (56a b - 52a )cos(x) +--R + +--R 3 2 5 +--R - 16a b - 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b - 72a b + a )cos(x) + (128a b - 344a b + 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 512a b + 2a )cos(x) + (- 128a b - 192a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b + 136a b - 20a )cos(x) + (88a b - 18a )cos(x) - 7a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 140a b)cos(x) + (192a b - 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (192a b - 256a b)cos(x) - 104a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 20a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b + 24a b)cos(x) + (- 192a b + 112a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b + 156a b)cos(x) + (192a b - 20a b)cos(x) +--R + +--R 2 3 4 3 4 2 2 3 4 +--R (192a b - 248a b)cos(x) - 224a b cos(x) + (- 32a b - 60a b)cos(x) +--R + +--R 4 +--R 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 64a b - 60a )cos(x) + (64a b - 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (96a b - 60a )cos(x) + (32a b - 24a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) + (48a b + 62a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 5 3 +--R (- 128a b + 90a )cos(x) + (- 160a b + 76a )cos(x) + 28a cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (80a b - 10a )cos(x) + (32a b - 14a )cos(x) - 4a +--R / +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (128a b - 304a b + 116a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 112a b + 104a b)cos(x) + 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) +--R + +--R 3 3 5 5 +--R (64a b - 40a b)cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 3 3 3 2 3 3 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (- 160a b + 16a b )cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 6 6 2 4 5 +--R (- 256b + 160a b )cos(x) + (- 512b + 736a b )cos(x) +--R + +--R 2 4 4 2 4 +--R (1024a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (512b + 128a b + 112a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (256b - 608a b + 232a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 224a b + 208a b )cos(x) + 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (256a b + 240a b )cos(x) + (- 256a b + 320a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 4 2 +--R (- 384a b + 240a b )cos(x) + (- 128a b + 96a b )cos(x) + 16a b +--R * +--R sin(2x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 160a b + 16a b)cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 256a b + 160a b )cos(x) + (- 512a b + 736a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (1024a b + 20a b)cos(x) + (512a b + 128a b + 112a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (256a b - 608a b + 232a b)cos(x) + (- 224a b + 208a b)cos(x) +--R + +--R 3 3 5 +--R 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (256a b + 240a b)cos(x) + (- 256a b + 320a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 384a b + 240a b)cos(x) + (- 128a b + 96a b)cos(x) + 16a b +--R * +--R tan(x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (128a b - 304a b + 116a b)cos(x) + (- 112a b + 104a b)cos(x) +--R + +--R 3 3 5 +--R 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 3 3 5 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) + (64a b - 40a b)cos(x) +--R + +--R 5 +--R - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R Type: Expression Integer +--E 24 + +--S 25 of 526 +t0804:= csc(2*x)*sin(x) +--R +--R +--R (25) csc(2x)sin(x) +--R Type: Expression Integer +--E 25 + +--S 26 of 526 +r0804:= 1/2*atanh(sin(x)) +--R +--R +--R atanh(sin(x)) +--R (26) ------------- +--R 2 +--R Type: Expression Integer +--E 26 + +--S 27 of 526 +a0804:= integrate(t0804,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (27) --------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 27 + +--S 28 of 526 +m0804:= a0804-r0804 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (28) ------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 28 + +--S 29 of 526 +d0804:= D(m0804,x) +--R +--R +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (29) --------------------------------------------------------------------- +--R 4 2 2 2 +--R 2sin(x) + (- 2cos(x) - 4cos(x) - 4)sin(x) + 2cos(x) + 4cos(x) + 2 +--R Type: Expression Integer +--E 29 + +--S 30 of 526 +t0805:= cos(4*x)*sec(2*x) +--R +--R +--R (30) cos(4x)sec(2x) +--R Type: Expression Integer +--E 30 + +--S 31 of 526 +r0805:= -1/2*atanh(sin(2*x))+sin(2*x) +--R +--R +--R - atanh(sin(2x)) + 2sin(2x) +--R (31) --------------------------- +--R 2 +--R Type: Expression Integer +--E 31 + +--S 32 of 526 +a0805:= integrate(t0805,x) +--R +--R +--R sin(2x) + cos(2x) + 1 sin(2x) - cos(2x) - 1 +--R - log(---------------------) + log(---------------------) + 2sin(2x) +--R cos(2x) + 1 cos(2x) + 1 +--R (32) -------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 32 + +--S 33 of 526 +m0805:= a0805-r0805 +--R +--R +--R (33) +--R sin(2x) + cos(2x) + 1 sin(2x) - cos(2x) - 1 +--R - log(---------------------) + log(---------------------) + atanh(sin(2x)) +--R cos(2x) + 1 cos(2x) + 1 +--R -------------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 33 + +--S 34 of 526 +d0805:= D(m0805,x) +--R +--R +--R (34) +--R 4 2 2 3 +--R 2sin(2x) + (2cos(2x) + cos(2x) - 2)sin(2x) + cos(2x) - cos(2x) +--R ------------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(2x) + (- cos(2x) - 2cos(2x) - 2)sin(2x) + cos(2x) + 2cos(2x) + 1 +--R Type: Expression Integer +--E 34 + +--S 35 of 526 +t0806:= x*cos(2*x)*sec(x)^3 +--R +--R +--R 3 +--R (35) x cos(2x)sec(x) +--R Type: Expression Integer +--E 35 + +--S 36 of 526 +r0806:= -3*%i*x*atan(exp(1)^(%i*x))+3/2*%i*polylog(2,-%i*exp(1)^(%i*x))-3/2*%i*polylog(2,%i*exp(1)^(%i*x))+1/2*sec(x)-1/2*x*sec(x)*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 36 + +--S 37 of 526 +a0806:= integrate(t0806,x) +--R +--R +--R x +--R ++ 3 +--R (36) | %J cos(2%J)sec(%J) d%J +--R ++ +--R Type: Union(Expression Integer,...) +--E 37 + +--S 38 of 526 +m0806:= a0806-r0806 +--R +--R +--R x +--R ++ 3 +--R (37) | %J cos(2%J)sec(%J) d%J - r0806 +--R ++ +--R Type: Expression Integer +--E 38 + +--S 39 of 526 +d0806:= D(m0806,x) +--R +--R +--R 3 +--R (38) x cos(2x)sec(x) +--R Type: Expression Integer +--E 39 + +--S 40 of 526 +t0807:= sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R \|sin(b x + a) +--R (39) --------------- +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression Integer +--E 40 + +--S 41 of 526 +r0807:= -1/2*atan(1-2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2))*2^(1/2)/b+1/2*atan(1+2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2))*2^(1/2)/b+1/4*log(1-2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2)+tan(a+b*x))*2^(1/2)/b-1/4*log(1+2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2)+tan(a+b*x))*2^(1/2)/b +--R +--R +--R (40) +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R - \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ - \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R \|2 log(---------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) - \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 41 + +--S 42 of 526 +a0807:= integrate(t0807,x) +--R +--R +--R x +-------------+ +--R ++ \|sin(%J b + a) +--R (41) | ---------------- d%J +--R ++ +-------------+ +--R \|cos(%J b + a) +--R Type: Union(Expression Integer,...) +--E 42 + +--S 43 of 526 +m0807:= a0807-r0807 +--R +--R +--R (42) +--R x +-------------+ +--R ++ \|sin(%J b + a) +--R 4b | ---------------- d%J +--R ++ +-------------+ +--R \|cos(%J b + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ - \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R - \|2 log(---------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) - \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 43 + +--S 44 of 526 +d0807:= D(m0807,x) +--R +--R +--R (43) +--R 2 2 +--R (- cos(b x + a)sin(b x + a) - cos(b x + a) )tan(b x + a) +--R + +--R 2 2 +--R (sin(b x + a) + 2cos(b x + a)sin(b x + a) - cos(b x + a) )tan(b x + a) +--R + +--R 2 +--R - sin(b x + a) + cos(b x + a)sin(b x + a) +--R * +--R +------------+ +--R \|sin(b x + a) +--R / +--R 2 +--R 2cos(b x + a)sin(b x + a)tan(b x + a) +--R + +--R 2 +--R 4cos(b x + a)sin(b x + a)tan(b x + a) - 4sin(b x + a) +--R + +--R 2cos(b x + a)sin(b x + a) +--R * +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression Integer +--E 44 + +--S 45 of 526 +t0808:= cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R \|cos(b x + a) +--R (44) --------------- +--R +------------+ +--R \|sin(b x + a) +--R Type: Expression Integer +--E 45 + +--S 46 of 526 +r0808:= -1/2*atan(-1+2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b-1/2*atan(1+2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b-1/4*log(1+cot(a+b*x)-2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b+1/4*log(1+cot(a+b*x)+2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b +--R +--R +--R (45) +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) + \|2 \|cos(b x + a) +--R \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) - \|2 \|cos(b x + a) +--R - \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) + \|2 \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) - \|2 \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 46 + +--S 47 of 526 +a0808:= integrate(t0808,x) +--R +--R +--R x +-------------+ +--R ++ \|cos(%J b + a) +--R (46) | ---------------- d%J +--R ++ +-------------+ +--R \|sin(%J b + a) +--R Type: Union(Expression Integer,...) +--E 47 + +--S 48 of 526 +m0808:= a0808-r0808 +--R +--R +--R (47) +--R x +-------------+ +--R ++ \|cos(%J b + a) +--R 4b | ---------------- d%J +--R ++ +-------------+ +--R \|sin(%J b + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) + \|2 \|cos(b x + a) +--R - \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) - \|2 \|cos(b x + a) +--R \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) + \|2 \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) - \|2 \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 48 + +--S 49 of 526 +d0808:= D(m0808,x) +--R +--R +--R (48) +--R 2 2 +--R (- cot(b x + a) - cot(b x + a))sin(b x + a) +--R + +--R 2 +--R - cos(b x + a)cot(b x + a) + 2cos(b x + a)cot(b x + a) +--R + +--R cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 2 2 +--R cos(b x + a) cot(b x + a) - cos(b x + a) +--R * +--R +------------+ +--R \|cos(b x + a) +--R / +--R 2 +--R 2cos(b x + a)cot(b x + a) + 4cos(b x + a)cot(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) +--R * +--R +------------+ +--R \|sin(b x + a) +--R Type: Expression Integer +--E 49 + +--S 50 of 526 +t0809:= sin(a+b*x)^(1/3)/cos(a+b*x)^(1/3) +--R +--R +--R 3+------------+ +--R \|sin(b x + a) +--R (49) --------------- +--R 3+------------+ +--R \|cos(b x + a) +--R Type: Expression Integer +--E 50 + +--S 51 of 526 +r0809:= -1/2*3^(1/2)*atan(1/3*(1-2*sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3))*3^(1/2))/b-1/2*log(1+sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3))/b+1/4*log(1-sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3)+sin(a+b*x)^(4/3)/cos(a+b*x)^(4/3))/b +--R +--R +--R (50) +--R 3+------------+2 3+------------+2 +--R \|sin(b x + a) + \|cos(b x + a) +--R - 2log(-----------------------------------) +--R 3+------------+2 +--R \|cos(b x + a) +--R + +--R log +--R 3+------------+2 +--R - cos(b x + a)\|sin(b x + a) +--R + +--R 3+------------+3+------------+ +--R sin(b x + a)\|cos(b x + a) \|sin(b x + a) +--R + +--R 3+------------+2 +--R cos(b x + a)\|cos(b x + a) +--R / +--R 3+------------+2 +--R cos(b x + a)\|cos(b x + a) +--R + +--R +-+3+------------+2 +-+3+------------+2 +--R +-+ 2\|3 \|sin(b x + a) - \|3 \|cos(b x + a) +--R 2\|3 atan(--------------------------------------------) +--R 3+------------+2 +--R 3\|cos(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 51 + +--S 52 of 526 +--a0809:= integrate(t0809,x) +--E 52 + +--S 53 of 526 +--m0809:= a0809-r0809 +--E 53 + +--S 54 of 526 +--d0809:= D(m0809,x) +--E 54 + +--S 55 of 526 +t0810:= cos(a+b*x)^(1/3)/sin(a+b*x)^(1/3) +--R +--R +--R 3+------------+ +--R \|cos(b x + a) +--R (51) --------------- +--R 3+------------+ +--R \|sin(b x + a) +--R Type: Expression Integer +--E 55 + +--S 56 of 526 +r0810:= 1/2*3^(1/2)*atan(1/3*(1-2*cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))*3^(1/2))/b-1/4*log(1+cos(a+b*x)^(4/3)/sin(a+b*x)^(4/3)-cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))/b+1/2*log(1+cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))/b +--R +--R +--R (52) +--R - +--R log +--R 3+------------+2 +--R sin(b x + a)\|sin(b x + a) +--R + +--R 3+------------+3+------------+ +--R cos(b x + a)\|cos(b x + a) \|sin(b x + a) +--R + +--R 3+------------+2 +--R - sin(b x + a)\|cos(b x + a) +--R / +--R 3+------------+2 +--R sin(b x + a)\|sin(b x + a) +--R + +--R 3+------------+2 3+------------+2 +--R \|sin(b x + a) + \|cos(b x + a) +--R 2log(-----------------------------------) +--R 3+------------+2 +--R \|sin(b x + a) +--R + +--R +-+3+------------+2 +-+3+------------+2 +--R +-+ \|3 \|sin(b x + a) - 2\|3 \|cos(b x + a) +--R 2\|3 atan(--------------------------------------------) +--R 3+------------+2 +--R 3\|sin(b x + a) +--R / +--R 4b +--R Type: Expression Integer +--E 56 + +--S 57 of 526 +--a0810:= integrate(t0810,x) +--E 57 + +--S 58 of 526 +--m0810:= a0810-r0810 +--E 58 + +--S 59 of 526 +--d0810:= D(m0810,x) +--E 59 + +--S 60 of 526 +t0811:= x*sin(x)*sec(x)^(1/2) +--R +--R +--R +------+ +--R (53) x sin(x)\|sec(x) +--R Type: Expression Integer +--E 60 + +--S 61 of 526 +r0811:= -2*x/sec(x)^(1/2)+4*cos(x)^(1/2)*EllipticE(1/2*x,2)*sec(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 PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 61 + +--S 62 of 526 +a0811:= integrate(t0811,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 62 + +--S 63 of 526 +m0811:= a0811-r0811 +--R +--R +--R (54) - r0811 + a0811 +--R Type: Polynomial Integer +--E 63 + +--S 64 of 526 +d0811:= D(m0811,x) +--R +--R +--R (55) 0 +--R Type: Polynomial Integer +--E 64 + +--S 65 of 526 +t0812:= x*cos(x)*csc(x)^(1/2) +--R +--R +--R +------+ +--R (56) x cos(x)\|csc(x) +--R Type: Expression Integer +--E 65 + +--S 66 of 526 +r0812:= 2*x/csc(x)^(1/2)-4*csc(x)^(1/2)*EllipticE(-1/4*%pi+1/2*x,2)*sin(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 66 + +--S 67 of 526 +a0812:= integrate(t0812,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 67 + +--S 68 of 526 +m0812:= a0812-r0812 +--R +--R +--R (57) - r0812 + a0812 +--R Type: Polynomial Integer +--E 68 + +--S 69 of 526 +d0812:= D(m0812,x) +--R +--R +--R (58) 0 +--R Type: Polynomial Integer +--E 69 + +--S 70 of 526 +t0813:= cos(x)/(cos(x)+1)^(1/2) +--R +--R +--R cos(x) +--R (59) ------------- +--R +----------+ +--R \|cos(x) + 1 +--R Type: Expression Integer +--E 70 + +--S 71 of 526 +r0813:= -2*(atanh(sin(1/2*x))*cos(1/2*x)-sin(x))/(cos(x)+1)^(1/2) +--R +--R +--R x x +--R - 2cos(-)atanh(sin(-)) + 2sin(x) +--R 2 2 +--R (60) -------------------------------- +--R +----------+ +--R \|cos(x) + 1 +--R Type: Expression Integer +--E 71 + +--S 72 of 526 +a0813:= integrate(t0813,x) +--R +--R +--R (61) +--R +-+ +-+ +--R (\|2 cos(x) + \|2 ) +--R * +--R +-+ +----------+ 2 +--R - 2\|2 sin(x)\|cos(x) + 1 - cos(x) + 2cos(x) + 3 +--R log(--------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +----------+ +--R 4sin(x)\|cos(x) + 1 +--R / +--R 2cos(x) + 2 +--R Type: Union(Expression Integer,...) +--E 72 + +--S 73 of 526 +m0813:= a0813-r0813 +--R +--R +--R (62) +--R +-+ +----------+ 2 +--R +-+ +----------+ - 2\|2 sin(x)\|cos(x) + 1 - cos(x) + 2cos(x) + 3 +--R \|2 \|cos(x) + 1 log(--------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R x x +--R 4cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +----------+ +--R 2\|cos(x) + 1 +--R Type: Expression Integer +--E 73 + +--S 74 of 526 +d0813:= D(m0813,x) +--R +--R +--R (63) +--R +-+ x x 2 +-+ x 2 +--R (2\|2 cos(-)sin(-) - 2\|2 cos(-))sin(x) +--R 2 2 2 +--R + +--R +-+ +-+ x 3 +-+ +-+ x +--R ((- 2\|2 cos(x) - 2\|2 )sin(-) + (2\|2 cos(x) + 2\|2 )sin(-)) +--R 2 2 +--R * +--R sin(x) +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R +-+ +-+ x 2 +-+ x 2 +-+ +--R (- 2\|2 cos(x) - 2\|2 )sin(-) + (- 2\|2 cos(-) + 2\|2 )cos(x) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R - 2\|2 cos(-) + 2\|2 +--R 2 +--R * +--R sin(x) +--R * +--R +----------+ +--R \|cos(x) + 1 +--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 \|cos(x) + 1 +--R + +--R +-+ 2 +-+ +-+ x 2 +-+ 2 +--R (2\|2 cos(x) + 4\|2 cos(x) + 2\|2 )sin(-) - 2\|2 cos(x) +--R 2 +--R + +--R +-+ +-+ +--R - 4\|2 cos(x) - 2\|2 +--R * +--R sin(x) +--R Type: Expression Integer +--E 74 + +--S 75 of 526 +t0814:= cos(x)/(1-cos(2*x))^(1/2) +--R +--R +--R cos(x) +--R (64) ---------------- +--R +-------------+ +--R \|- cos(2x) + 1 +--R Type: Expression Integer +--E 75 + +--S 76 of 526 +r0814:= 1/2*log(sin(x))*2^(1/2)*cos(sin(x)) +--R +--R +--R +-+ +--R \|2 cos(sin(x))log(sin(x)) +--R (65) -------------------------- +--R 2 +--R Type: Expression Integer +--E 76 + +--S 77 of 526 +a0814:= integrate(t0814,x) +--R +--R +--R +-+ sin(x) +-+ 2 +--R \|2 log(----------) - \|2 log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (66) ----------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 77 + +--S 78 of 526 +m0814:= a0814-r0814 +--R +--R +--R (67) +--R +-+ +-+ sin(x) +-+ 2 +--R - \|2 cos(sin(x))log(sin(x)) + \|2 log(----------) - \|2 log(----------) +--R cos(x) + 1 cos(x) + 1 +--R ------------------------------------------------------------------------ +--R 2 +--R Type: Expression Integer +--E 78 + +--S 79 of 526 +d0814:= D(m0814,x) +--R +--R +--R (68) +--R +-+ +-+ +-+ +--R \|2 cos(x)sin(x)log(sin(x))sin(sin(x)) - \|2 cos(x)cos(sin(x)) + \|2 cos(x) +--R --------------------------------------------------------------------------- +--R 2sin(x) +--R Type: Expression Integer +--E 79 + +--S 80 of 526 +t0815:= tan(x)*(2+3*cos(x))^(1/2) +--R +--R +--R +-----------+ +--R (69) tan(x)\|3cos(x) + 2 +--R Type: Expression Integer +--E 80 + +--S 81 of 526 +r0815:= 2*2^(1/2)*atanh(1/2*(2+3*cos(x))^(1/2)*2^(1/2))-2*(2+3*cos(x))^(1/2) +--R +--R +--R +-+ +-----------+ +--R +-+ \|2 \|3cos(x) + 2 +-----------+ +--R (70) 2\|2 atanh(------------------) - 2\|3cos(x) + 2 +--R 2 +--R Type: Expression Integer +--E 81 + +--S 82 of 526 +a0815:= integrate(t0815,x) +--R +--R +--R (71) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ +-+ +-----------+ 2 +--R (- 12\|2 cos(x) - 16\|2 )\|3cos(x) + 2 + 9cos(x) + 48cos(x) +--R + +--R 32 +--R / +--R 2 +--R cos(x) +--R + +--R +-----------+ +--R - 4\|3cos(x) + 2 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 82 + +--S 83 of 526 +m0815:= a0815-r0815 +--R +--R +--R (72) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ +-+ +-----------+ 2 +--R (- 12\|2 cos(x) - 16\|2 )\|3cos(x) + 2 + 9cos(x) + 48cos(x) +--R + +--R 32 +--R / +--R 2 +--R cos(x) +--R + +--R +-+ +-----------+ +--R +-+ \|2 \|3cos(x) + 2 +--R - 4\|2 atanh(------------------) +--R 2 +--R / +--R 2 +--R Type: Expression Integer +--E 83 + +--S 84 of 526 +d0815:= D(m0815,x) +--R +--R +--R (73) 0 +--R Type: Expression Integer +--E 84 + +--S 85 of 526 +t0816:= cot(x)*(1+sin(x))^(1/2) +--R +--R +--R +----------+ +--R (74) cot(x)\|sin(x) + 1 +--R Type: Expression Integer +--E 85 + +--S 86 of 526 +r0816:= -2*atanh((1+sin(x))^(1/2))+2*(1+sin(x))^(1/2) +--R +--R +--R +----------+ +----------+ +--R (75) - 2atanh(\|sin(x) + 1 ) + 2\|sin(x) + 1 +--R Type: Expression Integer +--E 86 + +--S 87 of 526 +a0816:= integrate(t0816,x) +--R +--R +--R (76) +--R +---------------------+ +--R | 4 +--R (- cos(x) - 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (2sin(x) + 2cos(x) + 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (- 2sin(x) - 2cos(x) - 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4sin(x) + 4cos(x) + 4 +--R / +--R +---------------------+ +--R | 4 +--R (2cos(x) + 2) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 87 + +--S 88 of 526 +m0816:= a0816-r0816 +--R +--R +--R (77) +--R +---------------------+ +--R | 4 +--R (- cos(x) - 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (2sin(x) + 2cos(x) + 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (- 2sin(x) - 2cos(x) - 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +----------+ +--R (4cos(x) + 4) |--------------------- atanh(\|sin(x) + 1 ) +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +----------+ +--R (- 4cos(x) - 4) |--------------------- \|sin(x) + 1 + 4sin(x) + 4cos(x) +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R / +--R +---------------------+ +--R | 4 +--R (2cos(x) + 2) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R Type: Expression Integer +--E 88 + +--S 89 of 526 +d0816:= D(m0816,x) +--R +--R +--R (78) +--R 5 4 2 3 +--R 2sin(x) + (cos(x) + 1)sin(x) + (3cos(x) + cos(x) - 2)sin(x) +--R + +--R 3 2 2 +--R (2cos(x) + 3cos(x) - 1)sin(x) +--R + +--R 4 3 2 +--R (2cos(x) + 4cos(x) + 2cos(x) )sin(x) +--R * +--R +---------------------+2 +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 4 2 3 +--R - 2sin(x) + (2cos(x) - 2)sin(x) + (- 4cos(x) + 2)sin(x) +--R + +--R 2 2 2 +--R (- 8cos(x) - 6cos(x) + 2)sin(x) + (- 4cos(x) - 4cos(x))sin(x) +--R * +--R +----------+ +--R \|sin(x) + 1 +--R + +--R 3 2 3 +--R (- 2cos(x) - 4cos(x) - 2cos(x))sin(x) +--R + +--R 4 3 2 2 +--R (- 2cos(x) - 8cos(x) - 10cos(x) - 4cos(x))sin(x) +--R + +--R 5 4 3 2 +--R (- 2cos(x) - 8cos(x) - 12cos(x) - 8cos(x) - 2cos(x))sin(x) +--R + +--R 5 4 3 2 +--R - 2cos(x) - 6cos(x) - 6cos(x) - 2cos(x) +--R * +--R +---------------------+3 +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 2 3 +--R (2cos(x) + 4cos(x) + 2cos(x))sin(x) +--R + +--R 3 2 2 +--R (6cos(x) + 12cos(x) + 6cos(x))sin(x) +--R + +--R 3 2 3 2 +--R (8cos(x) + 16cos(x) + 8cos(x))sin(x) + 4cos(x) + 8cos(x) + 4cos(x) +--R * +--R +---------------------+ +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R / +--R 2 3 +--R (2cos(x) + 4cos(x) + 2)sin(x) +--R + +--R 3 2 2 +--R (2cos(x) + 6cos(x) + 6cos(x) + 2)sin(x) +--R + +--R 4 3 2 +--R (2cos(x) + 6cos(x) + 6cos(x) + 2cos(x))sin(x) +--R * +--R +---------------------+3 +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 +--R (- 2cos(x) - 4cos(x) - 2)sin(x) +--R + +--R 2 2 2 +--R (- 4cos(x) - 8cos(x) - 4)sin(x) + (- 4cos(x) - 8cos(x) - 4)sin(x) +--R * +--R +---------------------+ +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R +----------+ +--R \|sin(x) + 1 +--R Type: Expression Integer +--E 89 + +--S 90 of 526 +t0817:= cot(x)/(3-cos(x))^(1/2) +--R +--R +--R cot(x) +--R (79) --------------- +--R +------------+ +--R \|- cos(x) + 3 +--R Type: Expression Integer +--E 90 + +--S 91 of 526 +r0817:= -1/2*atanh(1/2*(3-cos(x))^(1/2))-1/2*atanh(1/2*(3-cos(x))^(1/2)*2^(1/2))*2^(1/2) +--R +--R +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|- cos(x) + 3 \|- cos(x) + 3 +--R - \|2 atanh(-------------------) - atanh(---------------) +--R 2 2 +--R (80) --------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 91 + +--S 92 of 526 +a0817:= integrate(t0817,x) +--R +--R +--R (81) +--R log +--R 3 2 +------------+ 2 +--R (16cos(x) - 112cos(x) - 8cos(x) + 56)\|- cos(x) + 3 + cos(x) +--R + +--R - 30cos(x) + 97 +--R / +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 8\|2 cos(x) + 40\|2 cos(x) + 4\|2 cos(x) - 20\|2 ) +--R * +--R +------------+ +--R \|- cos(x) + 3 +--R + +--R 2 +--R cos(x) - 18cos(x) + 49 +--R / +--R 2 +--R cos(x) - 2cos(x) + 1 +--R / +--R 8 +--R Type: Union(Expression Integer,...) +--E 92 + +--S 93 of 526 +m0817:= a0817-r0817 +--R +--R +--R (82) +--R log +--R 3 2 +------------+ 2 +--R (16cos(x) - 112cos(x) - 8cos(x) + 56)\|- cos(x) + 3 + cos(x) +--R + +--R - 30cos(x) + 97 +--R / +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 8\|2 cos(x) + 40\|2 cos(x) + 4\|2 cos(x) - 20\|2 ) +--R * +--R +------------+ +--R \|- cos(x) + 3 +--R + +--R 2 +--R cos(x) - 18cos(x) + 49 +--R / +--R 2 +--R cos(x) - 2cos(x) + 1 +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|- cos(x) + 3 \|- cos(x) + 3 +--R 4\|2 atanh(-------------------) + 4atanh(---------------) +--R 2 2 +--R / +--R 8 +--R Type: Expression Integer +--E 93 + +--S 94 of 526 +d0817:= D(m0817,x) +--R +--R +--R (83) +--R +-+ 6 +-+ 5 +-+ 4 +--R 128\|2 cos(x) + (- 1920\|2 + 6)cos(x) + (9024\|2 - 168)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 12480\|2 + 1036)cos(x) + (- 4544\|2 - 1944)cos(x) +--R + +--R +-+ +--R (6720\|2 + 430)cos(x) +--R * +--R +------------+ +--R sin(x)\|- cos(x) + 3 +--R + +--R +-+ 7 +-+ 6 +--R (24\|2 - 48)cos(x) + (- 264\|2 + 720)cos(x) +--R + +--R +-+ 5 +-+ 4 +--R (584\|2 - 3856)cos(x) + (2432\|2 + 10336)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 10408\|2 - 17872)cos(x) + (6920\|2 + 20176)cos(x) +--R + +--R +-+ +--R (6600\|2 - 6384)cos(x) +--R * +--R sin(x) +--R / +--R +-+ 6 +-+ 5 +--R (8\|2 - 16)cos(x) + (- 304\|2 + 448)cos(x) +--R + +--R +-+ 4 +-+ 3 +--R (2812\|2 - 3992)cos(x) + (- 9656\|2 + 13664)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (10232\|2 - 14464)cos(x) + (4904\|2 - 6944)cos(x) - 5820\|2 + 8232 +--R * +--R +------------+ +--R \|- cos(x) + 3 +--R + +--R +-+ 8 +-+ 7 +-+ 6 +--R - 128\|2 cos(x) + 2304\|2 cos(x) - 14720\|2 cos(x) +--R + +--R +-+ 5 +-+ 4 +--R (38400\|2 - 1)cos(x) + (- 25504\|2 + 51)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 40128\|2 - 830)cos(x) + (36608\|2 + 5274)cos(x) +--R + +--R +-+ +-+ +--R (10176\|2 - 14401)cos(x) - 10080\|2 + 14259 +--R Type: Expression Integer +--E 94 + +--S 95 of 526 +t0818:= sin(x)/(1+sin(x)^2)^(1/2) +--R +--R +--R sin(x) +--R (84) -------------- +--R +-----------+ +--R | 2 +--R \|sin(x) + 1 +--R Type: Expression Integer +--E 95 + +--S 96 of 526 +r0818:= -asin(1/2*cos(x)*2^(1/2)) +--R +--R +--R +-+ +--R \|2 cos(x) +--R (85) - asin(----------) +--R 2 +--R Type: Expression Integer +--E 96 + +--S 97 of 526 +a0818:= integrate(t0818,x) +--R +--R +--R (86) +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 97 + +--S 98 of 526 +m0818:= a0818-r0818 +--R +--R +--R (87) +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R +-+ +--R \|2 cos(x) +--R 2asin(----------) +--R 2 +--R / +--R 2 +--R Type: Expression Integer +--E 98 + +--S 99 of 526 +d0818:= D(m0818,x) +--R +--R +--R (88) +--R 7 6 5 4 3 +--R - 16cos(x) - 16cos(x) + 48cos(x) + 48cos(x) - 36cos(x) +--R + +--R 2 +--R - 36cos(x) + 8cos(x) + 8 +--R * +--R 9 +--R sin(x) +--R + +--R 9 8 7 6 +--R 240cos(x) + 240cos(x) - 1136cos(x) - 1136cos(x) +--R + +--R 5 4 3 2 +--R 1752cos(x) + 1752cos(x) - 964cos(x) - 964cos(x) +--R + +--R 172cos(x) + 172 +--R * +--R 7 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 240cos(x) - 240cos(x) + 1680cos(x) + 1680cos(x) +--R + +--R 7 6 5 4 +--R - 4264cos(x) - 4264cos(x) + 4688cos(x) + 4688cos(x) +--R + +--R 3 2 +--R - 2073cos(x) - 2073cos(x) + 310cos(x) + 310 +--R * +--R 5 +--R sin(x) +--R + +--R 13 12 11 10 +--R 16cos(x) + 16cos(x) - 208cos(x) - 208cos(x) +--R + +--R 9 8 7 6 +--R 920cos(x) + 920cos(x) - 1836cos(x) - 1836cos(x) +--R + +--R 5 4 3 2 +--R 1705cos(x) + 1705cos(x) - 652cos(x) - 652cos(x) +--R + +--R 85cos(x) + 85 +--R * +--R 3 +--R sin(x) +--R + +--R 11 10 9 8 7 +--R - 4cos(x) - 4cos(x) + 24cos(x) + 24cos(x) - 52cos(x) +--R + +--R 6 5 4 3 2 +--R - 52cos(x) + 48cos(x) + 48cos(x) - 17cos(x) - 17cos(x) +--R + +--R 2cos(x) + 2 +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 9 8 7 6 5 +--R - 96cos(x) - 96cos(x) + 464cos(x) + 464cos(x) - 736cos(x) +--R + +--R 4 3 2 +--R - 736cos(x) + 424cos(x) + 424cos(x) - 80cos(x) - 80 +--R * +--R 8 +--R sin(x) +--R + +--R 11 10 9 8 +--R 320cos(x) + 320cos(x) - 2160cos(x) - 2160cos(x) +--R + +--R 7 6 5 4 +--R 5360cos(x) + 5360cos(x) - 5868cos(x) - 5868cos(x) +--R + +--R 3 2 +--R 2664cos(x) + 2664cos(x) - 416cos(x) - 416 +--R * +--R 6 +--R sin(x) +--R + +--R 13 12 11 10 +--R - 96cos(x) - 96cos(x) + 944cos(x) + 944cos(x) +--R + +--R 9 8 7 6 +--R - 3552cos(x) - 3552cos(x) + 6424cos(x) + 6424cos(x) +--R + +--R 5 4 3 2 +--R - 5670cos(x) - 5670cos(x) + 2174cos(x) + 2174cos(x) +--R + +--R - 292cos(x) - 292 +--R * +--R 4 +--R sin(x) +--R + +--R 13 12 11 10 +--R - 16cos(x) - 16cos(x) + 144cos(x) + 144cos(x) +--R + +--R 9 8 7 6 5 +--R - 500cos(x) - 500cos(x) + 836cos(x) + 836cos(x) - 678cos(x) +--R + +--R 4 3 2 +--R - 678cos(x) + 234cos(x) + 234cos(x) - 28cos(x) - 28 +--R * +--R 2 +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 8 +--R (192cos(x) - 928cos(x) + 1472cos(x) - 848cos(x) + 160)sin(x) +--R + +--R 10 8 6 4 +--R - 640cos(x) + 4320cos(x) - 10720cos(x) + 11736cos(x) +--R + +--R 2 +--R - 5328cos(x) + 832 +--R * +--R 6 +--R sin(x) +--R + +--R 12 10 8 6 +--R 192cos(x) - 1888cos(x) + 7104cos(x) - 12848cos(x) +--R + +--R 4 2 +--R 11340cos(x) - 4348cos(x) + 584 +--R * +--R 4 +--R sin(x) +--R + +--R 12 10 8 6 +--R 32cos(x) - 288cos(x) + 1000cos(x) - 1672cos(x) +--R + +--R 4 2 +--R 1356cos(x) - 468cos(x) + 56 +--R * +--R 2 +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 8 6 4 2 9 +--R (- 32cos(x) + 160cos(x) - 264cos(x) + 160cos(x) - 32)sin(x) +--R + +--R 10 8 6 4 2 +--R 480cos(x) - 3232cos(x) + 8048cos(x) - 8936cos(x) + 4200cos(x) +--R + +--R - 688 +--R * +--R 7 +--R sin(x) +--R + +--R 12 10 8 6 +--R - 480cos(x) + 4320cos(x) - 15248cos(x) + 26432cos(x) +--R + +--R 4 2 +--R - 22898cos(x) + 8912cos(x) - 1240 +--R * +--R 5 +--R sin(x) +--R + +--R 14 12 10 8 6 +--R 32cos(x) - 480cos(x) + 2672cos(x) - 7352cos(x) + 10754cos(x) +--R + +--R 4 2 +--R - 8124cos(x) + 2778cos(x) - 340 +--R * +--R 3 +--R sin(x) +--R + +--R 12 10 8 6 4 +--R - 8cos(x) + 64cos(x) - 200cos(x) + 304cos(x) - 226cos(x) +--R + +--R 2 +--R 72cos(x) - 8 +--R * +--R sin(x) +--R / +--R 9 8 7 6 5 +--R 96cos(x) + 96cos(x) - 464cos(x) - 464cos(x) + 736cos(x) +--R + +--R 4 3 2 +--R 736cos(x) - 424cos(x) - 424cos(x) + 80cos(x) + 80 +--R * +--R 7 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 320cos(x) - 320cos(x) + 2160cos(x) + 2160cos(x) +--R + +--R 7 6 5 4 +--R - 5360cos(x) - 5360cos(x) + 5868cos(x) + 5868cos(x) +--R + +--R 3 2 +--R - 2664cos(x) - 2664cos(x) + 416cos(x) + 416 +--R * +--R 5 +--R sin(x) +--R + +--R 13 12 11 10 9 +--R 96cos(x) + 96cos(x) - 944cos(x) - 944cos(x) + 3552cos(x) +--R + +--R 8 7 6 5 +--R 3552cos(x) - 6424cos(x) - 6424cos(x) + 5670cos(x) +--R + +--R 4 3 2 +--R 5670cos(x) - 2174cos(x) - 2174cos(x) + 292cos(x) + 292 +--R * +--R 3 +--R sin(x) +--R + +--R 13 12 11 10 9 +--R 16cos(x) + 16cos(x) - 144cos(x) - 144cos(x) + 500cos(x) +--R + +--R 8 7 6 5 4 +--R 500cos(x) - 836cos(x) - 836cos(x) + 678cos(x) + 678cos(x) +--R + +--R 3 2 +--R - 234cos(x) - 234cos(x) + 28cos(x) + 28 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | - 4cos(x) + 8 +--R \|- cos(x) + 2 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 8 +--R (32cos(x) - 160cos(x) + 264cos(x) - 160cos(x) + 32)sin(x) +--R + +--R 10 8 6 4 +--R - 480cos(x) + 3232cos(x) - 8048cos(x) + 8936cos(x) +--R + +--R 2 +--R - 4200cos(x) + 688 +--R * +--R 6 +--R sin(x) +--R + +--R 12 10 8 6 +--R 480cos(x) - 4320cos(x) + 15248cos(x) - 26432cos(x) +--R + +--R 4 2 +--R 22898cos(x) - 8912cos(x) + 1240 +--R * +--R 4 +--R sin(x) +--R + +--R 14 12 10 8 +--R - 32cos(x) + 480cos(x) - 2672cos(x) + 7352cos(x) +--R + +--R 6 4 2 +--R - 10754cos(x) + 8124cos(x) - 2778cos(x) + 340 +--R * +--R 2 +--R sin(x) +--R + +--R 12 10 8 6 4 +--R 8cos(x) - 64cos(x) + 200cos(x) - 304cos(x) + 226cos(x) +--R + +--R 2 +--R - 72cos(x) + 8 +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R Type: Expression Integer +--E 99 + +--S 100 of 526 +t0819:= sin(x)*(1+sin(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (89) sin(x)\|sin(x) + 1 +--R Type: Expression Integer +--E 100 + +--S 101 of 526 +r0819:= -asin(1/2*cos(x)*2^(1/2))-1/2*cos(x)*(2-cos(x)^2)^(1/2) +--R +--R +--R +-------------+ +-+ +--R | 2 \|2 cos(x) +--R - cos(x)\|- cos(x) + 2 - 2asin(----------) +--R 2 +--R (90) -------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 101 + +--S 102 of 526 +a0819:= integrate(t0819,x) +--R +--R +--R (91) +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R 6 5 4 3 2 +--R (8cos(x) + 8cos(x) - 24cos(x) - 24cos(x) + 17cos(x) + 17cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 3 +--R (16cos(x) - 56cos(x) + 48cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (16cos(x) + 16cos(x) - 24cos(x) - 24)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 32cos(x) + 96cos(x) - 68 +--R Type: Union(Expression Integer,...) +--E 102 + +--S 103 of 526 +m0819:= a0819-r0819 +--R +--R +--R (92) +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R +-------------+ +--R 4 3 2 | 2 +--R (8cos(x) + 8cos(x) - 12cos(x) - 12cos(x))sin(x)\|- cos(x) + 2 +--R + +--R +-+ +--R 3 2 \|2 cos(x) +--R (16cos(x) + 16cos(x) - 24cos(x) - 24)sin(x)asin(----------) +--R 2 +--R + +--R 6 5 4 3 2 +--R 8cos(x) + 8cos(x) - 24cos(x) - 24cos(x) + 17cos(x) + 17cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-------------+ +--R 5 3 | 2 +--R (- 16cos(x) + 48cos(x) - 34cos(x))\|- cos(x) + 2 +--R + +--R +-+ +--R 4 2 \|2 cos(x) +--R (- 32cos(x) + 96cos(x) - 68)asin(----------) +--R 2 +--R + +--R 5 3 +--R (16cos(x) - 56cos(x) + 48cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (16cos(x) + 16cos(x) - 24cos(x) - 24)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 32cos(x) + 96cos(x) - 68 +--R Type: Expression Integer +--E 103 + +--S 104 of 526 +d0819:= D(m0819,x) +--R +--R +--R (93) +--R 13 12 11 10 +--R 1024cos(x) + 1024cos(x) - 8192cos(x) - 8192cos(x) +--R + +--R 9 8 7 6 +--R 26112cos(x) + 26112cos(x) - 41984cos(x) - 41984cos(x) +--R + +--R 5 4 3 2 +--R 35392cos(x) + 35392cos(x) - 14592cos(x) - 14592cos(x) +--R + +--R 2304cos(x) + 2304 +--R * +--R 11 +--R sin(x) +--R + +--R 15 14 13 +--R - 28672cos(x) - 28672cos(x) + 273408cos(x) +--R + +--R 12 11 10 +--R 273408cos(x) - 1079552cos(x) - 1079552cos(x) +--R + +--R 9 8 7 +--R 2270208cos(x) + 2270208cos(x) - 2717008cos(x) +--R + +--R 6 5 4 +--R - 2717008cos(x) + 1824560cos(x) + 1824560cos(x) +--R + +--R 3 2 +--R - 626212cos(x) - 626212cos(x) + 84488cos(x) + 84488 +--R * +--R 9 +--R sin(x) +--R + +--R 17 16 15 +--R 71680cos(x) + 71680cos(x) - 809984cos(x) +--R + +--R 14 13 12 +--R - 809984cos(x) + 3890688cos(x) + 3890688cos(x) +--R + +--R 11 10 9 +--R - 10315008cos(x) - 10315008cos(x) + 16378800cos(x) +--R + +--R 8 7 6 +--R 16378800cos(x) - 15778608cos(x) - 15778608cos(x) +--R + +--R 5 4 3 +--R 8875528cos(x) + 8875528cos(x) - 2619332cos(x) +--R + +--R 2 +--R - 2619332cos(x) + 308716cos(x) + 308716 +--R * +--R 7 +--R sin(x) +--R + +--R 19 18 17 +--R - 28672cos(x) - 28672cos(x) + 394240cos(x) +--R + +--R 16 15 14 +--R 394240cos(x) - 2335232cos(x) - 2335232cos(x) +--R + +--R 13 12 11 +--R 7792128cos(x) + 7792128cos(x) - 16054512cos(x) +--R + +--R 10 9 8 +--R - 16054512cos(x) + 21018896cos(x) + 21018896cos(x) +--R + +--R 7 6 5 +--R - 17296488cos(x) - 17296488cos(x) + 8496880cos(x) +--R + +--R 4 3 2 +--R 8496880cos(x) - 2219321cos(x) - 2219321cos(x) +--R + +--R 233206cos(x) + 233206 +--R * +--R 5 +--R sin(x) +--R + +--R 21 20 19 18 +--R 1024cos(x) + 1024cos(x) - 21504cos(x) - 21504cos(x) +--R + +--R 17 16 15 +--R 180224cos(x) + 180224cos(x) - 823552cos(x) +--R + +--R 14 13 12 +--R - 823552cos(x) + 2305424cos(x) + 2305424cos(x) +--R + +--R 11 10 9 +--R - 4148816cos(x) - 4148816cos(x) + 4849928cos(x) +--R + +--R 8 7 6 +--R 4849928cos(x) - 3607708cos(x) - 3607708cos(x) +--R + +--R 5 4 3 +--R 1611481cos(x) + 1611481cos(x) - 382956cos(x) +--R + +--R 2 +--R - 382956cos(x) + 36565cos(x) + 36565 +--R * +--R 3 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 256cos(x) - 256cos(x) + 3072cos(x) + 3072cos(x) +--R + +--R 15 14 13 +--R - 15936cos(x) - 15936cos(x) + 46656cos(x) +--R + +--R 12 11 10 9 +--R 46656cos(x) - 84356cos(x) - 84356cos(x) + 96728cos(x) +--R + +--R 8 7 6 5 +--R 96728cos(x) - 69380cos(x) - 69380cos(x) + 29440cos(x) +--R + +--R 4 3 2 +--R 29440cos(x) - 6545cos(x) - 6545cos(x) + 578cos(x) + 578 +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 15 14 13 12 +--R 8192cos(x) + 8192cos(x) - 79872cos(x) - 79872cos(x) +--R + +--R 11 10 9 8 +--R 322816cos(x) + 322816cos(x) - 695936cos(x) - 695936cos(x) +--R + +--R 7 6 5 4 +--R 855744cos(x) + 855744cos(x) - 592352cos(x) - 592352cos(x) +--R + +--R 3 2 +--R 210560cos(x) + 210560cos(x) - 29568cos(x) - 29568 +--R * +--R 10 +--R sin(x) +--R + +--R 17 16 15 14 +--R - 57344cos(x) - 57344cos(x) + 652288cos(x) + 652288cos(x) +--R + +--R 13 12 11 +--R - 3159296cos(x) - 3159296cos(x) + 8462976cos(x) +--R + +--R 10 9 8 +--R 8462976cos(x) - 13612896cos(x) - 13612896cos(x) +--R + +--R 7 6 5 +--R 13330320cos(x) + 13330320cos(x) - 7658112cos(x) +--R + +--R 4 3 2 +--R - 7658112cos(x) + 2323208cos(x) + 2323208cos(x) - 283280cos(x) +--R + +--R - 283280 +--R * +--R 8 +--R sin(x) +--R + +--R 19 18 17 16 +--R 57344cos(x) + 57344cos(x) - 766976cos(x) - 766976cos(x) +--R + +--R 15 14 13 +--R 4447488cos(x) + 4447488cos(x) - 14613120cos(x) +--R + +--R 12 11 10 +--R - 14613120cos(x) + 29814336cos(x) + 29814336cos(x) +--R + +--R 9 8 7 +--R - 38874800cos(x) - 38874800cos(x) + 32061280cos(x) +--R + +--R 6 5 4 +--R 32061280cos(x) - 15903716cos(x) - 15903716cos(x) +--R + +--R 3 2 +--R 4233448cos(x) + 4233448cos(x) - 457280cos(x) - 457280 +--R * +--R 6 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 8192cos(x) - 8192cos(x) + 138240cos(x) + 138240cos(x) +--R + +--R 17 16 15 +--R - 1008384cos(x) - 1008384cos(x) + 4190592cos(x) +--R + +--R 14 13 12 +--R 4190592cos(x) - 10970464cos(x) - 10970464cos(x) +--R + +--R 11 10 9 +--R 18831024cos(x) + 18831024cos(x) - 21324528cos(x) +--R + +--R 8 7 6 +--R - 21324528cos(x) + 15574576cos(x) + 15574576cos(x) +--R + +--R 5 4 3 +--R - 6921094cos(x) - 6921094cos(x) + 1659606cos(x) +--R + +--R 2 +--R 1659606cos(x) - 161812cos(x) - 161812 +--R * +--R 4 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 1024cos(x) - 1024cos(x) + 15872cos(x) + 15872cos(x) +--R + +--R 17 16 15 +--R - 107264cos(x) - 107264cos(x) + 415296cos(x) +--R + +--R 14 13 12 +--R 415296cos(x) - 1016368cos(x) - 1016368cos(x) +--R + +--R 11 10 9 +--R 1633744cos(x) + 1633744cos(x) - 1732660cos(x) +--R + +--R 8 7 6 +--R - 1732660cos(x) + 1183124cos(x) + 1183124cos(x) +--R + +--R 5 4 3 2 +--R - 489566cos(x) - 489566cos(x) + 108554cos(x) + 108554cos(x) +--R + +--R - 9724cos(x) - 9724 +--R * +--R 2 +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 14 12 10 +--R - 16384cos(x) + 159744cos(x) - 645632cos(x) +--R + +--R 8 6 4 2 +--R 1391872cos(x) - 1711488cos(x) + 1184704cos(x) - 421120cos(x) +--R + +--R 59136 +--R * +--R 10 +--R sin(x) +--R + +--R 16 14 12 +--R 114688cos(x) - 1304576cos(x) + 6318592cos(x) +--R + +--R 10 8 6 +--R - 16925952cos(x) + 27225792cos(x) - 26660640cos(x) +--R + +--R 4 2 +--R 15316224cos(x) - 4646416cos(x) + 566560 +--R * +--R 8 +--R sin(x) +--R + +--R 18 16 14 +--R - 114688cos(x) + 1533952cos(x) - 8894976cos(x) +--R + +--R 12 10 8 +--R 29226240cos(x) - 59628672cos(x) + 77749600cos(x) +--R + +--R 6 4 2 +--R - 64122560cos(x) + 31807432cos(x) - 8466896cos(x) + 914560 +--R * +--R 6 +--R sin(x) +--R + +--R 20 18 16 +--R 16384cos(x) - 276480cos(x) + 2016768cos(x) +--R + +--R 14 12 10 +--R - 8381184cos(x) + 21940928cos(x) - 37662048cos(x) +--R + +--R 8 6 4 +--R 42649056cos(x) - 31149152cos(x) + 13842188cos(x) +--R + +--R 2 +--R - 3319212cos(x) + 323624 +--R * +--R 4 +--R sin(x) +--R + +--R 20 18 16 14 +--R 2048cos(x) - 31744cos(x) + 214528cos(x) - 830592cos(x) +--R + +--R 12 10 8 +--R 2032736cos(x) - 3267488cos(x) + 3465320cos(x) +--R + +--R 6 4 2 +--R - 2366248cos(x) + 979132cos(x) - 217108cos(x) + 19448 +--R * +--R 2 +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 14 12 10 8 +--R 2048cos(x) - 20480cos(x) + 84992cos(x) - 188416cos(x) +--R + +--R 6 4 2 +--R 238720cos(x) - 170752cos(x) + 62976cos(x) - 9216 +--R * +--R 11 +--R sin(x) +--R + +--R 16 14 12 10 +--R - 57344cos(x) + 661504cos(x) - 3252736cos(x) + 8858624cos(x) +--R + +--R 8 6 4 2 +--R - 14514848cos(x) + 14517152cos(x) - 8550664cos(x) + 2673824cos(x) +--R + +--R - 337952 +--R * +--R 9 +--R sin(x) +--R + +--R 18 16 14 +--R 143360cos(x) - 1906688cos(x) + 11021312cos(x) +--R + +--R 12 10 8 +--R - 36192768cos(x) + 74017632cos(x) - 97072416cos(x) +--R + +--R 6 4 2 +--R 80865488cos(x) - 40740776cos(x) + 11094760cos(x) - 1234864 +--R * +--R 7 +--R sin(x) +--R + +--R 20 18 16 14 +--R - 57344cos(x) + 903168cos(x) - 6247424cos(x) + 24925184cos(x) +--R + +--R 12 10 8 +--R - 63277536cos(x) + 106255840cos(x) - 118668560cos(x) +--R + +--R 6 4 2 +--R 86179712cos(x) - 38426162cos(x) + 9343696cos(x) - 932824 +--R * +--R 5 +--R sin(x) +--R + +--R 22 20 18 16 +--R 2048cos(x) - 47104cos(x) + 446464cos(x) - 2368000cos(x) +--R + +--R 14 12 10 +--R 7905056cos(x) - 17519328cos(x) + 26295120cos(x) +--R + +--R 8 6 4 2 +--R - 26615128cos(x) + 17653794cos(x) - 7211836cos(x) + 1604954cos(x) +--R + +--R - 146260 +--R * +--R 3 +--R sin(x) +--R + +--R 20 18 16 14 +--R - 512cos(x) + 7168cos(x) - 44160cos(x) + 157056cos(x) +--R + +--R 12 10 8 6 +--R - 355336cos(x) + 530880cos(x) - 525672cos(x) + 336400cos(x) +--R + +--R 4 2 +--R - 130850cos(x) + 27336cos(x) - 2312 +--R * +--R sin(x) +--R / +--R 13 12 11 10 +--R 8192cos(x) + 8192cos(x) - 63488cos(x) - 63488cos(x) +--R + +--R 9 8 7 6 +--R 195840cos(x) + 195840cos(x) - 304256cos(x) - 304256cos(x) +--R + +--R 5 4 3 2 +--R 247232cos(x) + 247232cos(x) - 97888cos(x) - 97888cos(x) +--R + +--R 14784cos(x) + 14784 +--R * +--R 9 +--R sin(x) +--R + +--R 15 14 13 12 +--R - 57344cos(x) - 57344cos(x) + 537600cos(x) + 537600cos(x) +--R + +--R 11 10 9 +--R - 2084096cos(x) - 2084096cos(x) + 4294784cos(x) +--R + +--R 8 7 6 5 +--R 4294784cos(x) - 5023328cos(x) - 5023328cos(x) + 3283664cos(x) +--R + +--R 4 3 2 +--R 3283664cos(x) - 1090784cos(x) - 1090784cos(x) + 141640cos(x) +--R + +--R 141640 +--R * +--R 7 +--R sin(x) +--R + +--R 17 16 15 14 +--R 57344cos(x) + 57344cos(x) - 652288cos(x) - 652288cos(x) +--R + +--R 13 12 11 +--R 3142912cos(x) + 3142912cos(x) - 8327296cos(x) +--R + +--R 10 9 8 +--R - 8327296cos(x) + 13159744cos(x) + 13159744cos(x) +--R + +--R 7 6 5 +--R - 12555312cos(x) - 12555312cos(x) + 6950656cos(x) +--R + +--R 4 3 2 +--R 6950656cos(x) - 2002404cos(x) - 2002404cos(x) + 228640cos(x) +--R + +--R 228640 +--R * +--R 5 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 8192cos(x) - 8192cos(x) + 121856cos(x) + 121856cos(x) +--R + +--R 15 14 13 +--R - 764672cos(x) - 764672cos(x) + 2661248cos(x) +--R + +--R 12 11 10 +--R 2661248cos(x) - 5647968cos(x) - 5647968cos(x) +--R + +--R 9 8 7 6 +--R 7535088cos(x) + 7535088cos(x) - 6254352cos(x) - 6254352cos(x) +--R + +--R 5 4 3 2 +--R 3065872cos(x) + 3065872cos(x) - 789350cos(x) - 789350cos(x) +--R + +--R 80906cos(x) + 80906 +--R * +--R 3 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 1024cos(x) - 1024cos(x) + 13824cos(x) + 13824cos(x) +--R + +--R 15 14 13 12 +--R - 79616cos(x) - 79616cos(x) + 256064cos(x) + 256064cos(x) +--R + +--R 11 10 9 8 +--R - 504240cos(x) - 504240cos(x) + 625264cos(x) + 625264cos(x) +--R + +--R 7 6 5 4 +--R - 482132cos(x) - 482132cos(x) + 218860cos(x) + 218860cos(x) +--R + +--R 3 2 +--R - 51846cos(x) - 51846cos(x) + 4862cos(x) + 4862 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | - 4cos(x) + 8 +--R \|- cos(x) + 2 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 12 10 8 6 +--R 2048cos(x) - 16384cos(x) + 52224cos(x) - 83968cos(x) +--R + +--R 4 2 +--R 70784cos(x) - 29184cos(x) + 4608 +--R * +--R 10 +--R sin(x) +--R + +--R 14 12 10 +--R - 57344cos(x) + 546816cos(x) - 2159104cos(x) +--R + +--R 8 6 4 2 +--R 4540416cos(x) - 5434016cos(x) + 3649120cos(x) - 1252424cos(x) +--R + +--R 168976 +--R * +--R 8 +--R sin(x) +--R + +--R 16 14 12 +--R 143360cos(x) - 1619968cos(x) + 7781376cos(x) +--R + +--R 10 8 6 +--R - 20630016cos(x) + 32757600cos(x) - 31557216cos(x) +--R + +--R 4 2 +--R 17751056cos(x) - 5238664cos(x) + 617432 +--R * +--R 6 +--R sin(x) +--R + +--R 18 16 14 +--R - 57344cos(x) + 788480cos(x) - 4670464cos(x) +--R + +--R 12 10 8 +--R 15584256cos(x) - 32109024cos(x) + 42037792cos(x) +--R + +--R 6 4 2 +--R - 34592976cos(x) + 16993760cos(x) - 4438642cos(x) + 466412 +--R * +--R 4 +--R sin(x) +--R + +--R 20 18 16 14 +--R 2048cos(x) - 43008cos(x) + 360448cos(x) - 1647104cos(x) +--R + +--R 12 10 8 +--R 4610848cos(x) - 8297632cos(x) + 9699856cos(x) +--R + +--R 6 4 2 +--R - 7215416cos(x) + 3222962cos(x) - 765912cos(x) + 73130 +--R * +--R 2 +--R sin(x) +--R + +--R 18 16 14 12 +--R - 512cos(x) + 6144cos(x) - 31872cos(x) + 93312cos(x) +--R + +--R 10 8 6 4 +--R - 168712cos(x) + 193456cos(x) - 138760cos(x) + 58880cos(x) +--R + +--R 2 +--R - 13090cos(x) + 1156 +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R Type: Expression Integer +--E 104 + +--S 105 of 526 +t0820:= sin(7+3*x)/(3+sin(7+3*x)^2)^(1/2) +--R +--R +--R sin(3x + 7) +--R (94) ------------------- +--R +----------------+ +--R | 2 +--R \|sin(3x + 7) + 3 +--R Type: Expression Integer +--E 105 + +--S 106 of 526 +r0820:= -1/3*asin(1/2*cos(7+3*x)) +--R +--R +--R cos(3x + 7) +--R asin(-----------) +--R 2 +--R (95) - ----------------- +--R 3 +--R Type: Expression Integer +--E 106 + +--S 107 of 526 +a0820:= integrate(t0820,x) +--R +--R +--R (96) +--R - +--R atan +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + 1)sin(3x + 7) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2 +--R - 2cos(3x + 7) + 2 +--R / +--R +-------------------------------+ +--R | 2 +--R 2 | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + cos(3x + 7)) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2cos(3x + 7)sin(3x + 7) +--R + +--R - +--R atan +--R 4 3 2 +--R 2cos(3x + 7) + 2cos(3x + 7) - 3cos(3x + 7) +--R + +--R - 3cos(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 3 +--R (4cos(3x + 7) - 12cos(3x + 7))sin(3x + 7) +--R / +--R 3 2 +--R (2cos(3x + 7) + 2cos(3x + 7) - 2cos(3x + 7) - 2)sin(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 4 2 +--R - 4cos(3x + 7) + 14cos(3x + 7) - 4 +--R / +--R 6 +--R Type: Union(Expression Integer,...) +--E 107 + +--S 108 of 526 +m0820:= a0820-r0820 +--R +--R +--R (97) +--R - +--R atan +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + 1)sin(3x + 7) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2 +--R - 2cos(3x + 7) + 2 +--R / +--R +-------------------------------+ +--R | 2 +--R 2 | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + cos(3x + 7)) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2cos(3x + 7)sin(3x + 7) +--R + +--R - +--R atan +--R 4 3 2 +--R 2cos(3x + 7) + 2cos(3x + 7) - 3cos(3x + 7) +--R + +--R - 3cos(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 3 +--R (4cos(3x + 7) - 12cos(3x + 7))sin(3x + 7) +--R / +--R 3 2 +--R (2cos(3x + 7) + 2cos(3x + 7) - 2cos(3x + 7) - 2)sin(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 4 2 +--R - 4cos(3x + 7) + 14cos(3x + 7) - 4 +--R + +--R cos(3x + 7) +--R 2asin(-----------) +--R 2 +--R / +--R 6 +--R Type: Expression Integer +--E 108 + +--S 109 of 526 +d0820:= D(m0820,x) +--R +--R +--R (98) +--R 7 6 5 +--R - 64cos(3x + 7) - 64cos(3x + 7) + 384cos(3x + 7) +--R + +--R 4 3 2 +--R 384cos(3x + 7) - 576cos(3x + 7) - 576cos(3x + 7) +--R + +--R 256cos(3x + 7) + 256 +--R * +--R 9 +--R sin(3x + 7) +--R + +--R 9 8 7 +--R 592cos(3x + 7) + 592cos(3x + 7) - 5440cos(3x + 7) +--R + +--R 6 5 4 +--R - 5440cos(3x + 7) + 16032cos(3x + 7) + 16032cos(3x + 7) +--R + +--R 3 2 +--R - 16096cos(3x + 7) - 16096cos(3x + 7) + 5056cos(3x + 7) +--R + +--R 5056 +--R * +--R 7 +--R sin(3x + 7) +--R + +--R 11 10 9 +--R 80cos(3x + 7) + 80cos(3x + 7) + 800cos(3x + 7) +--R + +--R 8 7 6 +--R 800cos(3x + 7) - 10744cos(3x + 7) - 10744cos(3x + 7) +--R + +--R 5 4 3 +--R 31456cos(3x + 7) + 31456cos(3x + 7) - 26612cos(3x + 7) +--R + +--R 2 +--R - 26612cos(3x + 7) + 6640cos(3x + 7) + 6640 +--R * +--R 5 +--R sin(3x + 7) +--R + +--R 13 12 11 +--R - 80cos(3x + 7) - 80cos(3x + 7) + 1152cos(3x + 7) +--R + +--R 10 9 8 +--R 1152cos(3x + 7) - 5136cos(3x + 7) - 5136cos(3x + 7) +--R + +--R 7 6 5 +--R 6952cos(3x + 7) + 6952cos(3x + 7) + 2421cos(3x + 7) +--R + +--R 4 3 2 +--R 2421cos(3x + 7) - 4764cos(3x + 7) - 4764cos(3x + 7) +--R + +--R 1156cos(3x + 7) + 1156 +--R * +--R 3 +--R sin(3x + 7) +--R + +--R 15 14 13 +--R - 16cos(3x + 7) - 16cos(3x + 7) + 160cos(3x + 7) +--R + +--R 12 11 10 +--R 160cos(3x + 7) - 504cos(3x + 7) - 504cos(3x + 7) +--R + +--R 9 8 7 +--R 392cos(3x + 7) + 392cos(3x + 7) + 391cos(3x + 7) +--R + +--R 6 5 4 +--R 391cos(3x + 7) - 144cos(3x + 7) - 144cos(3x + 7) +--R + +--R 3 2 +--R - 52cos(3x + 7) - 52cos(3x + 7) + 16cos(3x + 7) + 16 +--R * +--R sin(3x + 7) +--R * +--R +------------------+ +--R | 2 +--R \|- cos(3x + 7) + 4 +--R + +--R 9 8 7 +--R - 320cos(3x + 7) - 320cos(3x + 7) + 3008cos(3x + 7) +--R + +--R 6 5 4 +--R 3008cos(3x + 7) - 9216cos(3x + 7) - 9216cos(3x + 7) +--R + +--R 3 2 +--R 10112cos(3x + 7) + 10112cos(3x + 7) - 3584cos(3x + 7) - 3584 +--R * +--R 8 +--R sin(3x + 7) +--R + +--R 11 10 9 +--R 416cos(3x + 7) + 416cos(3x + 7) - 6112cos(3x + 7) +--R + +--R 8 7 6 +--R - 6112cos(3x + 7) + 31808cos(3x + 7) + 31808cos(3x + 7) +--R + +--R 5 4 3 +--R - 69392cos(3x + 7) - 69392cos(3x + 7) + 57088cos(3x + 7) +--R + +--R 2 +--R 57088cos(3x + 7) - 15104cos(3x + 7) - 15104 +--R * +--R 6 +--R sin(3x + 7) +--R + +--R 13 12 11 +--R 256cos(3x + 7) + 256cos(3x + 7) - 2688cos(3x + 7) +--R + +--R 10 9 8 +--R - 2688cos(3x + 7) + 7968cos(3x + 7) + 7968cos(3x + 7) +--R + +--R 7 6 5 +--R 1480cos(3x + 7) + 1480cos(3x + 7) - 34140cos(3x + 7) +--R + +--R 4 3 2 +--R - 34140cos(3x + 7) + 30696cos(3x + 7) + 30696cos(3x + 7) +--R + +--R - 7136cos(3x + 7) - 7136 +--R * +--R 4 +--R sin(3x + 7) +--R + +--R 15 14 13 +--R 32cos(3x + 7) + 32cos(3x + 7) - 224cos(3x + 7) +--R + +--R 12 11 10 +--R - 224cos(3x + 7) - 96cos(3x + 7) - 96cos(3x + 7) +--R + +--R 9 8 7 +--R 3512cos(3x + 7) + 3512cos(3x + 7) - 6650cos(3x + 7) +--R + +--R 6 5 4 +--R - 6650cos(3x + 7) + 744cos(3x + 7) + 744cos(3x + 7) +--R + +--R 3 2 +--R 1640cos(3x + 7) + 1640cos(3x + 7) - 416cos(3x + 7) - 416 +--R * +--R 2 +--R sin(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 8 6 4 +--R 640cos(3x + 7) - 6016cos(3x + 7) + 18432cos(3x + 7) +--R + +--R 2 +--R - 20224cos(3x + 7) + 7168 +--R * +--R 8 +--R sin(3x + 7) +--R + +--R 10 8 6 +--R - 832cos(3x + 7) + 12224cos(3x + 7) - 63616cos(3x + 7) +--R + +--R 4 2 +--R 138784cos(3x + 7) - 114176cos(3x + 7) + 30208 +--R * +--R 6 +--R sin(3x + 7) +--R + +--R 12 10 8 +--R - 512cos(3x + 7) + 5376cos(3x + 7) - 15936cos(3x + 7) +--R + +--R 6 4 2 +--R - 2960cos(3x + 7) + 68280cos(3x + 7) - 61392cos(3x + 7) + 14272 +--R * +--R 4 +--R sin(3x + 7) +--R + +--R 14 12 10 +--R - 64cos(3x + 7) + 448cos(3x + 7) + 192cos(3x + 7) +--R + +--R 8 6 4 +--R - 7024cos(3x + 7) + 13300cos(3x + 7) - 1488cos(3x + 7) +--R + +--R 2 +--R - 3280cos(3x + 7) + 832 +--R * +--R 2 +--R sin(3x + 7) +--R * +--R +------------------+ +--R | 2 +--R \|- cos(3x + 7) + 4 +--R + +--R 8 6 4 +--R - 128cos(3x + 7) + 1280cos(3x + 7) - 4224cos(3x + 7) +--R + +--R 2 +--R 5120cos(3x + 7) - 2048 +--R * +--R 9 +--R sin(3x + 7) +--R + +--R 10 8 6 +--R 1184cos(3x + 7) - 15616cos(3x + 7) + 75584cos(3x + 7) +--R + +--R 4 2 +--R - 160448cos(3x + 7) + 138880cos(3x + 7) - 40448 +--R * +--R 7 +--R sin(3x + 7) +--R + +--R 12 10 8 +--R 160cos(3x + 7) + 960cos(3x + 7) - 27888cos(3x + 7) +--R + +--R 6 4 2 +--R 148864cos(3x + 7) - 304872cos(3x + 7) + 226176cos(3x + 7) - 53120 +--R * +--R 5 +--R sin(3x + 7) +--R + +--R 14 12 10 +--R - 160cos(3x + 7) + 2944cos(3x + 7) - 19488cos(3x + 7) +--R + +--R 8 6 4 +--R 54992cos(3x + 7) - 50774cos(3x + 7) - 28896cos(3x + 7) +--R + +--R 2 +--R 40424cos(3x + 7) - 9248 +--R * +--R 3 +--R sin(3x + 7) +--R + +--R 16 14 12 +--R - 32cos(3x + 7) + 448cos(3x + 7) - 2288cos(3x + 7) +--R + +--R 10 8 6 +--R 4816cos(3x + 7) - 2354cos(3x + 7) - 3416cos(3x + 7) +--R + +--R 4 2 +--R 1048cos(3x + 7) + 448cos(3x + 7) - 128 +--R * +--R sin(3x + 7) +--R / +--R 9 8 7 +--R 320cos(3x + 7) + 320cos(3x + 7) - 3008cos(3x + 7) +--R + +--R 6 5 4 +--R - 3008cos(3x + 7) + 9216cos(3x + 7) + 9216cos(3x + 7) +--R + +--R 3 2 +--R - 10112cos(3x + 7) - 10112cos(3x + 7) + 3584cos(3x + 7) + 3584 +--R * +--R 7 +--R sin(3x + 7) +--R + +--R 11 10 9 +--R - 416cos(3x + 7) - 416cos(3x + 7) + 6112cos(3x + 7) +--R + +--R 8 7 6 +--R 6112cos(3x + 7) - 31808cos(3x + 7) - 31808cos(3x + 7) +--R + +--R 5 4 3 +--R 69392cos(3x + 7) + 69392cos(3x + 7) - 57088cos(3x + 7) +--R + +--R 2 +--R - 57088cos(3x + 7) + 15104cos(3x + 7) + 15104 +--R * +--R 5 +--R sin(3x + 7) +--R + +--R 13 12 11 +--R - 256cos(3x + 7) - 256cos(3x + 7) + 2688cos(3x + 7) +--R + +--R 10 9 8 +--R 2688cos(3x + 7) - 7968cos(3x + 7) - 7968cos(3x + 7) +--R + +--R 7 6 5 +--R - 1480cos(3x + 7) - 1480cos(3x + 7) + 34140cos(3x + 7) +--R + +--R 4 3 2 +--R 34140cos(3x + 7) - 30696cos(3x + 7) - 30696cos(3x + 7) +--R + +--R 7136cos(3x + 7) + 7136 +--R * +--R 3 +--R sin(3x + 7) +--R + +--R 15 14 13 +--R - 32cos(3x + 7) - 32cos(3x + 7) + 224cos(3x + 7) +--R + +--R 12 11 10 +--R 224cos(3x + 7) + 96cos(3x + 7) + 96cos(3x + 7) +--R + +--R 9 8 7 +--R - 3512cos(3x + 7) - 3512cos(3x + 7) + 6650cos(3x + 7) +--R + +--R 6 5 4 +--R 6650cos(3x + 7) - 744cos(3x + 7) - 744cos(3x + 7) +--R + +--R 3 2 +--R - 1640cos(3x + 7) - 1640cos(3x + 7) + 416cos(3x + 7) + 416 +--R * +--R sin(3x + 7) +--R * +--R +-------------------------------+ +--R +------------------+ | 2 +--R | 2 | - 4cos(3x + 7) + 16 +--R \|- cos(3x + 7) + 4 |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 8 6 4 +--R 128cos(3x + 7) - 1280cos(3x + 7) + 4224cos(3x + 7) +--R + +--R 2 +--R - 5120cos(3x + 7) + 2048 +--R * +--R 8 +--R sin(3x + 7) +--R + +--R 10 8 6 +--R - 1184cos(3x + 7) + 15616cos(3x + 7) - 75584cos(3x + 7) +--R + +--R 4 2 +--R 160448cos(3x + 7) - 138880cos(3x + 7) + 40448 +--R * +--R 6 +--R sin(3x + 7) +--R + +--R 12 10 8 +--R - 160cos(3x + 7) - 960cos(3x + 7) + 27888cos(3x + 7) +--R + +--R 6 4 2 +--R - 148864cos(3x + 7) + 304872cos(3x + 7) - 226176cos(3x + 7) +--R + +--R 53120 +--R * +--R 4 +--R sin(3x + 7) +--R + +--R 14 12 10 +--R 160cos(3x + 7) - 2944cos(3x + 7) + 19488cos(3x + 7) +--R + +--R 8 6 4 +--R - 54992cos(3x + 7) + 50774cos(3x + 7) + 28896cos(3x + 7) +--R + +--R 2 +--R - 40424cos(3x + 7) + 9248 +--R * +--R 2 +--R sin(3x + 7) +--R + +--R 16 14 12 +--R 32cos(3x + 7) - 448cos(3x + 7) + 2288cos(3x + 7) +--R + +--R 10 8 6 +--R - 4816cos(3x + 7) + 2354cos(3x + 7) + 3416cos(3x + 7) +--R + +--R 4 2 +--R - 1048cos(3x + 7) - 448cos(3x + 7) + 128 +--R * +--R +------------------+ +--R | 2 +--R \|- cos(3x + 7) + 4 +--R Type: Expression Integer +--E 109 + +--S 110 of 526 +t0821:= cos(x)/(1+cos(x)^2)^(1/2) +--R +--R +--R cos(x) +--R (99) -------------- +--R +-----------+ +--R | 2 +--R \|cos(x) + 1 +--R Type: Expression Integer +--E 110 + +--S 111 of 526 +r0821:= asin(1/2*sin(x)*2^(1/2)) +--R +--R +--R +-+ +--R \|2 sin(x) +--R (100) asin(----------) +--R 2 +--R Type: Expression Integer +--E 111 + +--S 112 of 526 +a0821:= integrate(t0821,x) +--R +--R +--R (101) +--R - +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R 4 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R sin(x) +--R atan(------) +--R cos(x) +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 112 + +--S 113 of 526 +m0821:= a0821-r0821 +--R +--R +--R (102) +--R - +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R 4 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R +-+ +--R sin(x) \|2 sin(x) +--R atan(------) - 2asin(----------) +--R cos(x) 2 +--R / +--R 2 +--R Type: Expression Integer +--E 113 + +--S 114 of 526 +d0821:= D(m0821,x) +--R +--R +--R (103) +--R 13 12 11 10 +--R - 64cos(x) - 64cos(x) - 112cos(x) - 112cos(x) +--R + +--R 9 8 7 6 5 +--R 40cos(x) + 40cos(x) + 89cos(x) + 89cos(x) - 6cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) - 16cos(x) - 16cos(x) - cos(x) - 1 +--R * +--R 2 +--R sin(x) +--R + +--R 15 14 13 12 11 +--R - 64cos(x) - 64cos(x) - 48cos(x) - 48cos(x) + 88cos(x) +--R + +--R 10 9 8 7 6 +--R 88cos(x) + 49cos(x) + 49cos(x) - 43cos(x) - 43cos(x) +--R + +--R 5 4 3 2 +--R - 14cos(x) - 14cos(x) + 7cos(x) + 7cos(x) + cos(x) + 1 +--R * +--R +-------------+ +--R | 2 +--R \|- sin(x) + 2 +--R + +--R 16 15 14 13 +--R - 256cos(x) - 256cos(x) - 256cos(x) - 256cos(x) +--R + +--R 12 11 10 9 8 +--R 192cos(x) + 192cos(x) + 192cos(x) + 192cos(x) - 34cos(x) +--R + +--R 7 6 5 4 3 +--R - 34cos(x) - 34cos(x) - 34cos(x) - 2cos(x) - 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 18 17 14 13 12 +--R - 256cos(x) - 256cos(x) + 448cos(x) + 448cos(x) - 64cos(x) +--R + +--R 11 10 9 8 7 +--R - 64cos(x) - 258cos(x) - 258cos(x) + 60cos(x) + 60cos(x) +--R + +--R 6 5 4 3 2 +--R 50cos(x) + 50cos(x) - 12cos(x) - 12cos(x) - 2cos(x) - 2cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 13 11 9 7 5 +--R 128cos(x) + 288cos(x) + 16cos(x) - 238cos(x) - 58cos(x) +--R + +--R 3 +--R 50cos(x) + 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 15 13 11 9 7 +--R 128cos(x) + 160cos(x) - 144cos(x) - 190cos(x) + 60cos(x) +--R + +--R 5 3 +--R 72cos(x) - 10cos(x) - 8cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|- sin(x) + 2 +--R + +--R 16 14 12 10 8 +--R 512cos(x) + 768cos(x) - 192cos(x) - 608cos(x) - 64cos(x) +--R + +--R 6 4 +--R 120cos(x) + 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 18 16 14 12 10 +--R 512cos(x) + 256cos(x) - 960cos(x) - 288cos(x) + 672cos(x) +--R + +--R 8 6 2 +--R 80cos(x) - 192cos(x) + 16cos(x) +--R / +--R 15 14 13 12 +--R 256cos(x) + 256cos(x) + 256cos(x) + 256cos(x) +--R + +--R 11 10 9 8 7 +--R - 192cos(x) - 192cos(x) - 192cos(x) - 192cos(x) + 34cos(x) +--R + +--R 6 5 4 3 2 +--R 34cos(x) + 34cos(x) + 34cos(x) + 2cos(x) + 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 16 13 12 11 +--R 256cos(x) + 256cos(x) - 448cos(x) - 448cos(x) + 64cos(x) +--R + +--R 10 9 8 7 6 +--R 64cos(x) + 258cos(x) + 258cos(x) - 60cos(x) - 60cos(x) +--R + +--R 5 4 3 2 +--R - 50cos(x) - 50cos(x) + 12cos(x) + 12cos(x) + 2cos(x) + 2 +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | 4cos(x) + 4 +--R \|- sin(x) + 2 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 15 13 11 9 +--R - 512cos(x) - 768cos(x) + 192cos(x) + 608cos(x) +--R + +--R 7 5 3 +--R 64cos(x) - 120cos(x) - 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 15 13 11 9 +--R - 512cos(x) - 256cos(x) + 960cos(x) + 288cos(x) - 672cos(x) +--R + +--R 7 5 +--R - 80cos(x) + 192cos(x) - 16cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|- sin(x) + 2 +--R Type: Expression Integer +--E 114 + +--S 115 of 526 +t0822:= cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2) +--R +--R +--R cos(3x + 5) +--R (104) ------------------- +--R +----------------+ +--R | 2 +--R \|cos(3x + 5) + 3 +--R Type: Expression Integer +--E 115 + +--S 116 of 526 +r0822:= 1/3*asin(1/2*sin(5+3*x)) +--R +--R +--R sin(3x + 5) +--R asin(-----------) +--R 2 +--R (105) ----------------- +--R 3 +--R Type: Expression Integer +--E 116 + +--S 117 of 526 +a0822:= integrate(t0822,x) +--R +--R +--R (106) +--R - +--R atan +--R 3 2 +--R (2cos(3x + 5) + 2cos(3x + 5) + cos(3x + 5) + 1)sin(3x + 5) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 3 +--R (- 2cos(3x + 5) - 4cos(3x + 5))sin(3x + 5) +--R / +--R 4 3 +--R (2cos(3x + 5) + 2cos(3x + 5) ) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 4 2 +--R - 2cos(3x + 5) - 3cos(3x + 5) + 3 +--R + +--R sin(3x + 5) +--R atan(-----------) +--R cos(3x + 5) +--R / +--R 6 +--R Type: Union(Expression Integer,...) +--E 117 + +--S 118 of 526 +m0822:= a0822-r0822 +--R +--R +--R (107) +--R - +--R atan +--R 3 2 +--R (2cos(3x + 5) + 2cos(3x + 5) + cos(3x + 5) + 1)sin(3x + 5) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 3 +--R (- 2cos(3x + 5) - 4cos(3x + 5))sin(3x + 5) +--R / +--R 4 3 +--R (2cos(3x + 5) + 2cos(3x + 5) ) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 4 2 +--R - 2cos(3x + 5) - 3cos(3x + 5) + 3 +--R + +--R sin(3x + 5) sin(3x + 5) +--R atan(-----------) - 2asin(-----------) +--R cos(3x + 5) 2 +--R / +--R 6 +--R Type: Expression Integer +--E 118 + +--S 119 of 526 +d0822:= D(m0822,x) +--R +--R +--R (108) +--R 13 12 11 +--R - 64cos(3x + 5) - 64cos(3x + 5) - 496cos(3x + 5) +--R + +--R 10 9 8 +--R - 496cos(3x + 5) - 1032cos(3x + 5) - 1032cos(3x + 5) +--R + +--R 7 6 5 +--R - 183cos(3x + 5) - 183cos(3x + 5) + 729cos(3x + 5) +--R + +--R 4 3 2 +--R 729cos(3x + 5) - 9cos(3x + 5) - 9cos(3x + 5) +--R + +--R - 81cos(3x + 5) - 81 +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 15 14 13 +--R - 64cos(3x + 5) - 64cos(3x + 5) - 432cos(3x + 5) +--R + +--R 12 11 10 +--R - 432cos(3x + 5) - 792cos(3x + 5) - 792cos(3x + 5) +--R + +--R 9 8 7 +--R 81cos(3x + 5) + 81cos(3x + 5) + 864cos(3x + 5) +--R + +--R 6 5 4 +--R 864cos(3x + 5) - 162cos(3x + 5) - 162cos(3x + 5) +--R + +--R 3 2 +--R - 216cos(3x + 5) - 216cos(3x + 5) + 81cos(3x + 5) + 81 +--R * +--R +------------------+ +--R | 2 +--R \|- sin(3x + 5) + 4 +--R + +--R 16 15 14 +--R - 256cos(3x + 5) - 256cos(3x + 5) - 1792cos(3x + 5) +--R + +--R 13 12 11 +--R - 1792cos(3x + 5) - 3904cos(3x + 5) - 3904cos(3x + 5) +--R + +--R 10 9 8 +--R - 1920cos(3x + 5) - 1920cos(3x + 5) + 2094cos(3x + 5) +--R + +--R 7 6 5 +--R 2094cos(3x + 5) + 1062cos(3x + 5) + 1062cos(3x + 5) +--R + +--R 4 3 2 +--R - 414cos(3x + 5) - 414cos(3x + 5) - 54cos(3x + 5) +--R + +--R - 54cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 18 17 16 +--R - 256cos(3x + 5) - 256cos(3x + 5) - 1536cos(3x + 5) +--R + +--R 15 14 13 +--R - 1536cos(3x + 5) - 2112cos(3x + 5) - 2112cos(3x + 5) +--R + +--R 12 11 10 +--R 1728cos(3x + 5) + 1728cos(3x + 5) + 2862cos(3x + 5) +--R + +--R 9 8 7 +--R 2862cos(3x + 5) - 1944cos(3x + 5) - 1944cos(3x + 5) +--R + +--R 6 5 4 +--R - 540cos(3x + 5) - 540cos(3x + 5) + 648cos(3x + 5) +--R + +--R 3 2 +--R 648cos(3x + 5) - 162cos(3x + 5) - 162cos(3x + 5) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 13 11 9 +--R 64cos(3x + 5) + 592cos(3x + 5) + 1704cos(3x + 5) +--R + +--R 7 5 3 +--R 1281cos(3x + 5) - 981cos(3x + 5) - 693cos(3x + 5) +--R + +--R 297cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 15 13 11 +--R 64cos(3x + 5) + 528cos(3x + 5) + 1368cos(3x + 5) +--R + +--R 9 7 5 +--R 729cos(3x + 5) - 1350cos(3x + 5) - 648cos(3x + 5) +--R + +--R 3 +--R 702cos(3x + 5) - 81cos(3x + 5) +--R * +--R +------------------+ +--R | 2 +--R \|- sin(3x + 5) + 4 +--R + +--R 16 14 12 +--R 256cos(3x + 5) + 2176cos(3x + 5) + 6304cos(3x + 5) +--R + +--R 10 8 6 +--R 6192cos(3x + 5) - 1392cos(3x + 5) - 3744cos(3x + 5) +--R + +--R 4 2 +--R 144cos(3x + 5) + 432cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 18 16 14 +--R 256cos(3x + 5) + 1920cos(3x + 5) + 4128cos(3x + 5) +--R + +--R 12 10 6 4 +--R 144cos(3x + 5) - 6048cos(3x + 5) + 3456cos(3x + 5) - 1296cos(3x + 5) +--R / +--R 15 14 13 +--R 256cos(3x + 5) + 256cos(3x + 5) + 1792cos(3x + 5) +--R + +--R 12 11 10 +--R 1792cos(3x + 5) + 3904cos(3x + 5) + 3904cos(3x + 5) +--R + +--R 9 8 7 +--R 1920cos(3x + 5) + 1920cos(3x + 5) - 2094cos(3x + 5) +--R + +--R 6 5 4 +--R - 2094cos(3x + 5) - 1062cos(3x + 5) - 1062cos(3x + 5) +--R + +--R 3 2 +--R 414cos(3x + 5) + 414cos(3x + 5) + 54cos(3x + 5) + 54 +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 17 16 15 +--R 256cos(3x + 5) + 256cos(3x + 5) + 1536cos(3x + 5) +--R + +--R 14 13 12 +--R 1536cos(3x + 5) + 2112cos(3x + 5) + 2112cos(3x + 5) +--R + +--R 11 10 9 +--R - 1728cos(3x + 5) - 1728cos(3x + 5) - 2862cos(3x + 5) +--R + +--R 8 7 6 +--R - 2862cos(3x + 5) + 1944cos(3x + 5) + 1944cos(3x + 5) +--R + +--R 5 4 3 2 +--R 540cos(3x + 5) + 540cos(3x + 5) - 648cos(3x + 5) - 648cos(3x + 5) +--R + +--R 162cos(3x + 5) + 162 +--R * +--R +-------------------------------+ +--R +------------------+ | 2 +--R | 2 | cos(3x + 5) + 3 +--R \|- sin(3x + 5) + 4 |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 15 13 11 +--R - 256cos(3x + 5) - 2176cos(3x + 5) - 6304cos(3x + 5) +--R + +--R 9 7 5 +--R - 6192cos(3x + 5) + 1392cos(3x + 5) + 3744cos(3x + 5) +--R + +--R 3 +--R - 144cos(3x + 5) - 432cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 17 15 13 +--R - 256cos(3x + 5) - 1920cos(3x + 5) - 4128cos(3x + 5) +--R + +--R 11 9 5 +--R - 144cos(3x + 5) + 6048cos(3x + 5) - 3456cos(3x + 5) +--R + +--R 3 +--R 1296cos(3x + 5) +--R * +--R +------------------+ +--R | 2 +--R \|- sin(3x + 5) + 4 +--R Type: Expression Integer +--E 119 + +--S 120 of 526 +t0823:= cos(x)/(4-cos(x)^2)^(1/2) +--R +--R +--R cos(x) +--R (109) ---------------- +--R +-------------+ +--R | 2 +--R \|- cos(x) + 4 +--R Type: Expression Integer +--E 120 + +--S 121 of 526 +r0823:= asinh(1/3*sin(x)*3^(1/2)) +--R +--R +--R +-+ +--R \|3 sin(x) +--R (110) asinh(----------) +--R 3 +--R Type: Expression Integer +--E 121 + +--S 122 of 526 +a0823:= integrate(t0823,x) +--R +--R +--R (111) +--R log +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 16 +--R (- 4cos(x) - 4cos(x) + 10cos(x) + 10)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 8cos(x) - 40cos(x) + 41 +--R / +--R 4 +--R Type: Union(Expression Integer,...) +--E 122 + +--S 123 of 526 +m0823:= a0823-r0823 +--R +--R +--R (112) +--R log +--R 3 2 +--R (- 4cos(x) - 4cos(x) + 10cos(x) + 10)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 8cos(x) - 40cos(x) + 41 +--R + +--R +-+ +--R \|3 sin(x) +--R - 4asinh(----------) +--R 3 +--R / +--R 4 +--R Type: Expression Integer +--E 123 + +--S 124 of 526 +d0823:= D(m0823,x) +--R +--R +--R (113) +--R 4 3 2 +--R (- 8cos(x) - 8cos(x) + 20cos(x) + 20cos(x))sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 2 5 3 +--R (- 12cos(x) + 42cos(x))sin(x) + 4cos(x) - 26cos(x) + 40cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|sin(x) + 3 +--R + +--R 6 5 4 3 2 +--R (- 8cos(x) - 8cos(x) + 40cos(x) + 40cos(x) - 41cos(x) - 41cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 3 +--R (- 16cos(x) + 104cos(x) - 160cos(x))sin(x) +--R / +--R 5 4 3 2 +--R (8cos(x) + 8cos(x) - 40cos(x) - 40cos(x) + 41cos(x) + 41) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R (16cos(x) - 104cos(x) + 160)sin(x) +--R * +--R +-----------+ +--R | 2 +--R \|sin(x) + 3 +--R Type: Expression Integer +--E 124 + +--S 125 of 526 +t0824:= sin(x)/(a*cos(x)+b*sin(x)) +--R +--R +--R sin(x) +--R (114) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 125 + +--S 126 of 526 +r0824:= -(-b*x+a*log(a*cos(x)+b*sin(x)))/(a^2+b^2) +--R +--R +--R - a log(b sin(x) + a cos(x)) + b x +--R (115) ---------------------------------- +--R 2 2 +--R b + a +--R Type: Expression Integer +--E 126 + +--S 127 of 526 +a0824:= integrate(t0824,x) +--R +--R +--R 2 - 2b sin(x) - 2a cos(x) +--R a log(----------) - a log(-----------------------) + b x +--R cos(x) + 1 cos(x) + 1 +--R (116) -------------------------------------------------------- +--R 2 2 +--R b + a +--R Type: Union(Expression Integer,...) +--E 127 + +--S 128 of 526 +m0824:= a0824-r0824 +--R +--R +--R (117) +--R 2 +--R a log(b sin(x) + a cos(x)) + a log(----------) +--R cos(x) + 1 +--R + +--R - 2b sin(x) - 2a cos(x) +--R - a log(-----------------------) +--R cos(x) + 1 +--R / +--R 2 2 +--R b + a +--R Type: Expression Integer +--E 128 + +--S 129 of 526 +d0824:= D(m0824,x) +--R +--R +--R (118) 0 +--R Type: Expression Integer +--E 129 + +--S 130 of 526 +t0825:= sin(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R sin(x) +--R (119) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 130 + +--S 131 of 526 +r0825:= -a^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-b*cos(x)/(a^2+b^2)-a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R a atanh(-------------------) + (- a sin(x) - b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (120) ---------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 131 + +--S 132 of 526 +a0825:= integrate(t0825,x) +--R +--R +--R (121) +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression Integer,...) +--E 132 + +--S 133 of 526 +m0825:= a0825-r0825 +--R +--R +--R (122) +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 2 a sin(x) - b cos(x) +--R - a atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 133 + +--S 134 of 526 +d0825:= D(m0825,x) +--R +--R +--R (123) +--R 3 3 2 2 3 2 3 2 3 +--R a sin(x) - a b cos(x)sin(x) + (a cos(x) - a )sin(x) - a b cos(x) +--R + +--R 2 +--R a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression Integer +--E 134 + +--S 135 of 526 +t0826:= sin(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R sin(x) +--R (124) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 135 + +--S 136 of 526 +r0826:= 1/2/(a^2+b^2)^2*(3*a^2*b*x+b^3*x-2*a^3*log(a*cos(x)+b*sin(x))-a^2*b*sin(x)*cos(x)-b^3*sin(x)*cos(x)-a^3+a^3*cos(x)^2-b^2*a+b^2*a*cos(x)^2) +--R +--R +--R (125) +--R 3 3 2 +--R - 2a log(b sin(x) + a cos(x)) + (- b - a b)cos(x)sin(x) +--R + +--R 2 3 2 3 2 2 3 +--R (a b + a )cos(x) + (b + 3a b)x - a b - a +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 136 + +--S 137 of 526 +a0826:= integrate(t0826,x) +--R +--R +--R (126) +--R 3 2 3 - 2b sin(x) - 2a cos(x) +--R 2a log(----------) - 2a log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 2 2 3 2 3 2 +--R (- b - a b)cos(x)sin(x) + (a b + a )cos(x) + (b + 3a b)x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 137 + +--S 138 of 526 +m0826:= a0826-r0826 +--R +--R +--R (127) +--R 3 3 2 +--R 2a log(b sin(x) + a cos(x)) + 2a log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2b sin(x) - 2a cos(x) 2 3 +--R - 2a log(-----------------------) + a b + a +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 138 + +--S 139 of 526 +d0826:= D(m0826,x) +--R +--R +--R (128) 0 +--R Type: Expression Integer +--E 139 + +--S 140 of 526 +t0827:= sin(x)/(a*cos(x)+b*sin(x))^2 +--R +--R +--R sin(x) +--R (129) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression Integer +--E 140 + +--S 141 of 526 +r0827:= -b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+a/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R (b sin(x) + a b cos(x))atanh(-------------------) + a\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (130) --------------------------------------------------------------- +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Expression Integer +--E 141 + +--S 142 of 526 +a0827:= integrate(t0827,x) +--R +--R +--R (131) +--R 2 +--R (b sin(x) + a b cos(x)) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b + a +--R / +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Union(Expression Integer,...) +--E 142 + +--S 143 of 526 +m0827:= a0827-r0827 +--R +--R +--R (132) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R a sin(x) - b cos(x) | 2 2 +--R - b atanh(-------------------) + \|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 143 + +--S 144 of 526 +d0827:= D(m0827,x) +--R +--R +--R (133) +--R 3 2 2 2 2 3 +--R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b)sin(x) - b cos(x) +--R + +--R 2 +--R b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression Integer +--E 144 + +--S 145 of 526 +t0828:= sin(x)^2/(a*cos(x)+b*sin(x))^2 +--R +--R +--R 2 +--R sin(x) +--R (134) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression Integer +--E 145 + +--S 146 of 526 +r0828:= -(a^2-b^2)*x/(a^2+b^2)^2+a/(a^2+b^2)/(b+a*cot(x))-2*a*b*log(a*cos(x)+b*sin(x))/(a^2+b^2)^2 +--R +--R +--R (135) +--R 2 2 2 3 +--R (- 2a b cot(x) - 2a b )log(b sin(x) + a cos(x)) + (a b - a )x cot(x) +--R + +--R 3 2 2 3 +--R (b - a b)x + a b + a +--R / +--R 4 3 2 5 5 2 3 4 +--R (a b + 2a b + a )cot(x) + b + 2a b + a b +--R Type: Expression Integer +--E 146 + +--S 147 of 526 +a0828:= integrate(t0828,x) +--R +--R +--R (136) +--R 2 2 2 +--R (2a b sin(x) + 2a b cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 - 2b sin(x) - 2a cos(x) +--R (- 2a b sin(x) - 2a b cos(x))log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 3 +--R ((b - a b)x + a b + a )sin(x) + (a b - a )x cos(x) +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)sin(x) + (a b + 2a b + a )cos(x) +--R Type: Union(Expression Integer,...) +--E 147 + +--S 148 of 526 +m0828:= a0828-r0828 +--R +--R +--R (137) +--R 2 2 3 3 2 2 +--R ((2a b cot(x) + 2a b )sin(x) + 2a b cos(x)cot(x) + 2a b cos(x)) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 2 2 3 3 2 2 +--R ((2a b cot(x) + 2a b )sin(x) + 2a b cos(x)cot(x) + 2a b cos(x)) +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 3 2 2 +--R ((- 2a b cot(x) - 2a b )sin(x) - 2a b cos(x)cot(x) - 2a b cos(x)) +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 4 2 2 4 +--R (a b + a )cot(x)sin(x) + (- a b - a )cos(x) +--R / +--R 5 3 3 5 6 2 4 4 2 +--R ((a b + 2a b + a b)cot(x) + b + 2a b + a b )sin(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (a b + 2a b + a )cos(x)cot(x) + (a b + 2a b + a b)cos(x) +--R Type: Expression Integer +--E 148 + +--S 149 of 526 +d0828:= D(m0828,x) +--R +--R +--R (138) +--R 2 2 4 2 3 2 +--R ((- a b + a )cot(x) + 2a b cot(x))sin(x) +--R + +--R 3 2 3 3 2 +--R (- 2a b cos(x)cot(x) - 2a b cos(x))sin(x) + 2a b cos(x) cot(x) +--R + +--R 2 2 4 2 +--R (a b - a )cos(x) +--R / +--R 2 4 4 2 2 5 3 3 6 2 4 2 +--R ((a b + a b )cot(x) + (2a b + 2a b )cot(x) + b + a b )sin(x) +--R + +--R 3 3 5 2 2 4 4 2 +--R (2a b + 2a b)cos(x)cot(x) + (4a b + 4a b )cos(x)cot(x) +--R + +--R 5 3 3 +--R (2a b + 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 4 2 6 2 2 3 3 5 2 +--R (a b + a )cos(x) cot(x) + (2a b + 2a b)cos(x) cot(x) +--R + +--R 2 4 4 2 2 +--R (a b + a b )cos(x) +--R Type: Expression Integer +--E 149 + +--S 150 of 526 +t0829:= sin(x)/(a*cos(x)+b*sin(x))^3 +--R +--R +--R sin(x) +--R (139) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression Integer +--E 150 + +--S 151 of 526 +r0829:= 1/2*a/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+b*sin(x)/a/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R (140) +--R 2 2 2 +--R 2b sin(x) + 2a b cos(x)sin(x) + a +--R -------------------------------------------------------------------------- +--R 4 3 2 2 2 3 4 3 2 5 2 +--R (2a b + 2a b )sin(x) + (4a b + 4a b)cos(x)sin(x) + (2a b + 2a )cos(x) +--R Type: Expression Integer +--E 151 + +--S 152 of 526 +a0829:= integrate(t0829,x) +--R +--R +--R 2 +--R - cos(x) + 1 +--R (141) -------------------------------------------------- +--R 2 2 3 2 2 +--R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b +--R Type: Union(Expression Integer,...) +--E 152 + +--S 153 of 526 +m0829:= a0829-r0829 +--R +--R +--R (142) +--R 3 3 4 2 2 2 4 2 2 2 +--R - 4a b cos(x)sin(x) + ((b - 7a b )cos(x) - b + a b )sin(x) +--R + +--R 3 3 2 2 4 4 2 2 2 2 2 +--R - 4a b cos(x) sin(x) + (- a b - a )cos(x) + 2a b cos(x) - a b +--R / +--R 2 5 4 3 3 +--R (4a b + 4a b )cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 3 4 2 +--R ((- 2a b + 8a b + 10a b )cos(x) + 2a b + 2a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 +--R ((- 4a b + 4a b + 8a b)cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 3 4 7 4 3 4 5 2 2 +--R (- 2a b + 2a )cos(x) + (2a b + 2a b )cos(x) +--R Type: Expression Integer +--E 153 + +--S 154 of 526 +d0829:= D(m0829,x) +--R +--R +--R (143) +--R 6 2 4 2 6 2 4 5 +--R ((b - 3a b )cos(x) + b + a b )sin(x) +--R + +--R 5 3 3 3 3 3 4 +--R ((7a b - 5a b )cos(x) + 4a b cos(x))sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 2 6 3 +--R ((6a b - 2a b )cos(x) + (b - a b + 2a b )cos(x) - b )sin(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R (6a b - 2a b )cos(x) + (- 5a b + 7a b )cos(x) +--R + +--R 5 3 3 +--R (- a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 4 +--R (- b + 9a b - 2a b )cos(x) + (2b - 14a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 +--R (- b + 6a b - 2a b )cos(x) - a b +--R * +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 5 +--R (- a b + 3a b )cos(x) + (3a b - 5a b )cos(x) +--R + +--R 5 3 3 3 5 +--R (- 3a b + 2a b )cos(x) + a b cos(x) +--R / +--R 2 7 4 5 2 5 +--R (4a b + 4a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 3 8 3 6 4 +--R ((- 4a b + 12a b + 16a b )cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 9 2 7 4 5 6 3 4 +--R (b - 13a b + 11a b + 25a b )cos(x) +--R + +--R 9 2 7 4 5 2 9 2 7 +--R (- 2b + 12a b + 14a b )cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 15a b + a b + 19a b )cos(x) +--R + +--R 8 3 6 5 4 3 8 3 6 +--R (- 6a b + 12a b + 18a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (3a b - 7a b - 3a b + 7a b)cos(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 2 +--R (- 6a b + 4a b + 10a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 7 3 6 7 2 5 +--R (a b - a b - a b + a )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 3 +--R (a b + a b )cos(x) +--R Type: Expression Integer +--E 154 + +--S 155 of 526 +t0830:= sin(x)^3/(a*cos(x)+b*sin(x))^3 +--R +--R +--R 3 +--R sin(x) +--R (144) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression Integer +--E 155 + +--S 156 of 526 +r0830:= -b*(3*a^2-b^2)*x/(a^2+b^2)^3+1/2*a/(a^2+b^2)/(b+a*cot(x))^2+2*a*b/(a^2+b^2)^2/(b+a*cot(x))+a*(a^2-3*b^2)*log(a*cos(x)+b*sin(x))/(a^2+b^2)^3 +--R +--R +--R (145) +--R 3 2 5 2 2 3 4 4 3 2 +--R ((- 6a b + 2a )cot(x) + (- 12a b + 4a b)cot(x) - 6a b + 2a b ) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 2 3 4 2 4 3 2 2 3 4 +--R (2a b - 6a b)x cot(x) + ((4a b - 12a b )x + 4a b + 4a b)cot(x) +--R + +--R 5 2 3 4 3 2 5 +--R (2b - 6a b )x + 5a b + 6a b + a +--R / +--R 2 6 4 4 6 2 8 2 +--R (2a b + 6a b + 6a b + 2a )cot(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 6 2 +--R (4a b + 12a b + 12a b + 4a b)cot(x) + 2b + 6a b + 6a b + 2a b +--R Type: Expression Integer +--E 156 + +--S 157 of 526 +a0830:= integrate(t0830,x) +--R +--R +--R (146) +--R 2 3 4 4 3 2 5 2 4 +--R (12a b - 4a b)cos(x)sin(x) + (- 6a b + 8a b - 2a )cos(x) + 6a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 3 4 4 3 2 5 2 4 +--R (- 12a b + 4a b)cos(x)sin(x) + (6a b - 8a b + 2a )cos(x) - 6a b +--R + +--R 3 2 +--R 2a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 4 3 2 2 3 4 +--R ((4a b - 12a b )x + 4a b + 4a b)cos(x)sin(x) +--R + +--R 5 2 3 4 4 3 2 5 2 5 2 3 +--R ((- 2b + 8a b - 6a b)x - 5a b - 6a b - a )cos(x) + (2b - 6a b )x +--R + +--R 4 3 2 5 +--R 5a b + 6a b + a +--R / +--R 7 3 5 5 3 7 +--R (4a b + 12a b + 12a b + 4a b)cos(x)sin(x) +--R + +--R 8 2 6 6 2 8 2 8 2 6 4 4 6 2 +--R (- 2b - 4a b + 4a b + 2a )cos(x) + 2b + 6a b + 6a b + 2a b +--R Type: Union(Expression Integer,...) +--E 157 + +--S 158 of 526 +m0830:= a0830-r0830 +--R +--R +--R (147) +--R 4 3 6 2 3 4 5 2 +--R (12a b - 4a b)cos(x)cot(x) + (24a b - 8a b )cos(x)cot(x) +--R + +--R 2 5 4 3 +--R (12a b - 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 2 +--R ((- 6a b + 8a b - 2a )cos(x) + 6a b - 2a b )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R ((- 12a b + 16a b - 4a b)cos(x) + 12a b - 4a b )cot(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (- 6a b + 8a b - 2a b )cos(x) + 6a b - 2a b +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 4 3 6 2 3 4 5 2 +--R (12a b - 4a b)cos(x)cot(x) + (24a b - 8a b )cos(x)cot(x) +--R + +--R 2 5 4 3 +--R (12a b - 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 2 +--R ((- 6a b + 8a b - 2a )cos(x) + 6a b - 2a b )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R ((- 12a b + 16a b - 4a b)cos(x) + 12a b - 4a b )cot(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (- 6a b + 8a b - 2a b )cos(x) + 6a b - 2a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 4 3 6 2 3 4 5 2 +--R (- 12a b + 4a b)cos(x)cot(x) + (- 24a b + 8a b )cos(x)cot(x) +--R + +--R 2 5 4 3 +--R (- 12a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 2 +--R ((6a b - 8a b + 2a )cos(x) - 6a b + 2a b )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R ((12a b - 16a b + 4a b)cos(x) - 12a b + 4a b )cot(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (6a b - 8a b + 2a b )cos(x) - 6a b + 2a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 4 3 6 2 2 5 4 3 6 +--R ((4a b + 4a b)cos(x)cot(x) + (- 6a b - 8a b - 2a b)cos(x))sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 2 +--R ((- 5a b - 6a b - a )cos(x) + 5a b + 6a b + a )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R ((- 6a b - 12a b - 6a b)cos(x) + 6a b + 8a b + 2a b)cot(x) +--R + +--R 3 4 5 2 7 2 +--R (- 5a b - 6a b - a )cos(x) +--R / +--R 3 7 5 5 7 3 9 2 +--R (4a b + 12a b + 12a b + 4a b)cos(x)cot(x) +--R + +--R 2 8 4 6 6 4 8 2 +--R (8a b + 24a b + 24a b + 8a b )cos(x)cot(x) +--R + +--R 9 3 7 5 5 7 3 +--R (4a b + 12a b + 12a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 8 4 6 8 2 10 2 2 8 4 6 6 4 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) + 2a b + 6a b + 6a b +--R + +--R 8 2 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 7 3 9 2 9 3 7 5 5 +--R (- 4a b - 8a b + 8a b + 4a b)cos(x) + 4a b + 12a b + 12a b +--R + +--R 7 3 +--R 4a b +--R * +--R cot(x) +--R + +--R 10 2 8 6 4 8 2 2 10 2 8 4 6 6 4 +--R (- 2b - 4a b + 4a b + 2a b )cos(x) + 2b + 6a b + 6a b + 2a b +--R Type: Expression Integer +--E 158 + +--S 159 of 526 +d0830:= D(m0830,x) +--R +--R +--R (148) +--R 5 3 7 2 5 3 7 3 +--R ((- 5a b + 3a b)cos(x) + 3a b + a b)cot(x) +--R + +--R 4 4 6 2 2 4 4 6 2 2 +--R ((- 3a b + 5a b )cos(x) + 9a b + 3a b )cot(x) +--R + +--R 3 5 5 3 2 3 5 5 3 +--R ((9a b + a b )cos(x) + 9a b + 3a b )cot(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 +--R (3a b - 9a b - 4a b )cos(x) + 3a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 3 4 4 6 2 8 3 +--R ((8a b - 8a b )cos(x) + (- 8a b + 5a b + a )cos(x))cot(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 +--R ((12a b - 8a b - 4a b)cos(x) + (- 12a b + 11a b + 3a b)cos(x)) +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 3 4 4 6 2 +--R ((8a b - 8a b )cos(x) + (7a b + 3a b )cos(x))cot(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 +--R (12a b - 8a b - 4a b)cos(x) + (- 7a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 2 3 5 +--R ((- 2a b + 7a b + a b)cos(x) + (4a b - 7a b - a b)cos(x) - 2a b ) +--R * +--R 3 +--R cot(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 3a b + 14a b + 8a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 +--R (6a b - 13a b - 5a b )cos(x) - 3a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 2 3 5 +--R ((7a b + 13a b - 2a b)cos(x) + (- 5a b - 7a b )cos(x) - 2a b )cot(x) +--R + +--R 4 4 6 2 8 4 2 6 4 4 6 2 2 2 6 4 4 +--R (8a b - a b - a )cos(x) + (3a b - 5a b - 2a b )cos(x) - 3a b - a b +--R / +--R 5 6 7 4 9 2 2 3 +--R (4a b + 8a b + 4a b )cos(x) cot(x) +--R + +--R 4 7 6 5 8 3 2 2 +--R (12a b + 24a b + 12a b )cos(x) cot(x) +--R + +--R 3 8 5 6 7 4 2 +--R (12a b + 24a b + 12a b )cos(x) cot(x) +--R + +--R 2 9 4 7 6 5 2 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (- 4a b - 4a b + 4a b + 4a b)cos(x) +--R + +--R 4 7 6 5 8 3 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 3 8 5 6 7 4 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 2 9 4 7 6 5 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R cot(x) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 4a b - 4a b + 4a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 8 7 4 11 4 +--R (a b - 2a b + a )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 2 3 8 5 6 7 4 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) + a b + 2a b + a b +--R * +--R 3 +--R cot(x) +--R + +--R 2 9 6 5 10 4 +--R (3a b - 6a b + 3a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 2 9 4 7 6 5 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 5 6 9 2 4 +--R (3a b - 6a b + 3a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 2 10 3 8 5 6 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R cot(x) +--R + +--R 11 4 7 8 3 4 11 2 9 4 7 6 5 2 +--R (b - 2a b + a b )cos(x) + (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 11 2 9 4 7 +--R b + 2a b + a b +--R Type: Expression Integer +--E 159 + +--S 160 of 526 +t0831:= cos(x)/(a*cos(x)+b*sin(x)) +--R +--R +--R cos(x) +--R (149) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 160 + +--S 161 of 526 +r0831:= (a*x+b*log(a*cos(x)+b*sin(x)))/(a^2+b^2) +--R +--R +--R b log(b sin(x) + a cos(x)) + a x +--R (150) -------------------------------- +--R 2 2 +--R b + a +--R Type: Expression Integer +--E 161 + +--S 162 of 526 +a0831:= integrate(t0831,x) +--R +--R +--R 2 - 2b sin(x) - 2a cos(x) +--R - b log(----------) + b log(-----------------------) + a x +--R cos(x) + 1 cos(x) + 1 +--R (151) ---------------------------------------------------------- +--R 2 2 +--R b + a +--R Type: Union(Expression Integer,...) +--E 162 + +--S 163 of 526 +m0831:= a0831-r0831 +--R +--R +--R (152) +--R 2 +--R - b log(b sin(x) + a cos(x)) - b log(----------) +--R cos(x) + 1 +--R + +--R - 2b sin(x) - 2a cos(x) +--R b log(-----------------------) +--R cos(x) + 1 +--R / +--R 2 2 +--R b + a +--R Type: Expression Integer +--E 163 + +--S 164 of 526 +d0831:= D(m0831,x) +--R +--R +--R (153) 0 +--R Type: Expression Integer +--E 164 + +--S 165 of 526 +t0832:= cos(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R cos(x) +--R (154) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 165 + +--S 166 of 526 +r0832:= -b^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+b*cos(x)/(a^2+b^2)+a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R b atanh(-------------------) + (a sin(x) + b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (155) -------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 166 + +--S 167 of 526 +a0832:= integrate(t0832,x) +--R +--R +--R (156) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) + b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression Integer,...) +--E 167 + +--S 168 of 526 +m0832:= a0832-r0832 +--R +--R +--R (157) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 2 a sin(x) - b cos(x) +--R - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 168 + +--S 169 of 526 +d0832:= D(m0832,x) +--R +--R +--R (158) +--R 2 3 3 2 2 2 2 3 3 +--R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b )sin(x) - b cos(x) +--R + +--R 3 +--R b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression Integer +--E 169 + +--S 170 of 526 +t0833:= cos(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R cos(x) +--R (159) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 170 + +--S 171 of 526 +r0833:= 1/2/(a^2+b^2)^2*(3*a*b^2*x+a^3*x+2*b^3*log(a*cos(x)+b*sin(x))+sin(x)*a^3*cos(x)+sin(x)*a*cos(x)*b^2-a^2*b+b*cos(x)^2*a^2-b^3+b^3*cos(x)^2) +--R +--R +--R (160) +--R 3 2 3 3 2 2 +--R 2b log(b sin(x) + a cos(x)) + (a b + a )cos(x)sin(x) + (b + a b)cos(x) +--R + +--R 2 3 3 2 +--R (3a b + a )x - b - a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 171 + +--S 172 of 526 +a0833:= integrate(t0833,x) +--R +--R +--R (161) +--R 3 2 3 - 2b sin(x) - 2a cos(x) +--R - 2b log(----------) + 2b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (a b + a )cos(x)sin(x) + (b + a b)cos(x) + (3a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 172 + +--S 173 of 526 +m0833:= a0833-r0833 +--R +--R +--R (162) +--R 3 3 2 +--R - 2b log(b sin(x) + a cos(x)) - 2b log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2b sin(x) - 2a cos(x) 3 2 +--R 2b log(-----------------------) + b + a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 173 + +--S 174 of 526 +d0833:= D(m0833,x) +--R +--R +--R (163) 0 +--R Type: Expression Integer +--E 174 + +--S 175 of 526 +t0834:= cos(x)/(a*cos(x)+b*sin(x))^2 +--R +--R +--R cos(x) +--R (164) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression Integer +--E 175 + +--S 176 of 526 +r0834:= -a*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-b/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R (a b sin(x) + a cos(x))atanh(-------------------) - b\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (165) --------------------------------------------------------------- +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Expression Integer +--E 176 + +--S 177 of 526 +a0834:= integrate(t0834,x) +--R +--R +--R (166) +--R 2 3 +--R (a b sin(x) + a cos(x)) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R 2 | 2 2 +--R (- b sin(x) - a b cos(x) - a b)\|b + a +--R / +--R +-------+ +--R 3 3 2 2 4 | 2 2 +--R ((a b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Union(Expression Integer,...) +--E 177 + +--S 178 of 526 +m0834:= a0834-r0834 +--R +--R +--R (167) +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R - a atanh(-------------------) - b\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 3 | 2 2 +--R (a b + a )\|b + a +--R Type: Expression Integer +--E 178 + +--S 179 of 526 +d0834:= D(m0834,x) +--R +--R +--R (168) +--R 2 3 2 2 2 2 3 +--R a sin(x) - a b cos(x)sin(x) + (a cos(x) - a )sin(x) - a b cos(x) +--R + +--R a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression Integer +--E 179 + +--S 180 of 526 +t0835:= cos(x)^2/(a*cos(x)+b*sin(x))^2 +--R +--R +--R 2 +--R cos(x) +--R (169) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression Integer +--E 180 + +--S 181 of 526 +r0835:= (a^2-b^2)*x/(a^2+b^2)^2+2*a*b*log(a*cos(x)+b*sin(x))/(a^2+b^2)^2-b/(a^2+b^2)/(a+b*tan(x)) +--R +--R +--R (170) +--R 2 2 3 2 +--R (2a b tan(x) + 2a b)log(b sin(x) + a cos(x)) + (- b + a b)x tan(x) +--R + +--R 2 3 3 2 +--R (- a b + a )x - b - a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)tan(x) + a b + 2a b + a +--R Type: Expression Integer +--E 181 + +--S 182 of 526 +a0835:= integrate(t0835,x) +--R +--R +--R (171) +--R 2 2 3 2 +--R (- 2a b sin(x) - 2a b cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 - 2b sin(x) - 2a cos(x) +--R (2a b sin(x) + 2a b cos(x))log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 3 4 2 2 2 2 4 +--R ((- a b + a b)x + b + a b )sin(x) + (- a b + a )x cos(x) +--R / +--R 5 3 3 5 2 4 4 2 6 +--R (a b + 2a b + a b)sin(x) + (a b + 2a b + a )cos(x) +--R Type: Union(Expression Integer,...) +--E 182 + +--S 183 of 526 +m0835:= a0835-r0835 +--R +--R +--R (172) +--R 2 3 3 2 3 2 4 +--R ((- 2a b sin(x) - 2a b cos(x))tan(x) - 2a b sin(x) - 2a b cos(x)) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 2a b sin(x) - 2a b cos(x))tan(x) - 2a b sin(x) - 2a b cos(x)) +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 3 3 2 3 2 4 +--R ((2a b sin(x) + 2a b cos(x))tan(x) + 2a b sin(x) + 2a b cos(x)) +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 5 2 3 4 3 2 2 3 4 +--R (b + a b )sin(x)tan(x) + (2a b + 2a b )sin(x) + (a b + a b)cos(x) +--R / +--R 6 3 4 5 2 2 5 4 3 6 +--R ((a b + 2a b + a b )sin(x) + (a b + 2a b + a b)cos(x))tan(x) +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (a b + 2a b + a b)sin(x) + (a b + 2a b + a )cos(x) +--R Type: Expression Integer +--E 183 + +--S 184 of 526 +d0835:= D(m0835,x) +--R +--R +--R (173) +--R 3 4 2 2 2 2 +--R (- 2a b cos(x)sin(x) + (b - a b )cos(x) )tan(x) +--R + +--R 3 2 3 2 4 2 2 2 +--R (2a b sin(x) + 2a b cos(x) )tan(x) + (- b + a b )sin(x) +--R + +--R 3 +--R - 2a b cos(x)sin(x) +--R / +--R 6 2 4 2 5 3 3 +--R (b + a b )sin(x) + (2a b + 2a b )cos(x)sin(x) +--R + +--R 2 4 4 2 2 +--R (a b + a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 3 3 2 2 4 4 2 +--R (2a b + 2a b )sin(x) + (4a b + 4a b )cos(x)sin(x) +--R + +--R 3 3 5 2 +--R (2a b + 2a b)cos(x) +--R * +--R tan(x) +--R + +--R 2 4 4 2 2 3 3 5 4 2 6 2 +--R (a b + a b )sin(x) + (2a b + 2a b)cos(x)sin(x) + (a b + a )cos(x) +--R Type: Expression Integer +--E 184 + +--S 185 of 526 +t0836:= cos(x)/(a*cos(x)+b*sin(x))^3 +--R +--R +--R cos(x) +--R (174) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression Integer +--E 185 + +--S 186 of 526 +r0836:= -1/2*b/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+sin(x)/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R (175) +--R 2 +--R 2b sin(x) + 2a cos(x)sin(x) - b +--R ------------------------------------------------------------------------ +--R 4 2 2 2 3 3 2 2 4 2 +--R (2b + 2a b )sin(x) + (4a b + 4a b)cos(x)sin(x) + (2a b + 2a )cos(x) +--R Type: Expression Integer +--E 186 + +--S 187 of 526 +a0836:= integrate(t0836,x) +--R +--R +--R 2 +--R 2a cos(x)sin(x) - b cos(x) + b +--R (176) -------------------------------------------------- +--R 3 2 2 4 2 2 2 +--R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b +--R Type: Union(Expression Integer,...) +--E 187 + +--S 188 of 526 +m0836:= a0836-r0836 +--R +--R +--R (177) +--R 4 3 2 3 +--R (2a b - 2a b )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 2 +--R ((- b + 5a b - 2a b)cos(x) + b - a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 +--R ((- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x))sin(x) +--R + +--R 2 3 4 4 4 2 2 3 +--R (- a b - a b)cos(x) + 2a b cos(x) + a b +--R / +--R 3 5 5 3 3 +--R (4a b + 4a b )cos(x)sin(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 2 +--R ((- 2a b + 8a b + 10a b )cos(x) + 2a b + 2a b )sin(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 +--R ((- 4a b + 4a b + 8a b)cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 4 4 8 4 4 4 6 2 2 +--R (- 2a b + 2a )cos(x) + (2a b + 2a b )cos(x) +--R Type: Expression Integer +--E 188 + +--S 189 of 526 +d0836:= D(m0836,x) +--R +--R +--R (178) +--R 5 3 3 2 5 +--R (a b - 3a b )cos(x) sin(x) +--R + +--R 2 4 4 2 3 6 2 4 4 +--R ((7a b - 5a b )cos(x) + (b - 3a b )cos(x))sin(x) +--R + +--R 3 3 5 4 5 3 3 2 5 3 +--R ((6a b - 2a b)cos(x) + (5a b + a b )cos(x) - a b )sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 3 2 4 2 +--R ((6a b - 2a b )cos(x) + (- 7a b + 5a b )cos(x) + 3a b cos(x))sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 4 +--R (- a b + 9a b - 2a b)cos(x) + (7a b - 11a b + 2a b)cos(x) +--R + +--R 5 3 3 2 5 +--R (- 7a b + 2a b )cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 7 6 2 4 4 2 5 +--R (- a b + 3a b )cos(x) + (- b + 4a b - 3a b )cos(x) +--R + +--R 6 2 4 3 6 +--R (2b - 3a b )cos(x) - b cos(x) +--R / +--R 2 7 4 5 2 5 +--R (4a b + 4a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 3 8 3 6 4 +--R ((- 4a b + 12a b + 16a b )cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 9 2 7 4 5 6 3 4 +--R (b - 13a b + 11a b + 25a b )cos(x) +--R + +--R 9 2 7 4 5 2 9 2 7 +--R (- 2b + 12a b + 14a b )cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 15a b + a b + 19a b )cos(x) +--R + +--R 8 3 6 5 4 3 8 3 6 +--R (- 6a b + 12a b + 18a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (3a b - 7a b - 3a b + 7a b)cos(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 2 +--R (- 6a b + 4a b + 10a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 7 3 6 7 2 5 +--R (a b - a b - a b + a )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 3 +--R (a b + a b )cos(x) +--R Type: Expression Integer +--E 189 + +--S 190 of 526 +t0837:= cos(x)^3/(a*cos(x)+b*sin(x))^3 +--R +--R +--R 3 +--R cos(x) +--R (179) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression Integer +--E 190 + +--S 191 of 526 +r0837:= (a^3*x-3*a*b^2*x)/(a^2+b^2)^3+b*(3*a^2-b^2)*log(a*cos(x)+b*sin(x))/(a^2+b^2)^3-1/2*b/(a^2+b^2)/(a+b*tan(x))^2-2*a*b/(a^2+b^2)^2/(a+b*tan(x)) +--R +--R +--R (180) +--R 5 2 3 2 4 3 2 2 3 4 +--R ((- 2b + 6a b )tan(x) + (- 4a b + 12a b )tan(x) - 2a b + 6a b) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b + 2a b )x tan(x) + ((- 12a b + 4a b)x - 4a b - 4a b )tan(x) +--R + +--R 3 2 5 5 2 3 4 +--R (- 6a b + 2a )x - b - 6a b - 5a b +--R / +--R 8 2 6 4 4 6 2 2 +--R (2b + 6a b + 6a b + 2a b )tan(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 8 +--R (4a b + 12a b + 12a b + 4a b)tan(x) + 2a b + 6a b + 6a b + 2a +--R Type: Expression Integer +--E 191 + +--S 192 of 526 +a0837:= integrate(t0837,x) +--R +--R +--R (181) +--R 3 4 5 2 2 5 4 3 6 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b)cos(x) +--R + +--R 2 5 4 3 +--R 2a b - 6a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 4 5 2 2 5 4 3 6 2 +--R (- 4a b + 12a b )cos(x)sin(x) + (2a b - 8a b + 6a b)cos(x) +--R + +--R 2 5 4 3 +--R - 2a b + 6a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 4 3 6 6 3 4 5 2 +--R ((- 12a b + 4a b)x + 2a b + 8a b + 6a b )cos(x)sin(x) +--R + +--R 3 4 5 2 7 7 2 5 4 3 2 3 4 5 2 +--R ((6a b - 8a b + 2a )x - b - 6a b - 5a b )cos(x) + (- 6a b + 2a b )x +--R + +--R 7 2 5 4 3 +--R b + 6a b + 5a b +--R / +--R 3 7 5 5 7 3 9 +--R (4a b + 12a b + 12a b + 4a b)cos(x)sin(x) +--R + +--R 2 8 4 6 8 2 10 2 2 8 4 6 6 4 8 2 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) + 2a b + 6a b + 6a b + 2a b +--R Type: Union(Expression Integer,...) +--E 192 + +--S 193 of 526 +m0837:= a0837-r0837 +--R +--R +--R (182) +--R 3 6 5 4 2 7 4 5 6 3 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b )cos(x) +--R + +--R 2 7 4 5 +--R 2a b - 6a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 5 6 3 3 6 5 4 7 2 2 +--R (8a b - 24a b )cos(x)sin(x) + (- 4a b + 16a b - 12a b )cos(x) +--R + +--R 3 6 5 4 +--R 4a b - 12a b +--R * +--R tan(x) +--R + +--R 5 4 7 2 4 5 6 3 8 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b)cos(x) +--R + +--R 4 5 6 3 +--R 2a b - 6a b +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 3 6 5 4 2 7 4 5 6 3 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b )cos(x) +--R + +--R 2 7 4 5 +--R 2a b - 6a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 5 6 3 3 6 5 4 7 2 2 +--R (8a b - 24a b )cos(x)sin(x) + (- 4a b + 16a b - 12a b )cos(x) +--R + +--R 3 6 5 4 +--R 4a b - 12a b +--R * +--R tan(x) +--R + +--R 5 4 7 2 4 5 6 3 8 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b)cos(x) +--R + +--R 4 5 6 3 +--R 2a b - 6a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 6 5 4 2 7 4 5 6 3 2 +--R (- 4a b + 12a b )cos(x)sin(x) + (2a b - 8a b + 6a b )cos(x) +--R + +--R 2 7 4 5 +--R - 2a b + 6a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 5 6 3 3 6 5 4 7 2 2 +--R (- 8a b + 24a b )cos(x)sin(x) + (4a b - 16a b + 12a b )cos(x) +--R + +--R 3 6 5 4 +--R - 4a b + 12a b +--R * +--R tan(x) +--R + +--R 5 4 7 2 4 5 6 3 8 2 +--R (- 4a b + 12a b )cos(x)sin(x) + (2a b - 8a b + 6a b)cos(x) +--R + +--R 4 5 6 3 +--R - 2a b + 6a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 8 3 6 5 4 9 2 7 4 5 2 +--R (2a b + 8a b + 6a b )cos(x)sin(x) + (- b - 6a b - 5a b )cos(x) +--R + +--R 9 2 7 4 5 +--R b + 6a b + 5a b +--R * +--R 2 +--R tan(x) +--R + +--R 2 7 4 5 6 3 +--R (4a b + 24a b + 20a b )cos(x)sin(x) +--R + +--R 8 3 6 5 4 7 2 2 8 3 6 5 4 +--R (- 2a b - 16a b - 10a b + 4a b )cos(x) + 2a b + 16a b + 14a b +--R * +--R tan(x) +--R + +--R 3 6 5 4 7 2 +--R (4a b + 20a b + 16a b )cos(x)sin(x) +--R + +--R 2 7 4 5 6 3 8 2 2 7 4 5 6 3 +--R (- 2a b - 11a b - 4a b + 5a b)cos(x) + 2a b + 12a b + 10a b +--R / +--R 3 9 5 7 7 5 9 3 +--R (4a b + 12a b + 12a b + 4a b )cos(x)sin(x) +--R + +--R 2 10 4 8 8 4 10 2 2 2 10 4 8 6 6 +--R (- 2a b - 4a b + 4a b + 2a b )cos(x) + 2a b + 6a b + 6a b +--R + +--R 8 4 +--R 2a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 8 6 6 8 4 10 2 +--R (8a b + 24a b + 24a b + 8a b )cos(x)sin(x) +--R + +--R 3 9 5 7 9 3 11 2 3 9 5 7 7 5 +--R (- 4a b - 8a b + 8a b + 4a b)cos(x) + 4a b + 12a b + 12a b +--R + +--R 9 3 +--R 4a b +--R * +--R tan(x) +--R + +--R 5 7 7 5 9 3 11 +--R (4a b + 12a b + 12a b + 4a b)cos(x)sin(x) +--R + +--R 4 8 6 6 10 2 12 2 4 8 6 6 8 4 10 2 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) + 2a b + 6a b + 6a b + 2a b +--R Type: Expression Integer +--E 193 + +--S 194 of 526 +d0837:= D(m0837,x) +--R +--R +--R (183) +--R 7 3 5 2 7 2 +--R ((3a b - 5a b )cos(x) + 2a b )sin(x) +--R + +--R 2 6 4 4 3 8 2 6 +--R ((8a b - 8a b )cos(x) + (b - 3a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 4 7 3 5 2 7 +--R (a b + 7a b - 2a b )cos(x) + (2a b - 4a b )cos(x) - 2a b +--R * +--R 3 +--R tan(x) +--R + +--R 2 6 4 4 2 2 6 2 +--R ((5a b - 3a b )cos(x) + 6a b )sin(x) +--R + +--R 7 3 5 5 3 3 7 3 5 +--R ((4a b + 8a b - 12a b )cos(x) + (- a b + 3a b )cos(x))sin(x) +--R + +--R 8 2 6 4 4 6 2 4 8 2 6 4 4 2 +--R (- b + 8a b + 14a b - 3a b )cos(x) + (2b - 2a b - 6a b )cos(x) +--R + +--R 8 2 6 +--R - b - 3a b +--R * +--R 2 +--R tan(x) +--R + +--R 3 5 5 3 2 3 5 2 +--R ((a b + 9a b )cos(x) + 6a b )sin(x) +--R + +--R 2 6 4 4 3 2 6 4 4 +--R ((8a b - 8a b )cos(x) + (- 5a b + 15a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 4 7 3 5 2 7 +--R (- 2a b + 13a b + 7a b )cos(x) + (4a b - 10a b )cos(x) - 2a b +--R * +--R tan(x) +--R + +--R 2 6 4 4 6 2 2 4 4 2 +--R ((- 4a b - 9a b + 3a b )cos(x) + 2a b )sin(x) +--R + +--R 7 3 5 5 3 3 7 3 5 5 3 +--R ((4a b + 8a b - 12a b )cos(x) + (- 4a b - 11a b + 5a b )cos(x)) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 4 8 2 6 4 4 2 8 2 6 +--R (- b - a b + 8a b )cos(x) + (2b + 4a b - 8a b )cos(x) - b - 3a b +--R / +--R 2 9 4 7 6 5 2 2 +--R (4a b + 8a b + 4a b )cos(x) sin(x) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 4a b - 4a b + 4a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 11 4 7 8 3 4 11 2 9 4 7 6 5 2 +--R (b - 2a b + a b )cos(x) + (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 11 2 9 4 7 +--R b + 2a b + a b +--R * +--R 3 +--R tan(x) +--R + +--R 3 8 5 6 7 4 2 2 +--R (12a b + 24a b + 12a b )cos(x) sin(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 2 9 4 7 6 5 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 10 5 6 9 2 4 +--R (3a b - 6a b + 3a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 2 10 3 8 5 6 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 7 6 5 8 3 2 2 +--R (12a b + 24a b + 12a b )cos(x) sin(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 3 8 5 6 7 4 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 9 6 5 10 4 +--R (3a b - 6a b + 3a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 2 9 4 7 6 5 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R tan(x) +--R + +--R 5 6 7 4 9 2 2 2 +--R (4a b + 8a b + 4a b )cos(x) sin(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (- 4a b - 4a b + 4a b + 4a b)cos(x) +--R + +--R 4 7 6 5 8 3 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 8 7 4 11 4 3 8 5 6 7 4 9 2 2 +--R (a b - 2a b + a )cos(x) + (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 +--R a b + 2a b + a b +--R Type: Expression Integer +--E 194 + +--S 195 of 526 +t0838:= tan(x)/(b*cos(x)+a*sin(x)) +--R +--R +--R tan(x) +--R (184) ------------------- +--R a sin(x) + b cos(x) +--R Type: Expression Integer +--E 195 + +--S 196 of 526 +r0838:= atanh(sin(x))/a+b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/a/(a^2+b^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R \|b + a atanh(sin(x)) - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (185) ------------------------------------------------------ +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression Integer +--E 196 + +--S 197 of 526 +a0838:= integrate(t0838,x) +--R +--R +--R (186) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Union(Expression Integer,...) +--E 197 + +--S 198 of 526 +m0838:= a0838-r0838 +--R +--R +--R (187) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R - \|b + a atanh(sin(x)) + b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression Integer +--E 198 + +--S 199 of 526 +d0838:= D(m0838,x) +--R +--R +--R (188) +--R 5 2 3 8 4 3 2 4 3 2 7 +--R (b - a b )sin(x) + ((- 4a b + 4a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 5 2 3 +--R (5a b - 5a b)cos(x) + (- 4a b - 3a b)cos(x) - 3b + a b +--R + +--R 4 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 5 3 4 3 2 5 2 +--R (- 2a b + 2a )cos(x) + (a b + 7a b + 2a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (13a b + 3a b - 2a )cos(x) - a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 4a b)cos(x) + (- 2a b - 7a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 5 2 3 4 +--R (b - 12a b - a b)cos(x) + a b cos(x) + 3b + a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 5 3 2 5 4 +--R (2a b - 4a b + 2a )cos(x) + (3a b + 3a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (3a b + 8a b - 3a )cos(x) + (- 4a b - 13a b - 5a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (- 14a b - 13a b + a )cos(x) - a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- a b + a b)cos(x) + (2a b - 3a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (2b - 3a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 2 3 +--R (- 2b + 8a b + 10a b)cos(x) + (4a b + 4a b)cos(x) - b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 5 +--R (- 3a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 4a b - 2a b - 2a )cos(x) + (- a b - 3a b - 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (3a b + 4a b + a )cos(x) + (5a b + 6a b + a )cos(x) + a b +--R + +--R 3 2 +--R a b +--R * +--R sin(x) +--R + +--R 4 7 2 3 4 6 2 3 4 5 +--R a b cos(x) + (2a b + 2a b)cos(x) + (2a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 3 +--R (- b - a b )cos(x) + (- a b - a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (b - a b - 2a b)cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 3 3 8 +--R (- a b - a b )sin(x) +--R + +--R 6 2 4 4 2 6 4 2 7 +--R ((- 2b + 2a b + 4a b )cos(x) - b + a b )sin(x) +--R + +--R 5 3 3 5 2 3 3 5 5 3 3 +--R (4a b - a b - 5a b)cos(x) + (- 3a b - 3a b)cos(x) + a b + 3a b +--R + +--R 5 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 6 3 +--R (- 2b - 2a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- b + 4a b + 7a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (6b + 9a b + a b - 2a )cos(x) + 3b + 2a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b + a b - 4a b)cos(x) + (2a b - 5a b - 7a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 3 3 +--R (- 7a b - 8a b - a b)cos(x) + (- a b - a b )cos(x) + a b - a b +--R + +--R 5 +--R - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (- 4a b - 2a b + 2a )cos(x) + (a b + 4a b + 3a )cos(x) +--R + +--R 6 2 4 4 2 6 3 +--R (4b + 11a b + 4a b - 3a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (2b - 7a b - 14a b - 5a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (- 6b - 18a b - 11a b + a )cos(x) - 3b - 4a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (a b + a b)cos(x) + (2a b - a b - 3a b)cos(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 2a b - 9a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 5 +--R (4a b + 14a b + 10a b)cos(x) + (2a b + 6a b + 4a b)cos(x) - a b +--R + +--R 3 3 +--R - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b - 2a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 2 4 4 2 6 4 6 2 4 4 2 6 3 +--R (- 2a b - 4a b - 2a )cos(x) + (- 2b - 3a b - 3a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- b + 3a b + 5a b + a )cos(x) + (2b + 7a b + 6a b + a )cos(x) +--R + +--R 6 2 4 4 2 +--R b + 2a b + a b +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 3 3 5 5 +--R (a b + a b)cos(x) + (2a b + 2a b)cos(x) + (a b + a b)cos(x) +--R + +--R 5 3 3 4 5 5 3 +--R (a b + a b )cos(x) + (a b - a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b - 3a b - 2a b)cos(x) + (- a b - 2a b - a b)cos(x) +--R / +--R 3 3 8 2 4 4 2 2 4 4 2 7 +--R a b sin(x) + ((a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 3 3 5 2 5 3 3 5 3 3 +--R (- 4a b + 3a b)cos(x) + (- a b - a b + 2a b)cos(x) - 3a b +--R + +--R 5 +--R - a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- a b + 6a b - a )cos(x) + (a b + 8a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b + 8a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (3a b - 4a b)cos(x) + (a b + 4a b - 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (2a b + 7a b - 8a b)cos(x) + (3a b + 4a b - a b)cos(x) +--R + +--R 3 3 5 +--R 3a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (- 3a b + a )cos(x) + (- 2a b - 7a b + 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- 2a b - 11a b + 3a )cos(x) + (- 2a b - 11a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b - 9a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R a b cos(x) + (a b + 3a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (- 2a b - 7a b + 7a b)cos(x) + (- 4a b - 8a b + 2a b)cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (- 3a b - 5a b - 2a b)cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (3a b - a )cos(x) + (2a b + 7a b - 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (3a b + 5a b - 2a )cos(x) + (a b + 3a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (a b + 4a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R - a b cos(x) + (- a b - 3a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (a b + 3a b + 2a b)cos(x) + (2a b + 5a b + 3a b)cos(x) +--R + +--R 5 3 3 5 +--R (a b + 2a b + a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 5 4 3 8 +--R (a b + a b )sin(x) +--R + +--R 6 3 4 5 2 3 4 5 2 7 +--R ((a b - 2a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 4a b - a b + 3a b)cos(x) + (- 3a b - a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - 3a b - 4a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 5a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + 7a b + 8a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 3a b + 5a b + 9a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (3a b - a b - 4a b)cos(x) + (7a b - 2a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 2 5 +--R (11a b + 3a b - 8a b)cos(x) + (7a b + 6a b - a b)cos(x) + 3a b +--R + +--R 4 3 6 +--R 5a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (- 3a b - 2a b + a )cos(x) + (- 8a b - 5a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (2a b - 11a b - 10a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (4a b - 8a b - 13a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (3a b - 4a b - 11a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (a b + a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 6a b)cos(x) + (- 10a b - 3a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 10a b - 8a b + 2a b)cos(x) + (- 5a b - 7a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - a b - 2a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (3a b + 2a b - a )cos(x) + (8a b + 5a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 6a b + 5a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + a b + 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- a b + a b + 5a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- a b - a b)cos(x) + (- 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b - a b - 2a b)cos(x) + (3a b + 5a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (3a b + 6a b + 3a b)cos(x) + (a b + 2a b + a b)cos(x) +--R Type: Expression Integer +--E 199 + +--S 200 of 526 +t0839:= sec(x)/(sec(x)-tan(x)) +--R +--R +--R sec(x) +--R (189) - --------------- +--R tan(x) - sec(x) +--R Type: Expression Integer +--E 200 + +--S 201 of 526 +r0839:= (1+sin(x))/cos(x) +--R +--R +--R sin(x) + 1 +--R (190) ---------- +--R cos(x) +--R Type: Expression Integer +--E 201 + +--S 202 of 526 +a0839:= integrate(t0839,x) +--R +--R +--R - 2cos(x) - 2 +--R (191) ------------------- +--R sin(x) - cos(x) - 1 +--R Type: Union(Expression Integer,...) +--E 202 + +--S 203 of 526 +m0839:= a0839-r0839 +--R +--R +--R 2 2 +--R - sin(x) + cos(x)sin(x) - 2cos(x) - cos(x) + 1 +--R (192) ------------------------------------------------ +--R 2 +--R cos(x)sin(x) - cos(x) - cos(x) +--R Type: Expression Integer +--E 203 + +--S 204 of 526 +d0839:= D(m0839,x) +--R +--R +--R (193) +--R 4 3 2 +--R - sin(x) + (2cos(x) + 1)sin(x) + sin(x) +--R + +--R 3 2 4 2 +--R (2cos(x) + cos(x) - 2cos(x) - 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 3 2 4 3 +--R cos(x) sin(x) + (- 2cos(x) - 2cos(x) )sin(x) + cos(x) + 2cos(x) +--R + +--R 2 +--R cos(x) +--R Type: Expression Integer +--E 204 + +--S 205 of 526 +t0840:= tan(x)/(csc(x)+cot(x)) +--R +--R +--R tan(x) +--R (194) --------------- +--R csc(x) + cot(x) +--R Type: Expression Integer +--E 205 + +--S 206 of 526 +r0840:= -x+atanh(sin(x)) +--R +--R +--R (195) atanh(sin(x)) - x +--R Type: Expression Integer +--E 206 + +--S 207 of 526 +a0840:= integrate(t0840,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (196) log(-------------------) - log(-------------------) - x +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 207 + +--S 208 of 526 +m0840:= a0840-r0840 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (197) log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression Integer +--E 208 + +--S 209 of 526 +d0840:= D(m0840,x) +--R +--R +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (198) ------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression Integer +--E 209 + +--S 210 of 526 +t0841:= tan(x)/(csc(x)-cot(x)) +--R +--R +--R tan(x) +--R (199) --------------- +--R csc(x) - cot(x) +--R Type: Expression Integer +--E 210 + +--S 211 of 526 +r0841:= x+atanh(sin(x)) +--R +--R +--R (200) atanh(sin(x)) + x +--R Type: Expression Integer +--E 211 + +--S 212 of 526 +a0841:= integrate(t0841,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (201) log(-------------------) - log(-------------------) + x +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 212 + +--S 213 of 526 +m0841:= a0841-r0841 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (202) log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression Integer +--E 213 + +--S 214 of 526 +d0841:= D(m0841,x) +--R +--R +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (203) ------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression Integer +--E 214 + +--S 215 of 526 +t0842:= cos(x)*sin(x)/(a*cos(x)+b*sin(x)) +--R +--R +--R cos(x)sin(x) +--R (204) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 215 + +--S 216 of 526 +r0842:= a*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-a*cos(x)/(a^2+b^2)+b*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R a sin(x) - b cos(x) | 2 2 +--R - a b atanh(-------------------) + (b sin(x) - a cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (205) ------------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 216 + +--S 217 of 526 +a0842:= integrate(t0842,x) +--R +--R +--R (206) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) - a cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression Integer,...) +--E 217 + +--S 218 of 526 +m0842:= a0842-r0842 +--R +--R +--R (207) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R a sin(x) - b cos(x) +--R a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 218 + +--S 291 of 526 +d0842:= D(m0842,x) +--R +--R +--R (208) +--R 2 3 2 2 2 2 2 +--R a b sin(x) - a b cos(x)sin(x) + (a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 +--R - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression Integer +--E 291 + +--S 220 of 526 +t0843:= cos(x)*sin(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R cos(x)sin(x) +--R (209) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 220 + +--S 221 of 526 +r0843:= 1/2/(a^2+b^2)^2*(a^3*x-a*b^2*x+2*a^2*b*log(a*cos(x)+b*sin(x))-cos(x)*sin(x)*a^3-cos(x)*sin(x)*b^2*a-b*cos(x)^2*a^2+a^2*b-b^3*cos(x)^2+b^3) +--R +--R +--R (210) +--R 2 2 3 +--R 2a b log(b sin(x) + a cos(x)) + (- a b - a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b - a b)cos(x) + (- a b + a )x + b + a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 221 + +--S 222 of 526 +a0843:= integrate(t0843,x) +--R +--R +--R (211) +--R 2 2 2 - 2b sin(x) - 2a cos(x) +--R - 2a b log(----------) + 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (- a b - a )cos(x)sin(x) + (- b - a b)cos(x) + (- a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 222 + +--S 223 of 526 +m0843:= a0843-r0843 +--R +--R +--R (212) +--R 2 2 2 +--R - 2a b log(b sin(x) + a cos(x)) - 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2b sin(x) - 2a cos(x) 3 2 +--R 2a b log(-----------------------) - b - a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 223 + +--S 224 of 526 +d0843:= D(m0843,x) +--R +--R +--R (213) 0 +--R Type: Expression Integer +--E 224 + +--S 225 of 526 +t0844:= cos(x)*sin(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R cos(x)sin(x) +--R (214) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 225 + +--S 226 of 526 +r0844:= a^3*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-a^3*cos(x)/(a^2+b^2)^2+a*cos(x)^3/(3*a^2+3*b^2)-a^4*sin(x)/b/(a^2+b^2)^2+a^2*sin(x)/b/(a^2+b^2)+b*sin(x)^3/(3*a^2+3*b^2) +--R +--R +--R (215) +--R 3 a sin(x) - b cos(x) +--R - 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 3 3 +--R ((b + a b)sin(x) + 3a b sin(x) + (a b + a )cos(x) - 3a cos(x)) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 226 + +--S 227 of 526 +a0844:= integrate(t0844,x) +--R +--R +--R (216) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((- b - a b)cos(x) + b + 4a b)sin(x) + (a b + a )cos(x) +--R + +--R 3 +--R - 3a cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression Integer,...) +--E 227 + +--S 228 of 526 +m0844:= a0844-r0844 +--R +--R +--R (217) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 a sin(x) - b cos(x) +--R 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 3 2 3 3 2 2 3 2 | 2 2 +--R ((- b - a b)sin(x) + ((- b - a b)cos(x) + b + a b)sin(x))\|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 228 + +--S 229 of 526 +d0844:= D(m0844,x) +--R +--R +--R (218) +--R 4 3 3 2 2 4 2 4 +--R 3a b sin(x) - 3a b cos(x)sin(x) + (3a b cos(x) - 3a b)sin(x) +--R + +--R 3 2 3 3 2 +--R - 3a b cos(x) + 3a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 4 2 5 5 3 3 5 2 4 +--R (- a b - a b )cos(x)sin(x) + (2a b + a b - a b)cos(x) sin(x) +--R + +--R 6 4 2 3 6 2 4 4 2 3 +--R ((- b + a b )cos(x) + (b + 3a b + 2a b )cos(x))sin(x) +--R + +--R 5 5 4 5 3 3 5 2 2 +--R ((a b - a b)cos(x) + (- a b + a b + 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 3 +--R (- b + a b + 2a b )cos(x) + (2b + a b - a b )cos(x) +--R + +--R 6 2 4 4 2 +--R (- b - 2a b - a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 4 +--R (- a b - a b )cos(x) + (2a b + 3a b + a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- a b - 2a b - a b)cos(x) +--R / +--R 2 5 4 3 6 3 6 3 4 7 2 +--R (3a b + 6a b + 3a b)sin(x) + (- 6a b - 9a b + 3a )cos(x)sin(x) +--R + +--R 7 4 3 6 2 7 2 5 4 3 6 +--R ((3b - 9a b - 6a b)cos(x) - 3b - 9a b - 9a b - 3a b)sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 7 +--R (3a b + 6a b + 3a b )cos(x) + (- 3a b - 9a b - 9a b - 3a )cos(x) +--R Type: Expression Integer +--E 229 + +--S 230 of 526 +t0845:= sin(x)*cos(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R cos(x) sin(x) +--R (219) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 230 + +--S 231 of 526 +r0845:= -1/2*(-b^3*x+a^2*b*x+2*a*b^2*log(a*cos(x)+b*sin(x))-a^2*b*sin(x)*cos(x)-b^3*sin(x)*cos(x)+cos(x)^2*a^3-a^3+b^2*a*cos(x)^2-b^2*a)/(a^2+b^2)^2 +--R +--R +--R (220) +--R 2 3 2 +--R - 2a b log(b sin(x) + a cos(x)) + (b + a b)cos(x)sin(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- a b - a )cos(x) + (b - a b)x + a b + a +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 231 + +--S 232 of 526 +a0845:= integrate(t0845,x) +--R +--R +--R (221) +--R 2 2 2 - 2b sin(x) - 2a cos(x) +--R 2a b log(----------) - 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 2 2 3 2 3 2 +--R (b + a b)cos(x)sin(x) + (- a b - a )cos(x) + (b - a b)x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 232 + +--S 233 of 526 +m0845:= a0845-r0845 +--R +--R +--R (222) +--R 2 2 2 +--R 2a b log(b sin(x) + a cos(x)) + 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2b sin(x) - 2a cos(x) 2 3 +--R - 2a b log(-----------------------) - a b - a +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 233 + +--S 234 of 526 +d0845:= D(m0845,x) +--R +--R +--R (223) 0 +--R Type: Expression Integer +--E 234 + +--S 235 of 526 +t0846:= sin(x)*cos(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R cos(x) sin(x) +--R (224) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression Integer +--E 235 + +--S 236 of 526 +r0846:= a*b^3*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-a*b^2*cos(x)/(a^2+b^2)^2-a*cos(x)^3/(3*a^2+3*b^2)-a^2*b*sin(x)/(a^2+b^2)^2+b*sin(x)/(a^2+b^2)-b*sin(x)^3/(3*a^2+3*b^2) +--R +--R +--R (225) +--R 3 a sin(x) - b cos(x) +--R - 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 3 2 3 3 2 +--R ((- b - a b)sin(x) + 3b sin(x) + (- a b - a )cos(x) - 3a b cos(x)) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 236 + +--S 237 of 526 +a0846:= integrate(t0846,x) +--R +--R +--R (226) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((b + a b)cos(x) + 2b - a b)sin(x) + (- a b - a )cos(x) +--R + +--R 2 +--R - 3a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression Integer,...) +--E 237 + +--S 238 of 526 +m0846:= a0846-r0846 +--R +--R +--R (227) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 a sin(x) - b cos(x) +--R 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 3 2 3 3 2 2 3 2 | 2 2 +--R ((b + a b)sin(x) + ((b + a b)cos(x) - b - a b)sin(x))\|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 238 + +--S 239 of 526 +d0846:= D(m0846,x) +--R +--R +--R (228) +--R 2 3 3 4 2 2 3 2 2 3 +--R 3a b sin(x) - 3a b cos(x)sin(x) + (3a b cos(x) - 3a b )sin(x) +--R + +--R 4 3 4 +--R - 3a b cos(x) + 3a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 4 2 5 5 3 3 5 2 4 +--R (a b + a b )cos(x)sin(x) + (- 2a b - a b + a b)cos(x) sin(x) +--R + +--R 6 4 2 3 6 2 4 4 2 3 +--R ((b - a b )cos(x) + (- b - 3a b - 2a b )cos(x))sin(x) +--R + +--R 5 5 4 5 3 3 5 2 2 +--R ((- a b + a b)cos(x) + (a b - a b - 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 3 +--R (b - a b - 2a b )cos(x) + (- 2b - a b + a b )cos(x) +--R + +--R 6 2 4 4 2 +--R (b + 2a b + a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 4 +--R (a b + a b )cos(x) + (- 2a b - 3a b - a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (a b + 2a b + a b)cos(x) +--R / +--R 2 5 4 3 6 3 6 3 4 7 2 +--R (3a b + 6a b + 3a b)sin(x) + (- 6a b - 9a b + 3a )cos(x)sin(x) +--R + +--R 7 4 3 6 2 7 2 5 4 3 6 +--R ((3b - 9a b - 6a b)cos(x) - 3b - 9a b - 9a b - 3a b)sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 7 +--R (3a b + 6a b + 3a b )cos(x) + (- 3a b - 9a b - 9a b - 3a )cos(x) +--R Type: Expression Integer +--E 239 + +--S 240 of 526 +t0847:= sec(x)^2/(a+b*tan(x)+c*sec(x)) +--R +--R +--R 2 +--R sec(x) +--R (229) ----------------------- +--R b tan(x) + c sec(x) + a +--R Type: Expression Integer +--E 240 + +--S 241 of 526 +r0847:= -2*a*c*atanh((b-(a-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/(b^2-c^2)/(a^2+b^2-c^2)^(1/2)-log(1-tan(1/2*x))/(b+c)-log(1+tan(1/2*x))/(b-c)+b*log(a+c+2*b*tan(1/2*x)-(a-c)*tan(1/2*x)^2)/(b^2-c^2) +--R +--R +--R (230) +--R +--------------+ +--R | 2 2 2 x 2 x +--R - b\|- c + b + a log((c - a)tan(-) + 2b tan(-) + c + a) +--R 2 2 +--R + +--R +--------------+ +--R | 2 2 2 x +--R (c + b)\|- c + b + a log(tan(-) + 1) +--R 2 +--R + +--R x +--R +--------------+ (c - a)tan(-) + b +--R | 2 2 2 x 2 +--R (- c + b)\|- c + b + a log(- tan(-) + 1) + 2a c atanh(-----------------) +--R 2 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression Integer +--E 241 + +--S 242 of 526 +a0847:= integrate(t0847,x) +--R +--R +--R (231) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (b c - a b)sin(x) + (- c + a c + b )cos(x) - a c + b +--R + +--R 2 +--R a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 2 3 +--R (- c + a c + (b + a )c - a b - a )sin(x) +--R + +--R 2 3 2 2 3 2 +--R (- b c + b + a b)cos(x) - b c + b + a b +--R / +--R b sin(x) + a cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R , +--R +--R +------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R ((c - a)sin(x) + b cos(x) + b)\|c - b - a +--R - 2a c atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 242 + +--S 243 of 526 +m0847a:= a0847.1-r0847 +--R +--R +--R (232) +--R a c +--R * +--R log +--R 2 2 2 2 +--R ((b c - a b)sin(x) + (- c + a c + b )cos(x) - a c + b + a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 2 3 +--R (- c + a c + (b + a )c - a b - a )sin(x) +--R + +--R 2 3 2 2 3 2 +--R (- b c + b + a b)cos(x) - b c + b + a b +--R / +--R b sin(x) + a cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 x 2 x +--R b\|- c + b + a log((c - a)tan(-) + 2b tan(-) + c + a) +--R 2 2 +--R + +--R +--------------+ +--R | 2 2 2 x +--R (- c - b)\|- c + b + a log(tan(-) + 1) +--R 2 +--R + +--R +--------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R + +--R x +--R +--------------+ (c - a)tan(-) + b +--R | 2 2 2 x 2 +--R (c - b)\|- c + b + a log(- tan(-) + 1) - 2a c atanh(-----------------) +--R 2 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression Integer +--E 243 + +--S 244 of 526 +d0847a:= D(m0847a,x) +--R +--R +--R (233) +--R 3 2 3 2 3 5 +--R (b c - 2a b c + a b )sin(x) +--R + +--R 2 2 3 2 3 2 2 2 4 +--R (- 2b + a )c + (6a b - 2a )c + (- 6a b + a )c +--R + +--R 3 2 +--R 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 4 +--R a c - 2a c + a c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R b c - 6a b c + (2b + 9a b)c + (- 2a b - 4a b)c - b +--R + +--R 2 3 +--R a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 3 5 4 4 +--R (- b c + (2b + a b)c + 2a b c - 2b - 2a b)cos(x) - b c +--R + +--R 3 2 2 3 3 5 2 3 4 +--R 2a b c - 2a b c + (2a b + 2a b)c - b - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 +--R a c + (- 5b - 3a )c + (11a b + 2a )c +--R + +--R 4 2 2 4 3 2 +--R (3b - 7a b )c - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R c - a c + (- 7b - 4a )c + (11a b + 4a )c +--R + +--R 4 2 2 4 3 2 +--R (7b + a b )c - 10a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R c - a c + (- 3b - 5a )c + (a b + 6a )c +--R + +--R 4 2 2 4 4 3 2 +--R (5b + 11a b - a )c - 8a b - 6a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 4 +--R a c + (- b - 4a )c + (a b + 4a )c + (b + 3a b - a )c +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 +--R 3b c - 10a b c + (- 3b + 11a b)c + (4a b - 4a b)c +--R + +--R 5 2 3 +--R b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R b c - 4a b c + (- 6b + 3a b)c + (4a b + 2a b)c + 4b +--R + +--R 2 3 4 +--R - 2a b - 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 2 2 +--R - 6b c + 16a b c + (- 2b - 15a b)c +--R + +--R 3 3 5 2 3 4 +--R (- 8a b + 6a b)c + 6b + 4a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 +--R - 5b c + 12a b c + (2b - 7a b)c + (- 12a b - 2a b)c +--R + +--R 5 2 3 4 +--R 4b + 6a b + 2a b +--R * +--R cos(x) +--R + +--R 4 3 3 2 3 3 5 2 3 4 +--R - b c + 2a b c + b c + (- 4a b - 2a b)c + b + 2a b + a b +--R * +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 4 +--R (3a c + (- b - 6a )c + (- a b + 4a )c + (b + a b - a )c) +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 3c + a c + (- 7b - 7a )c + (- a b + 4a )c +--R + +--R 4 2 2 4 +--R (5b + 3a b - a )c +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 7c - 6a c + (- 16b + 2a )c + (2a b - 4a )c +--R + +--R 4 2 2 4 +--R (10b + 4a b + a )c +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 3 2 3 2 4 2 2 4 +--R (5c - 2a c - 16b c + (2a b - 4a )c + (10b + 4a b + a )c) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 2 4 2 2 +--R (c + 3a c + (- 7b - 4a )c - a b c + (5b + 3a b )c)cos(x) +--R + +--R 4 2 2 3 2 2 4 2 2 +--R a c + (- b - a )c - a b c + (b + a b )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 4 5 +--R (2b c - 2a b )sin(x) +--R + +--R 3 2 2 3 3 5 2 3 +--R ((- 6b + 2a b)c + (8a b - 2a b)c + 2b - 4a b )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 2b + 2a b)c - 2a b c + 2b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (4b c - 12a b c + 8a b c)cos(x) +--R + +--R 2 3 2 2 3 2 2 3 2 2 2 2 +--R (- 2b c - 2a b c + 4a b )cos(x) - 4b c + 4a b c - 2a b c +--R + +--R 3 2 +--R 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 2 2 3 5 2 3 3 +--R (4a b c + (- 8b - 4a b)c + 8a b c + 4b - 4a b )cos(x) +--R + +--R 4 3 3 2 2 5 2 3 2 +--R (4b c + 2a b c + (- 12b - 6a b)c + 10b + 2a b )cos(x) +--R + +--R 4 3 3 2 2 3 3 +--R 4b c + 2a b c + (- 6b - 8a b)c + (- 12a b + 2a b)c +--R + +--R 5 2 3 +--R 8b + 10a b +--R * +--R cos(x) +--R + +--R 3 3 2 2 3 3 5 2 3 +--R 4a b c + (- 2b - 6a b)c + (- 4a b + 2a b)c + 2b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 4 2 2 4 4 +--R (4b c - 12a b c + (- 2b + 8a b )c + 2a b )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 2b c - 2a b c + 4a b )cos(x) +--R + +--R 2 3 2 2 4 2 2 4 3 2 +--R (- 12b c + 20a b c + (8b - 10a b )c - 8a b + 2a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 2 2 4 4 3 2 +--R (- 6b c + 10a b c + 8b c - 8a b - 4a b )cos(x) +--R + +--R 4 2 2 4 3 2 +--R (2b + 2a b )c - 2a b - 2a b +--R * +--R sin(x) +--R + +--R 3 3 2 2 3 5 5 +--R (4a b c + (- 2b - 6a b)c + 2a b c + 2b )cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 +--R (4b c + 2a b c + (- 10b - 8a b)c + 2a b c + 8b + 2a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 3 5 2 3 3 +--R (8b c - 6a b c - 18b c - 2a b c + 12b + 6a b )cos(x) +--R + +--R 4 3 3 2 3 5 2 3 2 +--R (4b c - 2a b c - 14b c - 2a b c + 8b + 6a b )cos(x) +--R + +--R 3 3 2 2 5 2 3 +--R (2a b c + (- 4b - 2a b)c + 2b + 2a b )cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 3 5 +--R (2a b c - 2a b )sin(x) +--R + +--R 2 3 2 3 2 4 2 2 4 +--R 2b c + (- 8a b + 2a )c + (- 2b + 8a b - 2a )c +--R + +--R 4 3 2 +--R 4a b - 4a b +--R * +--R cos(x) +--R + +--R 2 3 2 3 2 4 4 4 +--R 2b c + (- 4a b + 2a )c + (- 2b - 2a )c + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 +--R - 2b c + 8a b c + (4b - 14a b)c + (- 4a b + 8a b)c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 3 2 2 5 4 4 +--R (- 2a b c + (4b - 2a b)c - 4b + 4a b)cos(x) + 2b c +--R + +--R 3 2 2 3 3 5 2 3 4 +--R - 8a b c + 6a b c + (4a b - 2a b)c - 2b - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 +--R - 2a c + (- 2b + 6a )c + (- 2a b - 4a )c +--R + +--R 4 2 2 3 2 +--R (2b + 6a b )c - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - 2c + 4a c + (- 2b + 2a )c + (- 2a b - 4a )c +--R + +--R 4 +--R 4b c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 2 3 2 +--R - 2c + 4a c + 2a c + (2a b - 6a )c +--R + +--R 4 2 2 4 3 2 +--R (2b - 12a b + 2a )c + 8a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 3 2 2 2 4 3 2 +--R - 2a c + 6a c + (2a b - 6a )c + (- 6a b + 2a )c + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 3 3 5 4 +--R (2b c + (- 4b - 10a b)c + (2a b + 8a b)c + 2b )cos(x) +--R + +--R 4 3 3 2 2 3 5 +--R 4b c - 10a b c + (- 12b + 2a b)c + 8a b c + 8b +--R + +--R 2 3 4 +--R - 4a b + 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 3 2 2 3 3 5 +--R - 12a b c + (- 12b + 20a b)c + (8a b - 10a b)c + 12b +--R + +--R 2 3 4 +--R - 8a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 5 2 3 4 +--R (- 4b c + 2a b c + (- 4b + 6a b)c + 8b - 4a b - 4a b) +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 3 5 4 +--R - 2b c + 4a b c - 2a b c + (- 2a b + 2a b)c + 2b - 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 2 2 4 4 +--R (2a c + 2a c + (- 6a b - 6a )c + (2a b + 2a )c + 4a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 2c + 8a c + (- 4b - 2a )c + (- 22a b - 10a )c +--R + +--R 4 2 2 4 4 3 2 +--R (2b + 4a b + 2a )c + 16a b + 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 6c + 10a c + (- 14b - 8a )c + (- 32a b - 6a )c +--R + +--R 4 2 2 4 4 3 2 +--R (8b + 2a b - 2a )c + 24a b + 12a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 6c + 6a c + (- 18b - 4a )c + (- 24a b - 6a )c +--R + +--R 4 2 2 4 4 3 2 +--R (12b + 2a b - 2a )c + 16a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 2c + 4a c + (- 10b - 2a )c + (- 10a b - 4a )c +--R + +--R 4 2 2 4 3 2 +--R (8b + 4a b )c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 2 4 2 2 +--R 2a c + (- 2b - 2a )c - 2a b c + (2b + 2a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 5 +--R (- 2b c + 2a b )sin(x) +--R + +--R 3 2 2 3 3 5 2 3 +--R ((6b - 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10a b c - 8b c + 8a b + 4a b )cos(x) +--R + +--R 4 2 2 4 3 2 +--R (- 2b - 2a b )c + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 3 3 2 2 3 5 5 +--R (- 4a b c + (2b + 6a b)c - 2a b c - 2b )cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 +--R (- 4b c - 2a b c + (10b + 8a b)c - 2a b c - 8b - 2a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 3 5 2 3 3 +--R (- 8b c + 6a b c + 18b c + 2a b c - 12b - 6a b )cos(x) +--R + +--R 4 3 3 2 3 5 2 3 2 +--R (- 4b c + 2a b c + 14b c + 2a b c - 8b - 6a b )cos(x) +--R + +--R 3 3 2 2 5 2 3 +--R (- 2a b c + (4b + 2a b)c - 2b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 5 +--R (- b c + a b )sin(x) +--R + +--R 2 2 3 2 2 4 2 2 4 3 2 +--R ((4b - a )c - 2a b c + (- 2b - 2a b + a )c + 2a b )cos(x) +--R + +--R 2 2 3 4 4 +--R (2b - a )c + (- 2b + a )c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R - 3b c + 6a b c + (2b + a b)c + (- 2a b - 4a b)c - b +--R + +--R 2 3 +--R a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 5 4 +--R (b c + 2a b c + (2b + a b)c - 2a b c - 2b - 2a b)cos(x) +--R + +--R 4 3 3 5 2 3 4 +--R 3b c - 2a b c + 2a b c - b - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 3a c + (3b + a )c + (3a b + 2a )c + (- b - 3a b )c +--R + +--R 4 3 2 +--R - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - 3c - 3a c + (5b + 2a )c + (11a b + 4a )c +--R + +--R 4 2 2 4 3 2 +--R (- 3b - a b )c - 10a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - 3c - 3a c + (3b + 3a )c + (13a b + 4a )c +--R + +--R 4 2 2 4 4 3 2 +--R (- 3b + a b - a )c - 8a b - 6a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 4 +--R - 3a c + (b + 2a )c + (5a b + 2a )c + (- b - a b - a )c +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R - b c + 2a b c + (- b + 3a b)c + (2a b - 4a b)c + b +--R + +--R 2 3 +--R - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R 3b c - 2a b c + (- 6b + 3a b)c + (4a b - 2a b)c + 4b +--R + +--R 2 3 4 +--R - 2a b - 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 +--R 6b c - 4a b c + (- 10b - 5a b)c + 4a b c + 6b + 4a b +--R + +--R 4 +--R - a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R b c + 2a b c + (- 6b - 7a b)c + (- 4a b + 2a b)c + 4b +--R + +--R 2 3 4 +--R 6a b + 2a b +--R * +--R cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 4 +--R - b c + 2a b c + (- b - 2a b)c - 2a b c + b + 2a b + a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 4 2 2 4 5 +--R (- a c + b c + (- a b + 2a )c + (- b + a b - a )c)cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - c - a c + (3b + a )c + (- a b + 2a )c +--R + +--R 4 2 2 4 +--R (- 3b + a b - a )c +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 2 3 2 3 2 4 2 2 4 +--R (- c + (2b + 2a )c + (2a b - 2a )c + (- 2b - 2a b + a )c) +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 3 2 3 2 4 2 2 4 2 +--R (c - 2b c + (2a b - 2a )c + (2b - 2a b + a )c)cos(x) +--R + +--R 5 4 2 2 3 2 2 4 2 2 4 +--R (c + a c + (- 3b - 2a )c - a b c + (3b + a b )c)cos(x) + a c +--R + +--R 2 2 3 2 2 4 2 2 +--R (- b - a )c - a b c + (b + a b )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 2 4 2 3 4 2 4 3 2 2 4 4 2 5 +--R (- b c + 2a b c + b c + (- 2a b - 2a b )c + a b + a b )sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R b c - 4a b c + (- b + 4a b)c + (4a b + 2a b)c +--R + +--R 2 3 4 3 3 5 +--R (- 5a b - 5a b)c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 3 3 2 2 3 4 3 3 5 +--R - a b c + 2a b c + a b c + (- 2a b - 2a b)c + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 2 4 3 3 4 2 2 4 2 +--R a c + (- b - 3a )c + a c + (2b + 3a b + 3a )c +--R + +--R 4 3 2 5 6 4 2 +--R (- a b - 3a b - 2a )c - b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R c - a c + (- 2b - 4a )c + (a b + 4a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (3b + 3a b + 3a )c + (- 3a b - 3a )c - 2b - a b + a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 4 2 4 5 +--R c - 2a c + (- b - a )c + (a b + 3a )c + b c + (a b - a )c +--R + +--R 6 2 4 +--R - b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 3b c - 6a b c + (- 6b + a b)c + (10a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (3b - a b - 4a b)c - 4a b - 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 5b c - 7a b c + (- 12b - 5a b)c + (17a b + 6a b)c +--R + +--R 5 2 3 5 3 3 5 +--R (7b + 7a b )c - 10a b - 9a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 3b c - 2a b c + (- 8b - 9a b)c + (10a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (5b + 11a b + 6a b)c - 8a b - 10a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R b c - a b c + (- 2b - 3a b)c + (3a b + 2a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (b + 3a b + 2a b)c - 2a b - 3a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 +--R 3a c + (2b - 5a )c + (- 6a b - a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 2 4 +--R (- 3b + 5a b + 5a )c + (3a b + a b - 2a )c + b - a b +--R + +--R 4 2 +--R - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R 3c + a c - 10a c + (- 3a b + 2a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 2 4 +--R (- 7b + 7a b + 7a )c + (2a b - a b - 3a )c + 4b + a b +--R + +--R 4 2 +--R - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 7c - 9a c + (- 8b - 4a )c + (17a b + 8a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 5b - 3a b - 3a )c + (- 8a b - 7a b + a )c + 6b +--R + +--R 2 4 4 2 +--R 7a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 5c - 9a c + (- 8b + 2a )c + (19a b + 6a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- b - 7a b - 7a )c + (- 10a b - 7a b + 3a )c + 4b +--R + +--R 2 4 4 2 +--R 7a b + 3a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 2 2 4 2 +--R c - 2a c + (- 2b + a )c + (5a b + a )c + (- 2a b - 2a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (- 3a b - 2a b + a )c + b + 2a b + a b +--R * +--R sin(x) +--R + +--R 4 3 2 3 3 3 2 +--R 2a b c + (- b - a b)c + (- 2a b - 2a b)c +--R + +--R 5 2 3 4 +--R (b + 2a b + a b)c +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 3b c + 4a b c + (- 8b - 5a b)c + (- 4a b - 4a b)c +--R + +--R 5 2 3 4 +--R (5b + 7a b + 2a b)c +--R * +--R 4 +--R cos(x) +--R + +--R 5 3 2 3 5 2 3 3 +--R (10b c + (- 20b - 10a b)c + (10b + 10a b )c)cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 12b c - 4a b c + (- 22b - 10a b)c + (4a b + 4a b)c +--R + +--R 5 2 3 4 +--R (10b + 8a b - 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 6b c - 2a b c + (- 11b - 5a b)c + (2a b + 2a b)c +--R + +--R 5 2 3 4 +--R (5b + 4a b - a b)c +--R * +--R cos(x) +--R + +--R 5 3 2 3 5 2 3 +--R b c + (- 2b - a b)c + (b + a b )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 2 3 5 3 3 5 +--R (- 2b c + 2a b c + (2b + 2a b )c - 2a b - 2a b )sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 2 4 +--R 4b c - 6a b c - 6b c + (6a b + 6a b )c + 2b - 2a b +--R + +--R 4 2 +--R - 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 +--R 2b c - 2a b c - 4b c + (2a b + 2a b )c + 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 2 +--R (4a b c - 4a b c + (- 4a b - 4a b)c + (4a b + 4a b)c)cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c + 2a b c + (- 4b - 10a b)c + (- 2a b - 2a b)c +--R + +--R 2 3 4 +--R (6a b + 6a b)c +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c - 2a b c + (- 4b - 6a b)c + (2a b + 2a b)c +--R + +--R 2 3 4 +--R (2a b + 2a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 3 +--R (4b c - 4a b c - 8b c + (4a b + 4a b )c + 4b - 4a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 +--R 6b c + 2a b c + (- 16b - 4a b )c + (- 2a b - 2a b )c +--R + +--R 6 2 4 4 2 +--R 10b + 8a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 +--R 4b c + 8a b c + (- 12b - 8a b )c + (- 8a b - 8a b )c +--R + +--R 6 2 4 4 2 +--R 8b + 12a b + 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 2b c + 2a b c + (- 4b - 4a b )c + (- 2a b - 2a b )c + 2b +--R + +--R 2 4 4 2 +--R 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 3 3 2 +--R 4a b c + (2b - 4a b)c + (- 6a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- 2b + 2a b + 4a b)c + 2a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c + 2a b c + (- 4b - 10a b)c + (- 2a b - 2a b)c +--R + +--R 2 3 4 +--R (6a b + 6a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 8b c - 10a b c + (- 16b - 6a b)c + (18a b + 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (8b + 6a b - 2a b)c - 8a b - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c - 10a b c + (- 12b + 2a b)c + (18a b + 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (8b + 2a b - 6a b)c - 8a b - 8a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 5 4 +--R - 2a b c + (- 2b + 2a b)c + (4a b + 2a b)c + (2b - 2a b)c +--R + +--R 5 3 3 +--R - 2a b - 2a b +--R * +--R sin(x) +--R + +--R 2 3 4 2 4 3 2 6 2 4 5 +--R (2a b c - 2b c + (- 2a b - 2a b )c + 2b + 2a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 4b c + 4a b c + (- 12b - 4a b )c + (- 4a b - 4a b )c + 8b +--R + +--R 2 4 +--R 8a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 4 2 2 2 6 2 4 3 +--R (12b c + (- 24b - 12a b )c + 12b + 12a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 12b c - 4a b c + (- 20b - 12a b )c + (4a b + 4a b )c + 8b +--R + +--R 2 4 +--R 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 4b c - 2a b c + (- 6b - 4a b )c + (2a b + 2a b )c + 2b +--R + +--R 2 4 +--R 2a b +--R * +--R cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 4 3 2 2 4 4 2 5 +--R (- 2a b c + 2a b c + (2a b + 2a b )c - 2a b - 2a b )sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + 6a b c + (4b - 4a b)c + (- 10a b - 2a b)c +--R + +--R 5 2 3 4 5 5 +--R (- 2b + 4a b + 6a b)c + 4a b - 4a b +--R * +--R cos(x) +--R + +--R 5 4 3 3 3 3 2 5 4 +--R - 2b c + 4a b c + 4b c + (- 8a b - 2a b)c + (- 2b + 2a b)c +--R + +--R 5 3 3 5 +--R 4a b + 2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 +--R - 2a c + (- 2b + 6a )c + (4a b - 2a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 4 2 +--R (4b - 6a b - 6a )c + (- 2a b + 2a b + 4a )c - 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - 2c + 4a c + 6a c + (- 4a b - 10a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (6b - 4a b - 4a )c + (6a b + 6a )c - 4b - 2a b + 2a b +--R * +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - 2c + 6a c + 2b c + (- 8a b - 8a )c + (2b + 2a b + 2a )c +--R + +--R 4 3 2 5 6 2 4 +--R (2a b + 4a b + 2a )c - 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 2 3 3 2 5 2 3 4 +--R 2b c + (- 4b - 6a b)c + 4a b c + (2b + 6a b + 4a b)c +--R + +--R 3 3 5 +--R - 4a b - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c - 4a b c + (- 8b - 2a b)c + (4a b + 6a b)c +--R + +--R 5 2 3 4 3 3 5 +--R (4b + 2a b - 2a b)c - 2a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 2 +--R 2b c - 4a b c + (- 4b + 6a b)c + 4a b c +--R + +--R 5 2 3 4 3 3 5 +--R (2b - 6a b - 8a b)c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 4 3 3 5 +--R 2a b c - 2a b c + (- 2a b - 2a b)c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 +--R 2a c + (2b + 2a )c + (- 2a b - 6a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 +--R (- 4b - 4a b - 2a )c + (4a b + 4a )c + 2b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2c + 8a c + (4b - 6a )c + (- 12a b - 14a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 14b + 4a b + 4a )c + (4a b + 10a b + 6a )c + 8b +--R + +--R 2 4 4 2 +--R 2a b - 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R 6c + 8a c - 22a c + (- 16a b - 6a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 18b + 24a b + 16a )c + (8a b + 6a b - 2a )c + 12b +--R + +--R 2 4 4 2 +--R - 2a b - 14a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 4 2 3 3 +--R 6c + (- 4b - 18a )c + (- 4a b + 6a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 10b + 20a b + 12a )c + (4a b - 2a b - 6a )c + 8b +--R + +--R 2 4 4 2 +--R - 2a b - 10a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2c - 2a c + (- 2b - 4a )c + (2a b + 4a )c +--R + +--R 4 2 2 4 2 3 2 5 6 4 2 +--R (- 2b + 4a b + 2a )c + (- 2a b - 2a )c + 2b - 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 +--R 2a b c + 2a b c + (- 6a b - 2a b)c + (- 2a b - 2a b)c +--R + +--R 5 3 3 +--R 4a b + 4a b +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c + 12a b c + (- 4b + 2a b)c + (- 28a b - 12a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (2b - 2a b - 4a b)c + 16a b + 16a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 8b c + 24a b c + (- 16b - 8a b)c + (- 48a b - 24a b)c +--R + +--R 5 2 3 5 3 3 +--R (8b + 8a b )c + 24a b + 24a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 12b c + 20a b c + (- 24b - 16a b)c + (- 36a b - 20a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (12b + 16a b + 4a b)c + 16a b + 16a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 8b c + 6a b c + (- 16b - 10a b)c + (- 10a b - 6a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (8b + 10a b + 2a b)c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 5 3 2 3 5 2 3 +--R 2b c + (- 4b - 2a b)c + (2b + 2a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 2 3 5 3 3 5 +--R (2b c - 2a b c + (- 2b - 2a b )c + 2a b + 2a b )sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 2 4 +--R - 4b c + 6a b c + 6b c + (- 6a b - 6a b )c - 2b + 2a b +--R + +--R 4 2 +--R 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 +--R - 2b c + 2a b c + 4b c + (- 2a b - 2a b )c - 2b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 +--R (- 4a b c + 4a b c + (4a b + 4a b)c + (- 4a b - 4a b)c) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c - 2a b c + (4b + 10a b)c + (2a b + 2a b)c +--R + +--R 2 3 4 +--R (- 6a b - 6a b)c +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c + 2a b c + (4b + 6a b)c + (- 2a b - 2a b)c +--R + +--R 2 3 4 +--R (- 2a b - 2a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 +--R (- 4b c + 4a b c + 8b c + (- 4a b - 4a b )c - 4b + 4a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 +--R - 6b c - 2a b c + (16b + 4a b )c + (2a b + 2a b )c +--R + +--R 6 2 4 4 2 +--R - 10b - 8a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 4b c - 8a b c + (12b + 8a b )c + (8a b + 8a b )c - 8b +--R + +--R 2 4 4 2 +--R - 12a b - 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 2b c - 2a b c + (4b + 4a b )c + (2a b + 2a b )c - 2b +--R + +--R 2 4 4 2 +--R - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (- 2b + 4a b)c + (6a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (2b - 2a b - 4a b)c - 2a b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c - 2a b c + (4b + 10a b)c + (2a b + 2a b)c +--R + +--R 2 3 4 +--R (- 6a b - 6a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 8b c + 10a b c + (16b + 6a b)c + (- 18a b - 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- 8b - 6a b + 2a b)c + 8a b + 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c + 10a b c + (12b - 2a b)c + (- 18a b - 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- 8b - 2a b + 6a b)c + 8a b + 8a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 5 4 +--R 2a b c + (2b - 2a b)c + (- 4a b - 2a b)c + (- 2b + 2a b)c +--R + +--R 5 3 3 +--R 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 3 4 2 4 3 2 6 2 4 5 +--R (- 2a b c + 2b c + (2a b + 2a b )c - 2b - 2a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 4b c - 4a b c + (12b + 4a b )c + (4a b + 4a b )c - 8b +--R + +--R 2 4 +--R - 8a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 4 2 2 2 6 2 4 3 +--R (- 12b c + (24b + 12a b )c - 12b - 12a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 12b c + 4a b c + (20b + 12a b )c + (- 4a b - 4a b )c - 8b +--R + +--R 2 4 +--R - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 4b c + 2a b c + (6b + 4a b )c + (- 2a b - 2a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 2 2 4 4 2 5 +--R (b c + (- b - 2a b )c + a b + a b )sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 3b c + 2a b c + (5b + 4a b)c + (- 2a b - 4a b)c +--R + +--R 5 2 3 4 3 3 5 +--R (- 2b - 3a b - a b)c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + a b c + (4b + 2a b)c + (- a b - 2a b)c +--R + +--R 5 2 3 3 3 5 +--R (- 2b - 2a b )c + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 4 2 2 4 2 +--R - 3a c + (- b + a )c + (4a b + 5a )c + (2b - a b - a )c +--R + +--R 4 3 2 5 6 4 2 +--R (- a b - 3a b - 2a )c - b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - 3c - 3a c + (2b + 6a )c + (3a b + 6a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (3b - 3a b - 3a )c + (- 3a b - 3a )c - 2b - a b + a b +--R * +--R cos(x) +--R + +--R 6 2 2 4 2 3 3 4 2 2 4 2 +--R - 3c + (3b + 5a )c + (- a b + a )c + (b - 2a b - 2a )c +--R + +--R 4 5 6 2 4 +--R (a b - a )c - b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 3 3 2 5 2 3 +--R - b c - 2a b c + (2b + a b)c + 6a b c + (- b - a b )c +--R + +--R 5 3 3 5 +--R - 4a b - 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - b c - 9a b c + (4b - a b)c + (19a b + 8a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (- 3b - a b + 2a b)c - 10a b - 9a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - b c - 10a b c + (4b - a b)c + (18a b + 12a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (- 3b - a b + 2a b)c - 8a b - 10a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 5 2 3 +--R - b c - 3a b c + (2b + a b)c + (5a b + 4a b)c + (- b - a b )c +--R + +--R 5 3 3 5 +--R - 2a b - 3a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 2 4 2 +--R - a c - a c + 3a c + (- b + 3a b + a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (a b - a b - 2a )c + b - a b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - c - a c + 4b c + (- a b + 4a )c + (- 7b + a b + a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (2a b - a b - 3a )c + 4b + a b - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - c + a c + (8b + 2a )c + (- a b - 2a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (- 13b - 9a b - a )c + (a b + a )c + 6b + 7a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R c + a c + 4b c + (a b - 4a )c + (- 9b - 9a b - a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (- 2a b + a b + 3a )c + 4b + 7a b + 3a b +--R * +--R cos(x) +--R + +--R 6 2 4 2 3 3 4 2 2 2 4 5 6 +--R c - a c + (a b - a )c + (- 2b - 2a b )c + (- a b + a )c + b +--R + +--R 2 4 4 2 +--R 2a b + a b +--R * +--R sin(x) +--R + +--R 3 2 3 5 4 5 +--R ((b - a b)c + (- b + a b)c)cos(x) +--R + +--R 5 3 2 3 5 2 3 4 4 +--R (- b c + (4b - a b)c + (- 3b - a b + 2a b)c)cos(x) +--R + +--R 5 3 2 3 5 2 3 3 +--R (- 2b c + (4b + 2a b)c + (- 2b - 2a b )c)cos(x) +--R + +--R 3 2 3 5 4 2 +--R ((- 2b + 2a b)c + (2b - 2a b)c)cos(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (2b c + (- 5b - a b)c + (3b + 2a b - a b)c)cos(x) + b c +--R + +--R 3 2 3 5 2 3 +--R (- 2b - a b)c + (b + a b )c +--R / +--R 2 4 2 3 4 2 2 2 4 2 4 +--R (b c - 2a b c + (- b + a b )c + 2a b c - a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 2 4 +--R b c - 2a b c + (- b + a b )c + 2a b c - a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - b c + 3a b c + (2b - 3a b)c + (- 4a b + a b)c +--R + +--R 5 2 3 5 3 3 +--R (- b + 3a b )c + a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 3 3 2 5 5 5 4 +--R (2b c - 2a b c - 2b c + 2a b )cos(x) + b c - 3a b c +--R + +--R 2 3 3 3 2 5 2 3 5 3 3 +--R 3a b c + (2a b - a b)c + (- b - 3a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 4 2 2 2 +--R - a c + (- b + 2a )c + (4a b - a )c + (b - 4a b )c +--R + +--R 4 3 2 2 4 +--R (- 3a b + a b )c + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - c + a c - b c + (6a b + a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (2b - 5a b - a )c + (- 7a b - a b )c + 5a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 3 3 4 2 2 4 2 +--R - c + a c + (4a b + a )c + (b - 4a b - a )c +--R + +--R 4 3 2 2 4 4 2 +--R (- 5a b - a b )c + 4a b + a b +--R * +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 2 4 3 2 +--R - a c + 2a c + (2a b - a )c - 3a b c + (- a b + a b )c +--R + +--R 2 4 +--R a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R b c - 3a b c + (- 2b + 3a b)c + (4a b - a b)c +--R + +--R 5 2 3 5 3 3 +--R (b - 3a b )c - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c - 6a b c + (- 6b + 6a b)c + (10a b - 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (4b - 6a b )c - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 3 3 2 5 5 2 +--R (- 6b c + 6a b c + 6b c - 6a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + 6a b c + (- 2b - 6a b)c + (- 2a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (4b + 6a b )c - 4a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 2 +--R - b c + 3a b c - 3a b c + (- 2a b + a b)c +--R + +--R 5 2 3 5 3 3 +--R (b + 3a b )c - a b - a b +--R * +--R sin(x) +--R + +--R 5 2 4 2 3 3 2 2 2 4 3 2 +--R a c - 2a c + (- 2a b + a )c + 3a b c + (a b - a b )c +--R + +--R 2 4 +--R - a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R c + a c + (- 2b - 4a )c + (- 4a b + a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (b + 8a b + a )c + (3a b - a b )c - 4a b - a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 2 4 3 3 4 2 2 4 2 +--R 3c - 2a c + (- 7b - 2a )c - 2a c + (4b + 8a b + 3a )c +--R + +--R 4 3 2 2 4 4 2 +--R (2a b + 2a b )c - 6a b - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 3c - 2a c + (- 9b - 2a )c + (4a b - 2a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (6b + 6a b + 3a )c + (- 2a b + 2a b )c - 4a b - 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R c + a c + (- 5b - 4a )c + (2a b + a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (4b + 5a b + a )c + (- 3a b - a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 5 2 2 4 3 3 4 2 2 2 4 3 2 +--R a c + (- b - 2a )c + a c + (b + 2a b )c + (- a b - a b )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 5 3 3 3 2 +--R (2b c - 2a b c - 2b c + 2a b )cos(x) + 2b c - 2a b c +--R + +--R 5 5 +--R - 2b c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 2b c + 4a b c + (4b - 2a b )c - 4a b c - 2b +--R + +--R 2 4 +--R 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 6 2 4 2 3 2 2 2 4 +--R (4b c - 4b )cos(x) + 2b c - 4a b c + 2a b c + 4a b c +--R + +--R 6 2 4 +--R - 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 3 3 2 5 2 3 +--R - 2a b c + (- 2b + 2a b)c + 6a b c + (2b - 2a b )c +--R + +--R 5 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 3 3 3 3 2 5 5 +--R - 2b c - 2b c + (10a b + 2a b)c + 4b c - 10a b +--R + +--R 3 3 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 2 5 5 3 3 +--R (- 2b c + (8a b + 2a b)c + 2b c - 8a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 2 3 5 +--R - 2a b c + 2a b c + 4a b c - 2a b c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R 2b c - 4a b c + (- 4b + 2a b )c + 4a b c + 2b +--R + +--R 2 4 +--R - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R 4b c - 8a b c + (- 12b + 4a b )c + 8a b c + 8b +--R + +--R 2 4 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 6 2 +--R (- 12b c + 12b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 4b c + 8a b c + (- 4b - 4a b )c - 8a b c + 8b +--R + +--R 2 4 +--R 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 2 2 2 4 6 2 4 +--R - 2b c + 4a b c - 2a b c - 4a b c + 2b + 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 3 5 5 +--R (2a b c - 2a b c - 4a b c + 2a b c + 2a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c + 4a b c + (- 4b - 4a b)c + (- 12a b - 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (2b + 4a b )c + 8a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 6b c + 2a b c + (- 14b - 2a b)c + (- 14a b - 6a b)c +--R + +--R 5 2 3 5 3 3 +--R (8b + 2a b )c + 12a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 6b c + 2a b c + (- 18b - 2a b)c + (- 10a b - 6a b)c +--R + +--R 5 2 3 5 3 3 +--R (12b + 2a b )c + 8a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c + 4a b c + (- 10b - 4a b)c + (- 6a b - 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (8b + 4a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 2 5 2 3 +--R 2a b c + (- 2b - 2a b)c - 2a b c + (2b + 2a b )c +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 4 2 4 2 3 +--R (2a b c - 2a b c - 2a b c + 2a b )cos(x) + 2a b c +--R + +--R 2 2 2 4 2 4 +--R - 2a b c - 2a b c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 5 +--R - 2a b c + 4a b c + (4a b - 2a b)c - 4a b c - 2a b +--R + +--R 3 3 +--R 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 5 4 2 3 3 2 +--R (4a b c - 4a b )cos(x) + 2a b c - 4a b c + 2a b c +--R + +--R 2 3 5 3 3 +--R 4a b c - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 3 2 2 2 4 3 2 +--R - 2a c + (- 2a b + 2a )c + 6a b c + (2a b - 2a b )c +--R + +--R 2 4 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 3 2 2 4 2 4 2 4 +--R - 2a c - 2a b c + (10a b + 2a )c + 4a b c - 10a b +--R + +--R 4 2 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 4 2 4 2 4 4 2 +--R (- 2a c + (8a b + 2a )c + 2a b c - 8a b - 2a b )cos(x) +--R + +--R 2 4 3 3 2 2 2 3 2 2 4 +--R - 2a c + 2a c + 4a b c - 2a b c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 5 +--R 2a b c - 4a b c + (- 4a b + 2a b)c + 4a b c + 2a b +--R + +--R 3 3 +--R - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 2 3 3 3 2 2 3 5 +--R 4a b c - 8a b c + (- 12a b + 4a b)c + 8a b c + 8a b +--R + +--R 3 3 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 5 2 +--R (- 12a b c + 12a b )cos(x) +--R + +--R 4 2 3 3 3 2 2 3 5 +--R - 4a b c + 8a b c + (- 4a b - 4a b)c - 8a b c + 8a b +--R + +--R 3 3 +--R 4a b +--R * +--R cos(x) +--R + +--R 4 2 3 3 2 2 3 5 3 3 +--R - 2a b c + 4a b c - 2a b c - 4a b c + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 4 3 3 2 2 2 3 2 2 4 5 +--R (2a c - 2a c - 4a b c + 2a b c + 2a b )cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R 2a c + 4a c + (- 4a b - 4a )c + (- 12a b - 2a )c +--R + +--R 4 3 2 2 4 4 2 +--R (2a b + 4a b )c + 8a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R 6a c + 2a c + (- 14a b - 2a )c + (- 14a b - 6a )c +--R + +--R 4 3 2 2 4 4 2 +--R (8a b + 2a b )c + 12a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R 6a c + 2a c + (- 18a b - 2a )c + (- 10a b - 6a )c +--R + +--R 4 3 2 2 4 4 2 +--R (12a b + 2a b )c + 8a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R 2a c + 4a c + (- 10a b - 4a )c + (- 6a b - 2a )c +--R + +--R 4 3 2 2 4 4 2 +--R (8a b + 4a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 3 2 2 2 4 3 2 +--R 2a c + (- 2a b - 2a )c - 2a b c + (2a b + 2a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 5 3 3 3 2 +--R (- 2b c + 2a b c + 2b c - 2a b )cos(x) - 2b c + 2a b c +--R + +--R 5 5 +--R 2b c - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R 2b c - 4a b c + (- 4b + 2a b )c + 4a b c + 2b +--R + +--R 2 4 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 6 2 4 2 3 2 2 2 4 +--R (- 4b c + 4b )cos(x) - 2b c + 4a b c - 2a b c - 4a b c +--R + +--R 6 2 4 +--R 2b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 3 3 2 5 2 3 +--R 2a b c + (2b - 2a b)c - 6a b c + (- 2b + 2a b )c +--R + +--R 5 +--R 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 3 3 3 3 2 5 5 +--R 2b c + 2b c + (- 10a b - 2a b)c - 4b c + 10a b +--R + +--R 3 3 +--R 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 2 5 5 3 3 +--R (2b c + (- 8a b - 2a b)c - 2b c + 8a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 2 3 5 +--R 2a b c - 2a b c - 4a b c + 2a b c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 2b c + 4a b c + (4b - 2a b )c - 4a b c - 2b +--R + +--R 2 4 +--R 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 4b c + 8a b c + (12b - 4a b )c - 8a b c - 8b +--R + +--R 2 4 +--R 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 6 2 +--R (12b c - 12b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 2 4 +--R (4b c - 8a b c + (4b + 4a b )c + 8a b c - 8b - 4a b ) +--R * +--R cos(x) +--R + +--R 2 4 2 3 2 2 2 4 6 2 4 +--R 2b c - 4a b c + 2a b c + 4a b c - 2b - 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 3 5 5 +--R (- 2a b c + 2a b c + 4a b c - 2a b c - 2a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c - 4a b c + (4b + 4a b)c + (12a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 2b - 4a b )c - 8a b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 6b c - 2a b c + (14b + 2a b)c + (14a b + 6a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 8b - 2a b )c - 12a b - 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 6b c - 2a b c + (18b + 2a b)c + (10a b + 6a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 12b - 2a b )c - 8a b - 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c - 4a b c + (10b + 4a b)c + (6a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 8b - 4a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 2 5 2 3 +--R - 2a b c + (2b + 2a b)c + 2a b c + (- 2b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 2 2 4 2 4 4 2 2 2 +--R (- b c + (b + a b )c - a b )cos(x) - b c + (b + a b )c +--R + +--R 2 4 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 3 3 2 5 2 3 +--R b c - a b c + (- 2b - a b)c + a b c + (b + a b )c +--R + +--R 5 3 3 +--R a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 3 3 2 5 5 5 4 2 3 +--R (- 2b c - 2a b c + 2b c + 2a b )cos(x) - b c + a b c + a b c +--R + +--R 3 3 2 5 2 3 5 3 3 +--R (- 2a b - a b)c + (b - a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 2 3 3 4 2 2 2 +--R a c + b c + (- 2a b - a )c + (- b - 2a b )c +--R + +--R 4 3 2 2 4 +--R (a b + a b )c + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R c + a c + b c + (- 4a b - a )c + (- 2b - 5a b - a )c +--R + +--R 4 3 2 2 4 4 2 +--R (3a b + a b )c + 5a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 3 3 4 2 2 4 2 +--R c + a c + (- 4a b - a )c + (- b - 4a b - a )c +--R + +--R 4 3 2 2 4 4 2 +--R (3a b + a b )c + 4a b + a b +--R * +--R cos(x) +--R + +--R 5 2 3 3 2 2 2 4 3 2 2 4 +--R a c + (- 2a b - a )c - a b c + (a b + a b )c + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 3 3 2 5 2 3 +--R - b c + a b c + (2b + a b)c - a b c + (- b - a b )c +--R + +--R 5 3 3 +--R - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + 2a b c + (6b + 2a b)c + (2a b - 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 4b - 2a b )c - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 3 3 2 5 5 2 +--R (6b c + 6a b c - 6b c - 6a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c - 2a b c + (2b - 2a b)c + (6a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 4b + 2a b )c - 4a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 2 5 2 3 5 +--R b c - a b c - a b c + (2a b + a b)c + (- b + a b )c - a b +--R + +--R 3 3 +--R - a b +--R * +--R sin(x) +--R + +--R 5 2 3 3 2 2 2 4 3 2 2 4 5 +--R (- a c + (2a b + a )c + a b c + (- a b - a b )c - a b )cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - c - 3a c + 2b c + (8a b + 3a )c + (- b + 4a b + a )c +--R + +--R 4 3 2 2 4 4 2 +--R (- 5a b - 3a b )c - 4a b - a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - 3c - 4a c + 7b c + (14a b + 4a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (- 4b + 6a b + 3a )c + (- 10a b - 4a b )c - 6a b - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - 3c - 4a c + 9b c + (14a b + 4a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (- 6b + 4a b + 3a )c + (- 10a b - 4a b )c - 4a b - 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - c - 3a c + 5b c + (8a b + 3a )c + (- 4b + a b + a )c +--R + +--R 4 3 2 2 4 4 2 +--R (- 5a b - 3a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 5 2 4 2 3 3 4 2 4 3 2 +--R - a c + b c + (2a b + a )c - b c + (- a b - a b )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 6 5 3 4 3 3 3 +--R - b c + 2a b c + 2b c + (- 4a b - 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b + a b + a b)c + (2a b + 2a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 6 5 3 4 3 3 3 +--R - b c + 2a b c + 2b c + (- 4a b - 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b + a b + a b)c + (2a b + 2a b )c - a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 2 5 2 4 4 2 2 4 3 +--R - a c + (- b + 2a )c + 3a b c + (2b - 3a b - 2a )c +--R + +--R 4 5 2 6 2 4 4 2 6 5 2 +--R (- 3a b + a )c + (- b + a b + 2a b )c + a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R - c + a c + 2a c - 2a c + (3b - a b - a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 +--R (- 3a b + a b + a )c + (- 2b - a b + a b )c + 2a b +--R + +--R 3 4 5 2 +--R a b - a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 2 3 4 4 2 2 4 3 +--R - c + 2a c + b c + (- 3a b - 2a )c + (b + 2a b + a )c +--R + +--R 3 2 2 6 2 4 4 2 6 3 4 +--R a b c + (- b - 2a b - a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R b c - 3a b c + (- 2b + a b)c + (6a b + 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (b - 3a b - 2a b)c + (- 3a b - 3a b )c + 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R 2b c - 7a b c + (- 4b + 3a b)c + (14a b + 7a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (2b - 8a b - 5a b)c + (- 7a b - 7a b )c + 5a b + 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R b c - 5a b c + (- 2b + 3a b)c + (10a b + 5a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (b - 7a b - 4a b)c + (- 5a b - 5a b )c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 5 2 4 3 3 3 2 3 4 2 +--R - a b c + a b c + (2a b + a b)c + (- 2a b - a b)c +--R + +--R 5 3 3 2 5 4 3 +--R (- a b - a b )c + a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 5 2 4 4 2 2 4 3 +--R a c + (b - 2a )c - 3a b c + (- 2b + 3a b + 2a )c +--R + +--R 4 5 2 6 2 4 4 2 6 5 2 +--R (3a b - a )c + (b - a b - 2a b )c - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R c + a c + (2b - 6a )c + (- 6a b + 2a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (- 7b + 7a b + 5a )c + (9a b - a b - 3a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 +--R (4b - a b - 5a b )c - 4a b - a b + 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R 3c - 3a c - 6a c + 6a c + (- 9b + 3a b + 3a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 +--R (9a b - 3a b - 3a )c + (6b + 3a b - 3a b )c - 6a b +--R + +--R 3 4 5 2 +--R - 3a b + 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R 3c - 5a c + (- 2b - 2a )c + (6a b + 6a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (- 5b - 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2a b )c + 8a b + 8a b +--R * +--R cos(x) +--R + +--R 2 4 4 3 2 2 6 3 4 +--R 2a b c + (- 4a b - 2a b )c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 2 4 3 3 3 +--R - 2a b c + (- 2b + 2a b)c + (4a b + 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 7 4 3 +--R (4b - 2a b - 2a b)c + (- 2a b - 2a b )c - 2b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 2b c - 4a b c + (- 4b + 8a b)c + (8a b + 4a b)c +--R + +--R 5 2 3 4 2 5 3 3 7 2 5 +--R (14b - 6a b - 6a b)c + (- 4a b - 4a b )c - 8b - 2a b +--R + +--R 4 3 +--R 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 4 5 2 3 4 2 7 2 5 +--R - 6b c + 12a b c + (18b - 6a b - 6a b)c - 12b - 6a b +--R + +--R 4 3 +--R 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 6b c + 4a b c + (4b + 8a b)c + (- 8a b - 4a b)c +--R + +--R 5 2 3 4 2 5 3 3 7 2 5 +--R (10b - 2a b - 2a b)c + (4a b + 4a b )c - 8b - 6a b +--R + +--R 4 3 +--R 2a b +--R * +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 5 2 +--R - 2b c + 2a b c + (2b + 2a b)c + (- 4a b - 2a b)c + 2b c +--R + +--R 5 3 3 7 2 5 +--R (2a b + 2a b )c - 2b - 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 6 3 4 5 +--R (- 2a b c + (4a b + 2a b )c - 2a b - 2a b )cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 2b c - 8a b c + (4b + 2a b )c + (16a b + 8a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 2b - 2a b )c - 8a b - 8a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 8b c - 12a b c + (16b + 8a b )c + (24a b + 12a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 8b - 8a b )c - 12a b - 12a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 12b c - 8a b c + (24b + 12a b )c + (16a b + 8a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 12b - 12a b )c - 8a b - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 8b c - 2a b c + (16b + 8a b )c + (4a b + 2a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 8b - 8a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 2 5 4 2 2 3 6 2 4 +--R - 2b c + (4b + 2a b )c + (- 2b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 2 4 5 2 3 4 2 2 5 4 3 +--R (b c + (- 2b - 2a b)c + (b + 3a b + a b)c - a b - a b )cos(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 5 4 3 +--R b c + (- 2b - 2a b)c + (b + 3a b + a b)c - a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 5 2 3 4 4 2 2 3 +--R a c + b c + (- a b - 2a )c + (- 2b - a b )c +--R + +--R 4 3 2 5 2 6 2 4 6 5 2 +--R (- a b + 2a b + a )c + (b + a b )c + a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R c + a c - 2a c - 2a c + (- 3b + a b + a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 3 4 +--R (- 3a b + a b + a )c + (2b + a b - a b )c + 2a b + a b +--R + +--R 5 2 +--R - a b +--R * +--R cos(x) +--R + +--R 7 2 2 5 2 4 4 2 2 4 3 +--R c + (- b - 2a )c + a b c + (- b + 2a b + a )c +--R + +--R 4 3 2 2 6 4 2 6 3 4 +--R (- 2a b - a b )c + (b - a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - b c + a b c + (2b + 3a b)c + (- 2a b - a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b - 5a b - 2a b)c + (a b + a b )c + 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 2b c + 3a b c + (4b + 7a b)c + (- 6a b - 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 2b - 12a b - 5a b)c + (3a b + 3a b )c + 5a b + 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - b c + 3a b c + (2b + 5a b)c + (- 6a b - 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b - 9a b - 4a b)c + (3a b + 3a b )c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 5 2 4 3 3 3 2 3 4 2 +--R a b c + a b c + (- 2a b - a b)c + (- 2a b - a b)c +--R + +--R 5 3 3 2 5 4 3 +--R (a b + a b )c + a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 5 2 3 4 4 2 2 3 +--R - a c - b c + (a b + 2a )c + (2b + a b )c +--R + +--R 4 3 2 5 2 6 2 4 6 5 2 +--R (a b - 2a b - a )c + (- b - a b )c - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R - c - 3a c + (- 2b + 2a )c + (2a b + 6a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (7b + a b - a )c + (5a b - 5a b - 3a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 +--R (- 4b - 3a b + a b )c - 4a b - a b + 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R - 3c - 3a c + 6a c + 6a c + (9b - 3a b - 3a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 +--R (9a b - 3a b - 3a )c + (- 6b - 3a b + 3a b )c - 6a b +--R + +--R 3 4 5 2 +--R - 3a b + 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R - 3c - a c + (2b + 6a )c + (- 2a b + 2a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (5b - 5a b - 3a )c + (7a b + a b - a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 +--R (- 4b - a b + 3a b )c - 4a b - 3a b + a b +--R * +--R cos(x) +--R + +--R 7 2 2 5 2 4 4 2 2 4 3 4 3 2 2 +--R - c + (b + 2a )c - a b c + (b - 2a b - a )c + (2a b + a b )c +--R + +--R 6 4 2 6 3 4 +--R (- b + a b )c - a b - a b +--R * +--R sin(x) +--R + +--R 5 2 4 3 3 3 2 3 4 2 +--R - a b c - a b c + (2a b + a b)c + (2a b + a b)c +--R + +--R 5 3 3 2 5 4 3 +--R (- a b - a b )c - a b - a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - b c - 5a b c + (2b - 3a b)c + (10a b + 5a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b + 7a b + 4a b)c + (- 5a b - 5a b )c - 4a b - 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 4b c - 10a b c + (8b - 2a b)c + (20a b + 10a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 4b + 8a b + 6a b)c + (- 10a b - 10a b )c - 6a b - 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 6b c - 10a b c + (12b + 2a b)c + (20a b + 10a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 6b + 2a b + 4a b)c + (- 10a b - 10a b )c - 4a b - 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 4b c - 5a b c + (8b + 3a b)c + (10a b + 5a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 4b - 2a b + a b)c + (- 5a b - 5a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 5 2 3 2 +--R - b c - a b c + (2b + a b)c + (2a b + a b)c + (- b - a b )c +--R + +--R 5 3 3 +--R (- a b - a b )c +--R Type: Expression Integer +--E 244 + +--S 245 of 526 +m0847b:= a0847.2-r0847 +--R +--R +--R (234) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x 2 x +--R b\|- c + b + a \|c - b - a log((c - a)tan(-) + 2b tan(-) + c + a) +--R 2 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x +--R (- c - b)\|- c + b + a \|c - b - a log(tan(-) + 1) +--R 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|- c + b + a \|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|- c + b + a \|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|- c + b + a \|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x +--R (c - b)\|- c + b + a \|c - b - a log(- tan(-) + 1) +--R 2 +--R + +--R x +--R +------------+ (c - a)tan(-) + b +--R | 2 2 2 2 +--R - 2a c\|c - b - a atanh(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R +------------+ +--R +--------------+ | 2 2 2 +--R | 2 2 2 ((c - a)sin(x) + b cos(x) + b)\|c - b - a +--R - 2a c\|- c + b + a atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b + a \|c - b - a +--R Type: Expression Integer +--E 245 + +--S 246 of 526 +d0847b:= D(m0847b,x) +--R +--R +--R (235) +--R 2 2 2 2 2 6 +--R (b c - 2a b c + a b )sin(x) +--R + +--R 3 2 3 2 3 3 +--R (- b c + 3a b c + (b - 4a b)c - a b + 2a b)cos(x) +--R + +--R 3 2 3 3 +--R (b - a b)c - a b + a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (- a c + (b + a )c + 3a b c - 2b - 2a b )cos(x) +--R + +--R 4 2 2 2 2 4 2 2 4 3 +--R (- c + (2b + a )c + 6a b c - 4b - 4a b )cos(x) - c + a c +--R + +--R 2 2 2 4 2 2 +--R b c + 3a b c - 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 3 3 3 +--R (- 4b c + 8a b c + 4b c - 8a b )cos(x) +--R + +--R 3 2 3 2 3 3 2 +--R (- 8b c + 16a b c + (8b + 8a b)c - 20a b - 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 6b c + 14a b c + (4b + 10a b)c - 16a b - 6a b)cos(x) +--R + +--R 3 2 2 3 3 +--R - 2b c + 6a b c + 2a b c - 4a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 4 +--R (- 4a c + (- 3b + 6a )c + 6a b c + 2b - 7a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 3 +--R (- 4c - 4a c + (- 4b + 16a )c + 4a b c + 8b - 16a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 +--R (- 10c + 8a c + (2b + 14a )c - 16a b c + 12b - 10a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 2 2 4 4 +--R (- 8c + 12a c + (4b + 4a )c - 20a b c + 8b )cos(x) - 2c +--R + +--R 3 2 2 2 4 2 2 +--R 4a c + b c - 6a b c + 2b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 3 2 3 3 5 +--R (- 3b c - 3a b c + (3b + 4a b)c + a b - 2a b)cos(x) +--R + +--R 3 2 3 2 3 3 4 +--R (- 16b c - 8a b c + (15b + 9a b)c + 5a b - 5a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (- 32b c - 8a b c + (30b + 2a b)c + 10a b - 2a b)cos(x) +--R + +--R 3 2 3 2 3 3 2 +--R (- 30b c - 6a b c + (30b - 8a b)c + 10a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 13b c - 5a b c + (15b - 6a b)c + 5a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R - 2b c - 2a b c + (3b - a b)c + a b + a b +--R * +--R sin(x) +--R + +--R 3 2 2 2 2 6 +--R (- 3a c + (b + a )c + a b c)cos(x) +--R + +--R 4 3 2 2 2 2 5 +--R (- 3c - 12a c + (6b + 3a )c + 6a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 +--R (- 13c - 19a c + (15b + 2a )c + 15a b c)cos(x) +--R + +--R 4 3 2 2 2 2 3 +--R (- 22c - 16a c + (20b - 2a )c + 20a b c)cos(x) +--R + +--R 4 3 2 2 2 2 2 +--R (- 18c - 9a c + (15b - 3a )c + 15a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 3 2 2 +--R (- 7c - 4a c + (6b - a )c + 6a b c)cos(x) - c - a c + b c +--R + +--R 2 +--R a b c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 3 3 6 +--R (2b c - 2a b )sin(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 5 +--R ((- 4b c + 4a b c + 4b - 4a b )cos(x) - 2b c + 4b - 2a b )sin(x) +--R + +--R 2 3 3 2 +--R (- 4a b c - 2b c + 6a b )cos(x) +--R + +--R 3 2 3 3 3 3 +--R (- 4b c - 4a b c - 2b c + 10a b )cos(x) - 4b c + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 +--R (- 8b c + 8b )cos(x) +--R + +--R 2 2 2 4 2 2 2 +--R (- 20b c - 8a b c + 20b + 8a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 +--R (- 20b c - 8a b c + 16b + 12a b )cos(x) - 8b c + 4b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 4 +--R (- 8a b c - 2b c + 10a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (- 8b c - 20a b c + 8b c + 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (- 20b c - 16a b c + 28b c + 8a b )cos(x) +--R + +--R 3 2 3 3 3 3 3 +--R (- 16b c - 4a b c + 24b c - 4a b )cos(x) - 4b c + 6b c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 5 +--R (- 4b c - 4a b c + 4b + 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 4 +--R (- 18b c - 8a b c + 16b + 10a b )cos(x) +--R + +--R 2 2 4 2 2 3 +--R (- 28b c + 24b + 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 +--R (- 16b c + 8a b c + 16b - 8a b )cos(x) +--R + +--R 2 4 2 2 2 2 2 2 +--R (4a b c + 4b - 8a b )cos(x) + 2b c - 2a b +--R * +--R sin(x) +--R + +--R 2 3 3 6 +--R (- 4a b c + 2b c + 2a b )cos(x) +--R + +--R 3 2 3 3 5 +--R (- 4b c - 16a b c + 10b c + 10a b )cos(x) +--R + +--R 3 2 3 3 4 +--R (- 16b c - 24a b c + 20b c + 20a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (- 24b c - 16a b c + 20b c + 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (- 16b c - 4a b c + 10b c + 10a b )cos(x) +--R + +--R 3 3 3 +--R (- 4b c + 2b c + 2a b )cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 2 2 6 +--R (2a b c - 2a b )sin(x) +--R + +--R 3 2 3 2 3 3 3 +--R (2b c - 6a b c + (- 2b + 4a b)c + 6a b - 4a b)cos(x) + 2b c +--R + +--R 2 3 3 3 +--R - 4a b c - 2b c + 6a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (2a c + (4b - 6a )c - 4a b c - 4b + 8a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 4 +--R (2c - 4a c + (6b - 6a )c - 2a b c - 8b + 12a b )cos(x) + 2c +--R + +--R 3 2 2 2 4 2 2 +--R - 6a c + 2b c + 2a b c - 4b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 2 3 2 +--R (4b c + (- 4b - 8a b)c + 8a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (8b c - 4a b c + (- 8b - 8a b)c + 12a b)cos(x) + 4b c +--R + +--R 2 3 3 +--R - 4a b c - 4b c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 4 2 2 4 +--R ((- 4b - 4a )c - 2a b c + 4b + 6a b )cos(x) +--R + +--R 3 2 2 2 2 4 2 2 3 +--R (- 4a c + (- 16b - 8a )c + 4a b c + 16b + 8a b )cos(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (- 8a c + (- 24b - 4a )c + 16a b c + 24b - 4a b )cos(x) +--R + +--R 3 2 2 2 4 2 2 2 2 +--R (- 4a c - 16b c + 12a b c + 16b - 8a b )cos(x) - 4b c +--R + +--R 2 4 2 2 +--R 2a b c + 4b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 3 2 3 3 5 +--R (- 2b c - 10a b c + (2b - 4a b)c + 10a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 4 +--R (- 14b c - 44a b c + (14b - 8a b)c + 42a b + 10a b)cos(x) +--R + +--R 3 2 3 3 3 3 +--R (- 36b c - 72a b c + 36b c + 68a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 2 +--R (- 44b c - 52a b c + (44b + 8a b)c + 52a b - 8a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 26b c - 14a b c + (26b + 4a b)c + 18a b - 8a b)cos(x) +--R + +--R 3 3 3 3 +--R - 6b c + 6b c + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 3 2 2 2 2 2 6 +--R (- 2a c - 6a c + 4a b c + 4a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 5 +--R (- 2c - 16a c + (2b - 26a )c + 22a b c + 20a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 4 +--R (- 10c - 46a c + (10b - 44a )c + 50a b c + 40a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 3 +--R (- 20c - 64a c + (20b - 36a )c + 60a b c + 40a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 2 +--R (- 20c - 46a c + (20b - 14a )c + 40a b c + 20a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 4 +--R (- 10c - 16a c + (10b - 2a )c + 14a b c + 4a b )cos(x) - 2c +--R + +--R 3 2 2 2 +--R - 2a c + 2b c + 2a b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 6 +--R (- 2b c + 2a b )sin(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 5 +--R ((4b c - 4a b c - 4b + 4a b )cos(x) + 2b c - 4b + 2a b )sin(x) +--R + +--R 2 3 3 2 +--R (4a b c + 2b c - 6a b )cos(x) +--R + +--R 3 2 3 3 3 3 +--R (4b c + 4a b c + 2b c - 10a b )cos(x) + 4b c - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 2 2 2 4 2 2 2 +--R (8b c - 8b )cos(x) + (20b c + 8a b c - 20b - 8a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 +--R (20b c + 8a b c - 16b - 12a b )cos(x) + 8b c - 4b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 4 +--R (8a b c + 2b c - 10a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (8b c + 20a b c - 8b c - 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (20b c + 16a b c - 28b c - 8a b )cos(x) +--R + +--R 3 2 3 3 3 3 3 +--R (16b c + 4a b c - 24b c + 4a b )cos(x) + 4b c - 6b c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 5 +--R (4b c + 4a b c - 4b - 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 4 +--R (18b c + 8a b c - 16b - 10a b )cos(x) +--R + +--R 2 2 4 2 2 3 +--R (28b c - 24b - 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 +--R (16b c - 8a b c - 16b + 8a b )cos(x) +--R + +--R 2 4 2 2 2 2 2 2 +--R (- 4a b c - 4b + 8a b )cos(x) - 2b c + 2a b +--R * +--R sin(x) +--R + +--R 2 3 3 6 +--R (4a b c - 2b c - 2a b )cos(x) +--R + +--R 3 2 3 3 5 +--R (4b c + 16a b c - 10b c - 10a b )cos(x) +--R + +--R 3 2 3 3 4 +--R (16b c + 24a b c - 20b c - 20a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (24b c + 16a b c - 20b c - 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (16b c + 4a b c - 10b c - 10a b )cos(x) +--R + +--R 3 3 3 +--R (4b c - 2b c - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 6 +--R (- b c + a b )sin(x) +--R + +--R 3 2 3 3 3 3 3 2 +--R (3b c - a b c - 3b c - a b + 2a b)cos(x) + 2b c + (- 3b + a b)c +--R + +--R 3 3 +--R - a b + a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (3a c + (3b + a )c - 3a b c - 2b - 2a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 4 +--R (3c + 4a c + (4b + a )c - 4a b c - 4b - 4a b )cos(x) + 3c +--R + +--R 3 2 2 2 4 2 2 +--R a c + b c - a b c - 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 3 3 3 +--R (4b c + 8a b c - 4b c - 8a b )cos(x) +--R + +--R 3 2 3 3 3 2 +--R (12b c + 24a b c - 12b c - 20a b - 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (14b c + 22a b c + (- 12b - 2a b)c - 16a b - 6a b)cos(x) + 6b c +--R + +--R 2 3 2 3 3 +--R 6a b c + (- 4b - 2a b)c - 4a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 4 +--R (4a c + (- b + 6a )c - 4a b c + 2b - 7a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 3 +--R (4c + 16a c + (- 12b + 16a )c - 16a b c + 8b - 16a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 2 +--R (10c + 24a c + (- 26b + 14a )c - 24a b c + 12b - 10a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 4 3 +--R (8c + 16a c + (- 20b + 4a )c - 16a b c + 8b )cos(x) + 2c + 4a c +--R + +--R 2 2 2 4 2 2 +--R - 5b c - 4a b c + 2b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 3 3 3 5 +--R (b c + a b c - b c + a b - 2a b)cos(x) +--R + +--R 3 3 2 3 3 4 +--R (2b c + (- b - a b)c + 5a b - 5a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (- 4b c - 8a b c + (6b - 2a b)c + 10a b - 2a b)cos(x) +--R + +--R 3 2 3 3 3 2 +--R (- 14b c - 14a b c + 14b c + 10a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (- 13b c - 9a b c + (11b + 2a b)c + 5a b + 4a b)cos(x) - 4b c +--R + +--R 2 3 2 3 3 +--R - 2a b c + (3b + a b)c + a b + a b +--R * +--R sin(x) +--R + +--R 3 2 2 2 2 6 +--R (a c + (- b + a )c - a b c)cos(x) +--R + +--R 4 3 2 2 2 2 5 +--R (c + 4a c + (- 4b + 3a )c - 4a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 4 2 2 3 +--R (3c + 5a c + (- 5b + 2a )c - 5a b c)cos(x) + (2c - 2a c )cos(x) +--R + +--R 4 3 2 2 2 2 2 +--R (- 2c - 5a c + (5b - 3a )c + 5a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 3 2 2 2 +--R (- 3c - 4a c + (4b - a )c + 4a b c)cos(x) - c - a c + b c + a b c +--R / +--R 4 3 3 2 2 3 2 3 4 +--R (b c - 2a b c + (- b + a b)c + 2a b c - a b )cos(x) + b c +--R + +--R 3 3 2 2 3 2 3 +--R - 2a b c + (- b + a b)c + 2a b c - a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R a c + (2b - 2a )c + (- 3a b + a )c + (- 2b + 2a b )c +--R + +--R 4 3 2 +--R 2a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 4 2 2 +--R c - a c + (3b - a )c + (- 3a b + a )c + (- 4b + a b )c +--R + +--R 4 3 2 +--R 4a b - a b +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 4 2 2 4 +--R c - 2a c + (b + a )c + (- 2b - a b )c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 3 3 +--R (4a b c - 4a b c - 4a b c + 4a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (2b c + 8a b c + (- 2b - 10a b)c - 8a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (4b c + 4a b c + (- 4b - 8a b)c - 4a b c + 8a b )cos(x) +--R + +--R 4 3 2 2 2 3 +--R 2b c + (- 2b - 2a b)c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 3 2 4 2 2 4 +--R (- 2b + 2a )c + (2a b - 2a )c + (2b - 2a b )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R 2a c + (- 8b + 4a )c + (6a b - 6a )c + (8b - 4a b )c +--R + +--R 4 3 2 +--R - 8a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 3 2 3 2 4 4 3 2 +--R (6a c - 12b c + (6a b - 6a )c + 12b c - 12a b + 6a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R 6a c + (- 8b - 4a )c + (2a b - 2a )c + (8b + 4a b )c +--R + +--R 4 3 2 +--R - 8a b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 4 2 2 4 +--R 2a c + (- 2b - 2a )c + (2b + 2a b )c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (- b c - 2a b c + (b + 3a b)c + 2a b c - 3a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (- 7b c - 6a b c + (7b + 13a b)c + 6a b c - 13a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (- 18b c - 4a b c + (18b + 22a b)c + 4a b c - 22a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (- 22b c + 4a b c + (22b + 18a b)c - 4a b c - 18a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (- 13b c + 6a b c + (13b + 7a b)c - 6a b c - 7a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R - 3b c + 2a b c + (3b + a b)c - 2a b c - a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 6 +--R (- a c + (a b + a )c - a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 5 +--R (- c - 5a c + (b + a )c + (5a b + 5a )c - a b c - 5a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R - 5c - 10a c + (5b + 5a )c + (10a b + 10a )c - 5a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R - 10c - 10a c + (10b + 10a )c + (10a b + 10a )c - 10a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R - 10c - 5a c + (10b + 10a )c + (5a b + 5a )c - 10a b c +--R + +--R 3 2 +--R - 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 +--R (- 5c - a c + (5b + 5a )c + (a b + a )c - 5a b c - a b )cos(x) +--R + +--R 5 2 2 3 2 2 +--R - c + (b + a )c - a b c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 4 4 2 3 2 2 4 +--R (2b c - 2a b c - 2b c + 2a b )cos(x) + 2b c - 2a b c - 2b c +--R + +--R 4 +--R 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (2a b c + (4b - 2a b)c - 2a b c - 4b + 2a b )cos(x) +--R + +--R 4 3 2 2 5 2 3 4 3 +--R (2b c + (6b - 2a b)c - 8b + 2a b )cos(x) + 2b c - 2a b c +--R + +--R 3 2 3 5 +--R 2b c + 2a b c - 4b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 +--R (8a b c - 8a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (4b c + 20a b c - 4b c - 20a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 4 +--R (8b c + 16a b c - 8b c - 16a b )cos(x) + 4b c + 4a b c - 4b c +--R + +--R 4 +--R - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 5 2 3 4 +--R ((- 4b + 4a b)c + 4b - 4a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 3 +--R (4a b c + (- 16b + 12a b)c - 4a b c + 16b - 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (12a b c + (- 24b + 12a b)c - 12a b c + 24b - 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 +--R (12a b c + (- 16b + 4a b)c - 12a b c + 16b - 4a b )cos(x) +--R + +--R 3 3 2 3 5 +--R 4a b c - 4b c - 4a b c + 4b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 4 4 5 +--R (- 2b c - 6a b c + 2b c + 6a b )cos(x) +--R + +--R 2 3 2 2 4 4 4 +--R (- 14b c - 26a b c + 14b c + 26a b )cos(x) +--R + +--R 2 3 2 2 4 4 3 +--R (- 36b c - 44a b c + 36b c + 44a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (- 44b c - 36a b c + 44b c + 36a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 +--R (- 26b c - 14a b c + 26b c + 14a b )cos(x) - 6b c - 2a b c +--R + +--R 4 4 +--R 6b c + 2a b +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 3 6 +--R (- 2a b c - 2a b c + 2a b c + 2a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (- 2b c - 12a b c + (2b - 10a b)c + 12a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (- 10b c - 30a b c + (10b - 20a b)c + 30a b c + 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (- 20b c - 40a b c + (20b - 20a b)c + 40a b c + 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (- 20b c - 30a b c + (20b - 10a b)c + 30a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (- 10b c - 12a b c + (10b - 2a b)c + 12a b c + 2a b )cos(x) +--R + +--R 4 3 3 2 3 +--R - 2b c - 2a b c + 2b c + 2a b c +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 3 3 2 2 +--R (2a b c - 2a b c - 2a b c + 2a b )cos(x) + 2a b c - 2a b c +--R + +--R 3 2 3 +--R - 2a b c + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 2 +--R (2a c + (4a b - 2a )c - 2a b c - 4a b + 2a b )cos(x) +--R + +--R 4 2 3 2 4 3 2 4 2 3 +--R (2a c + (6a b - 2a )c - 8a b + 2a b )cos(x) + 2a c - 2a c +--R + +--R 2 2 2 2 4 +--R 2a b c + 2a b c - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 3 3 +--R (8a b c - 8a b )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (4a b c + 20a b c - 4a b c - 20a b )cos(x) +--R + +--R 3 2 2 3 2 3 3 2 2 +--R (8a b c + 16a b c - 8a b c - 16a b )cos(x) + 4a b c + 4a b c +--R + +--R 3 2 3 +--R - 4a b c - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 2 4 3 2 4 +--R ((- 4a b + 4a )c + 4a b - 4a b )cos(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 3 +--R (4a c + (- 16a b + 12a )c - 4a b c + 16a b - 12a b )cos(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 2 +--R (12a c + (- 24a b + 12a )c - 12a b c + 24a b - 12a b )cos(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 +--R (12a c + (- 16a b + 4a )c - 12a b c + 16a b - 4a b )cos(x) +--R + +--R 2 3 2 2 2 2 4 +--R 4a c - 4a b c - 4a b c + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 3 5 +--R (- 2a b c - 6a b c + 2a b c + 6a b )cos(x) +--R + +--R 3 2 2 3 2 3 4 +--R (- 14a b c - 26a b c + 14a b c + 26a b )cos(x) +--R + +--R 3 2 2 3 2 3 3 +--R (- 36a b c - 44a b c + 36a b c + 44a b )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 44a b c - 36a b c + 44a b c + 36a b )cos(x) +--R + +--R 3 2 2 3 2 3 3 +--R (- 26a b c - 14a b c + 26a b c + 14a b )cos(x) - 6a b c +--R + +--R 2 2 3 2 3 +--R - 2a b c + 6a b c + 2a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 2 2 3 2 6 +--R (- 2a c - 2a c + 2a b c + 2a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 5 +--R (- 2a c - 12a c + (2a b - 10a )c + 12a b c + 10a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 4 +--R (- 10a c - 30a c + (10a b - 20a )c + 30a b c + 20a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 3 +--R (- 20a c - 40a c + (20a b - 20a )c + 40a b c + 20a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 2 +--R (- 20a c - 30a c + (20a b - 10a )c + 30a b c + 10a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 +--R (- 10a c - 12a c + (10a b - 2a )c + 12a b c + 2a b )cos(x) +--R + +--R 4 2 3 2 2 2 2 +--R - 2a c - 2a c + 2a b c + 2a b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 4 4 2 3 2 2 4 +--R (- 2b c + 2a b c + 2b c - 2a b )cos(x) - 2b c + 2a b c + 2b c +--R + +--R 4 +--R - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (- 2a b c + (- 4b + 2a b)c + 2a b c + 4b - 2a b )cos(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 2b c + (- 6b + 2a b)c + 8b - 2a b )cos(x) - 2b c +--R + +--R 3 3 2 3 5 +--R 2a b c - 2b c - 2a b c + 4b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 +--R (- 8a b c + 8a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (- 4b c - 20a b c + 4b c + 20a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 +--R (- 8b c - 16a b c + 8b c + 16a b )cos(x) - 4b c - 4a b c +--R + +--R 4 4 +--R 4b c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 5 2 3 4 +--R ((4b - 4a b)c - 4b + 4a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 3 +--R (- 4a b c + (16b - 12a b)c + 4a b c - 16b + 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (- 12a b c + (24b - 12a b)c + 12a b c - 24b + 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 +--R (- 12a b c + (16b - 4a b)c + 12a b c - 16b + 4a b )cos(x) +--R + +--R 3 3 2 3 5 +--R - 4a b c + 4b c + 4a b c - 4b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 4 4 5 +--R (2b c + 6a b c - 2b c - 6a b )cos(x) +--R + +--R 2 3 2 2 4 4 4 +--R (14b c + 26a b c - 14b c - 26a b )cos(x) +--R + +--R 2 3 2 2 4 4 3 +--R (36b c + 44a b c - 36b c - 44a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (44b c + 36a b c - 44b c - 36a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 +--R (26b c + 14a b c - 26b c - 14a b )cos(x) + 6b c + 2a b c +--R + +--R 4 4 +--R - 6b c - 2a b +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 3 6 +--R (2a b c + 2a b c - 2a b c - 2a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (2b c + 12a b c + (- 2b + 10a b)c - 12a b c - 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (10b c + 30a b c + (- 10b + 20a b)c - 30a b c - 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (20b c + 40a b c + (- 20b + 20a b)c - 40a b c - 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (20b c + 30a b c + (- 20b + 10a b)c - 30a b c - 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (10b c + 12a b c + (- 10b + 2a b)c - 12a b c - 2a b )cos(x) +--R + +--R 4 3 3 2 3 +--R 2b c + 2a b c - 2b c - 2a b c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 3 4 3 2 2 2 3 +--R ((- b c + (b + a b)c - a b )cos(x) - b c + (b + a b)c - a b ) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 2 3 2 4 4 3 2 2 +--R (- a c - 2b c + (- a b + a )c + 2b c + 2a b - a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 4 2 2 +--R - c - a c + (- 3b + a )c + (- 3a b + a )c + (4b - a b )c +--R + +--R 4 3 2 +--R 4a b - a b +--R * +--R cos(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 +--R - c + (- b + a )c - 2a b c + (2b - a b )c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 3 3 +--R (- 4a b c - 4a b c + 4a b c + 4a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (- 2b c - 12a b c + (2b - 10a b)c + 12a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (- 4b c - 12a b c + (4b - 8a b)c + 12a b c + 8a b )cos(x) - 2b c +--R + +--R 3 3 2 2 3 2 3 +--R - 4a b c + (2b - 2a b)c + 4a b c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 3 2 4 2 2 4 +--R (2b - 2a )c + (2a b - 2a )c + (- 2b + 2a b )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 2a c + (8b - 8a )c + (10a b - 6a )c + (- 8b + 8a b )c +--R + +--R 4 3 2 +--R - 8a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 6a c + (12b - 12a )c + (18a b - 6a )c + (- 12b + 12a b )c +--R + +--R 4 3 2 +--R - 12a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 6a c + (8b - 8a )c + (14a b - 2a )c + (- 8b + 8a b )c +--R + +--R 4 3 2 +--R - 8a b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 2 4 2 2 4 +--R - 2a c + (2b - 2a )c + 4a b c + (- 2b + 2a b )c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (b c + 4a b c + (- b + 3a b)c - 4a b c - 3a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (7b c + 20a b c + (- 7b + 13a b)c - 20a b c - 13a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (18b c + 40a b c + (- 18b + 22a b)c - 40a b c - 22a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (22b c + 40a b c + (- 22b + 18a b)c - 40a b c - 18a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (13b c + 20a b c + (- 13b + 7a b)c - 20a b c - 7a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R 3b c + 4a b c + (- 3b + a b)c - 4a b c - a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 6 +--R (a c + 2a c + (- a b + a )c - 2a b c - a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 +--R (c + 7a c + (- b + 11a )c + (- 7a b + 5a )c - 11a b c - 5a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R 5c + 20a c + (- 5b + 25a )c + (- 20a b + 10a )c - 25a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R 10c + 30a c + (- 10b + 30a )c + (- 30a b + 10a )c - 30a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R 10c + 25a c + (- 10b + 20a )c + (- 25a b + 5a )c - 20a b c +--R + +--R 3 2 +--R - 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 +--R (5c + 11a c + (- 5b + 7a )c + (- 11a b + a )c - 7a b c - a b ) +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 2 2 2 2 +--R c + 2a c + (- b + a )c - 2a b c - a b c +--R Type: Expression Integer +--E 246 + +--S 247 of 526 +t0848:= csc(x)^2/(a+b*cot(x)+c*csc(x)) +--R +--R +--R 2 +--R csc(x) +--R (236) ----------------------- +--R c csc(x) + b cot(x) + a +--R Type: Expression Integer +--E 247 + +--S 248 of 526 +r0848:= -2*a*c*atanh((a-(b-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/(b^2-c^2)/(a^2+b^2-c^2)^(1/2)+log(tan(1/2*x))/(b+c)-b*log(b+c+2*a*tan(1/2*x)-(b-c)*tan(1/2*x)^2)/(b^2-c^2) +--R +--R +--R (237) +--R +--------------+ +--R | 2 2 2 x 2 x +--R b\|- c + b + a log((c - b)tan(-) + 2a tan(-) + c + b) +--R 2 2 +--R + +--R x +--R +--------------+ (c - b)tan(-) + a +--R | 2 2 2 x 2 +--R (c - b)\|- c + b + a log(tan(-)) + 2a c atanh(-----------------) +--R 2 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression Integer +--E 248 + +--S 249 of 526 +a0848:= integrate(t0848,x) +--R +--R +--R (238) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (a c - a b)sin(x) + (- c + b c + a )cos(x) - b c + b +--R + +--R 2 +--R a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 3 2 +--R (- c + b c + (b + a )c - b - a b)sin(x) +--R + +--R 2 2 3 2 2 3 +--R (- a c + a b + a )cos(x) - a c + a b + a +--R / +--R a sin(x) + b cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) +--R (c - b)\|- c + b + a log(----------) +--R cos(x) + 1 +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R , +--R +--R +------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 sin(x) +--R (c - b)\|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R ((c - b)sin(x) + a cos(x) + a)\|c - b - a +--R - 2a c atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 249 + +--S 250 of 526 +m0848a:= a0848.1-r0848 +--R +--R +--R (239) +--R a c +--R * +--R log +--R 2 2 2 2 +--R ((a c - a b)sin(x) + (- c + b c + a )cos(x) - b c + b + a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 3 2 +--R (- c + b c + (b + a )c - b - a b)sin(x) +--R + +--R 2 2 3 2 2 3 +--R (- a c + a b + a )cos(x) - a c + a b + a +--R / +--R a sin(x) + b cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 x 2 x +--R - b\|- c + b + a log((c - b)tan(-) + 2a tan(-) + c + b) +--R 2 2 +--R + +--R +--------------+ +--R | 2 2 2 x +--R (- c + b)\|- c + b + a log(tan(-)) +--R 2 +--R + +--R +--------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R x +--R +--------------+ (c - b)tan(-) + a +--R | 2 2 2 sin(x) 2 +--R (c - b)\|- c + b + a log(----------) - 2a c atanh(-----------------) +--R cos(x) + 1 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression Integer +--E 250 + +--S 251 of 526 +d0848a:= D(m0848a,x) +--R +--R +--R (240) +--R 2 2 2 2 2 2 2 2 3 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 3 2 2 3 3 3 2 +--R (a c - a b c + (- a b - a )c + a b - a b)cos(x) +--R + +--R 3 3 3 2 2 3 3 +--R (- 2a c - 2a b)cos(x) - a c + a b c + (a b - a )c - a b +--R + +--R 3 +--R - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 2 2 2 3 +--R (b c + (- b - a b)c - a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + b c - a c + (- b - 3a b)c - b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (c + b c - 2a c + (- b - 3a b)c - b - a b )cos(x) + b c +--R + +--R 2 2 3 2 +--R - a c + (- b - a b)c +--R * +--R sin(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (2a c - 2a b c)sin(x) +--R + +--R 3 2 2 3 3 2 +--R (- 2a c + 6a b c - 6a b c + 2a b )cos(x) + 2a c - 2a b c +--R + +--R 2 3 +--R - 2a b c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (- 2b c + (4b + 2a )c - 2b c - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (- 2c + 2b c + 2a c + (2b + 2a b)c - 2b - 4a b )cos(x) +--R + +--R 3 2 2 3 2 4 2 2 +--R - 2b c + 2b c + (2b + 2a b)c - 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (- 2a c + 6a b c - 6a b c + 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (2a c - 2a b c - 2a b c + 2a b )cos(x) +--R + +--R 3 2 2 +--R (4a c - 8a b c + 4a b c)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 2 2 4 +--R (- 2b c + 4b c + (- 2b + 2a b)c - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (- 2c + 2b c + 2a c + (2b + 2a b)c - 2b - 4a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (- 2c + 2b c + 4a c + (2b - 2a b)c - 2b - 2a b )cos(x) +--R + +--R 3 2 2 2 3 2 +--R (- 2b c + (4b + 2a )c + (- 2b - 2a b)c)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 4 +--R 4a c sin(x) +--R + +--R 2 2 2 2 2 2 2 2 2 3 +--R ((- 6a c + 8a b c - 2a b )cos(x) + 2a c - 2a b )sin(x) +--R + +--R 3 2 2 3 3 3 2 +--R (2a c - 6a b c + (2a b + 2a )c + 2a b + 2a b)cos(x) +--R + +--R 3 3 3 3 2 +--R (- 4a c + 4a b + 4a b)cos(x) - 2a c - 2a b c +--R + +--R 2 3 3 3 +--R (2a b - 2a )c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (2b c - 4a c + (- 2b + 6a b)c - 6a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (2c + 2b c + 2a c + (- 2b - 6a b)c - 2b - 8a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 2b c + 4a c + (- 2b - 14a b)c - 2b - 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R 2b c - 2a c + (- 2b - 2a b)c +--R * +--R sin(x) +--R + +--R 2 2 3 4 +--R (- 4a b c + 4a b c + 4a b)cos(x) +--R + +--R 3 3 3 3 3 +--R (- 4a c + 4a c + 4a b + 8a b)cos(x) +--R + +--R 3 3 3 3 2 +--R (- 4a c + 8a c + 4a b + 4a b)cos(x) +--R + +--R 2 2 3 +--R (- 4a b c + (4a b + 4a )c)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (2a c + 2a b c)sin(x) +--R + +--R 3 2 2 3 3 2 +--R (- 2a c + 2a b c + 2a b c - 2a b )cos(x) + 2a c + 2a b c +--R + +--R 2 3 +--R - 2a b c - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 2b c + 2a c + (2b + 4a b)c + 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (- 2c - 2b c + 2a c + (2b + 6a b)c + 2b + 4a b )cos(x) +--R + +--R 3 2 2 3 2 4 2 2 +--R - 2b c - 2b c + (2b + 2a b)c + 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (- 2a c + 2a b c + 2a b c - 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (2a c + 2a b c - 2a b c - 2a b )cos(x) +--R + +--R 3 2 +--R (4a c - 4a b c)cos(x) +--R * +--R sin(x) +--R + +--R 3 3 2 2 2 4 +--R (- 2b c + (2b + 2a b)c + 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (- 2c - 2b c + 2a c + (2b + 6a b)c + 2b + 4a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (- 2c - 2b c + 4a c + (2b + 6a b)c + 2b + 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 2b c + 2a c + (2b + 2a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 2 2 3 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 3 2 2 3 3 3 2 +--R (a c - a b c + (- a b - a )c + a b - a b)cos(x) +--R + +--R 3 3 3 2 2 3 3 3 +--R (- 2a c - 2a b)cos(x) - a c + a b c + (a b - a )c - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 2 2 2 3 +--R (b c + (- b - a b)c - a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + b c - a c + (- b - 3a b)c - b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (c + b c - 2a c + (- b - 3a b)c - b - a b )cos(x) + b c +--R + +--R 2 2 3 2 +--R - a c + (- b - a b)c +--R * +--R sin(x) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 4 2 3 2 4 3 2 4 +--R (a c + (- 2a b - a )c + a b + a b )cos(x) + a c +--R + +--R 2 3 2 4 3 2 +--R (- 2a b - a )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 2 2 4 5 4 2 +--R (b c + a c - 2b c + (- a b - a )c + b - a b)cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R c + b c + (- 2b + a )c + (- 2b + a b)c +--R + +--R 4 2 2 4 5 2 3 4 +--R (b - a b - 2a )c + b - a b - 2a b +--R * +--R cos(x) +--R + +--R 5 2 3 2 2 4 4 2 3 4 +--R c - 2b c + a b c + (b - a )c - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 3 +--R (a b c + a b c + (- a b - a b)c - a b - a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R a c + 3a b c + (a b - a )c + (- 3a b - 3a b)c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R 2a c + 3a b c + (- a b - 2a )c + (- 3a b - 3a b)c - a b +--R + +--R 3 2 +--R - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R a c + a b c + (- a b - a )c + (- a b - a b)c +--R * +--R sin(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 3 3 4 +--R (- 2a c + 2a b c + (2a b + 2a )c + (- 2a b - 2a b)c)sin(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 +--R (- 2b c + 4b c + 2a b c + (- 4b - 4a b )c + 2b + 2a b ) +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c + 2b c + (4b + 2a )c + (- 4b - 2a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 2b - 2a b )c + 2b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 2 4 3 2 2 +--R (- 2a c + (4a b + 2a )c - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 2a c - 2a b c + (6a b + 2a )c + (2a b + 2a b)c - 4a b +--R + +--R 3 2 +--R - 4a b +--R * +--R cos(x) +--R + +--R 3 2 2 3 3 4 3 2 +--R - 2a b c + 2a b c + (2a b + 2a b)c - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 +--R (- 2b c + 4b c + 2a b c + (- 4b - 4a b )c + 2b + 2a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c + 2b c + (4b + 2a )c + (- 4b - 2a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 2b - 2a b )c + 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 2 2 4 2 2 +--R (- 2c + 4b c + 2a c + (- 4b - 4a b)c + (2b + 2a b )c)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 4 +--R (- 2a b c + 2a b c + (2a b + 2a b)c - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 2a c - 2a b c + (6a b + 2a )c + (2a b + 2a b)c - 4a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 4a c + 2a b c + (6a b + 4a )c + (- 2a b - 2a b)c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R (- 2a c + 2a b c + (2a b + 2a )c + (- 2a b - 2a b)c)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 4 4 +--R (- 4a c + (4a b + 4a )c)sin(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (2a c - 4a b c - 2a c + (4a b + 4a b)c - 2a b - 2a b )cos(x) +--R + +--R 4 2 3 2 4 3 2 +--R - 2a c + (4a b + 2a )c - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 +--R 2b c - 2a c + (- 4b - 4a b)c + (2a b + 2a )c + 2b +--R + +--R 2 3 4 +--R 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 2b c + (- 4b - 2a )c + (- 4b - 6a b)c +--R + +--R 4 2 2 5 2 3 4 +--R (2b + 2a b )c + 2b + 6a b + 4a b +--R * +--R cos(x) +--R + +--R 5 2 3 2 2 4 4 2 3 4 +--R 2c - 4b c - 2a b c + (2b - 2a )c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 3 +--R (- 2a b c + 6a b c + (2a b + 2a b)c - 6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R - 2a c + 6a b c + (10a b + 2a )c + (- 6a b - 6a b)c +--R + +--R 4 3 2 +--R - 8a b - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 3 4 3 2 +--R (10a b c + 2a b c + (- 10a b - 10a b)c - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R 2a c + 2a b c + (- 2a b - 2a )c + (- 2a b - 2a b)c +--R * +--R sin(x) +--R + +--R 2 2 2 3 4 4 +--R (- 4a b c + 4a b + 4a b)cos(x) +--R + +--R 2 3 2 2 2 2 4 2 3 4 3 +--R (- 4a c - 8a b c + (4a b + 4a )c + 8a b + 8a b)cos(x) +--R + +--R 2 3 2 2 2 2 4 2 3 4 2 +--R (- 8a c - 4a b c + (8a b + 8a )c + 4a b + 4a b)cos(x) +--R + +--R 2 3 2 2 4 +--R (- 4a c + (4a b + 4a )c)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 3 3 4 +--R (- 2a c - 2a b c + (2a b + 2a )c + (2a b + 2a b)c)sin(x) +--R + +--R 4 3 2 2 5 2 3 5 4 +--R (- 2b c + (4b + 2a b)c - 2b - 2a b )cos(x) - 2c - 2b c +--R + +--R 2 2 3 3 2 2 4 2 2 5 2 3 +--R (4b + 2a )c + (4b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (- 2a c - 4a b c + 2a c + (4a b + 4a b)c + 2a b + 2a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R - 2a c - 6a b c + (- 2a b + 2a )c + (6a b + 6a b)c +--R + +--R 4 3 2 +--R 4a b + 4a b +--R * +--R cos(x) +--R + +--R 3 2 2 3 3 4 3 2 +--R - 2a b c - 2a b c + (2a b + 2a b)c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 5 2 3 3 +--R (- 2b c + (4b + 2a b)c - 2b - 2a b )cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c - 2b c + (4b + 2a )c + (4b + 2a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 2b - 2a b )c - 2b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 4 2 2 +--R (- 2c + (4b + 2a )c + (- 2b - 2a b )c)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 4 +--R (- 2a b c - 2a b c + (2a b + 2a b)c + 2a b + 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 2a c - 6a b c + (- 2a b + 2a )c + (6a b + 6a b)c + 4a b +--R + +--R 3 2 +--R 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 4a c - 6a b c + (2a b + 4a )c + (6a b + 6a b)c + 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R (- 2a c - 2a b c + (2a b + 2a )c + (2a b + 2a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 3 2 4 3 2 4 +--R (a c + (- 2a b - a )c + a b + a b )cos(x) + a c +--R + +--R 2 3 2 4 3 2 +--R (- 2a b - a )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 2 2 4 5 4 2 +--R (b c + a c - 2b c + (- a b - a )c + b - a b)cos(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 4 +--R c + b c + (- 2b + a )c + (- 2b + a b)c + (b - a b - 2a )c +--R + +--R 5 2 3 4 +--R b - a b - 2a b +--R * +--R cos(x) +--R + +--R 5 2 3 2 2 4 4 2 3 4 +--R c - 2b c + a b c + (b - a )c - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 3 +--R (a b c + a b c + (- a b - a b)c - a b - a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R a c + 3a b c + (a b - a )c + (- 3a b - 3a b)c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R 2a c + 3a b c + (- a b - 2a )c + (- 3a b - 3a b)c - a b +--R + +--R 3 2 +--R - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R a c + a b c + (- a b - a )c + (- a b - a b)c +--R * +--R sin(x) +--R / +--R 2 3 2 2 2 2 2 3 2 3 2 2 +--R (2a c - 2a b c - 2a b c + 2a b )cos(x) + 2a c - 2a b c +--R + +--R 2 2 2 3 +--R - 2a b c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 3 2 3 4 3 2 2 +--R (- 2a c + 4a b c + 2a c - 4a b c + 2a b - 2a b )cos(x) +--R + +--R 3 2 3 2 4 3 3 2 3 +--R (4a c - 4a b )cos(x) + 2a c - 4a b c + 2a c + 4a b c +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 2 4 2 3 3 +--R (- 2b c + 2b c + (2b + 2a b)c - 2b c - 2a b )cos(x) +--R + +--R 5 2 2 3 3 2 2 2 2 5 +--R - 2c + (2b + 2a )c + (2b + 4a b)c - 2a b c - 2b +--R + +--R 2 3 +--R - 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 3 2 2 2 2 5 +--R - 2c + (2b + 4a )c + (2b + 2a b)c - 4a b c - 2b +--R + +--R 2 3 +--R - 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 3 2 4 2 2 +--R - 2b c + (2b + 2a )c + 2b c + (- 2b - 2a b )c +--R * +--R sin(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 3 2 3 2 3 2 3 +--R ((4a c - 4a b )cos(x) + 4a c - 4a b )sin(x) +--R + +--R 2 3 2 2 2 2 4 2 3 4 2 +--R (- 4a c + 4a b c + (4a b + 4a )c - 4a b + 4a b)cos(x) +--R + +--R 4 4 2 3 2 2 2 2 4 +--R (8a c + 8a b)cos(x) + 4a c - 4a b c + (- 4a b + 4a )c +--R + +--R 2 3 4 +--R 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 2 3 +--R (- 4a b c + (4a b + 4a b)c + 4a b )cos(x) +--R + +--R 4 3 3 2 3 3 4 +--R - 4a c - 4a b c + 4a c + (4a b + 12a b)c + 4a b +--R + +--R 3 2 +--R 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 3 3 4 +--R - 4a c - 4a b c + 8a c + (4a b + 12a b)c + 4a b +--R + +--R 3 2 +--R 4a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 3 +--R - 4a b c + 4a c + (4a b + 4a b)c +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 2 +--R (2a c + 2a b c - 2a b c - 2a b )cos(x) + 2a c + 2a b c +--R + +--R 2 2 2 3 +--R - 2a b c - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 2 3 4 3 2 2 +--R (- 2a c + (4a b + 2a )c + 4a b c - 2a b + 2a b )cos(x) +--R + +--R 3 2 3 3 2 4 2 3 2 +--R (4a c + 8a b c + 4a b )cos(x) + 2a c + (- 4a b + 2a )c +--R + +--R 3 4 3 2 +--R 4a b c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 2 4 2 2 2 3 +--R (- 2b c - 2b c + (2b + 2a b)c + (2b + 4a b )c + 2a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c - 4b c + (- 2b + 2a )c + (2b + 8a b)c +--R + +--R 4 2 2 5 2 3 +--R (4b + 10a b )c + 2b + 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c - 4b c + (- 2b + 4a )c + (2b + 10a b)c +--R + +--R 4 2 2 5 2 3 +--R (4b + 8a b )c + 2b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 3 2 2 4 2 2 +--R - 2b c + (- 2b + 2a )c + (2b + 4a b)c + (2b + 2a b )c +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c + 2a b c + (4a b + 2a )c + (- 4a b - 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c + 2a b c + (4a b + 2a )c + (- 4a b - 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 2 4 3 2 3 +--R - 2b c + (2b - 2a )c + (4b + 2a b)c +--R + +--R 4 2 2 4 2 5 2 3 6 4 2 +--R (- 4b + 2a b + 2a )c + (- 2b - 2a b )c + 2b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 4 4 2 2 4 2 6 2 4 +--R - 2c + (6b - 2a )c + (- 6b + 4a b + 4a )c + 2b - 2a b +--R + +--R 4 2 +--R - 4a b +--R * +--R cos(x) +--R + +--R 6 5 2 4 3 2 3 +--R - 2c + 2b c + 4b c + (- 4b - 2a b)c +--R + +--R 4 2 2 4 2 5 2 3 2 4 4 2 +--R (- 2b + 2a b + 2a )c + (2b + 2a b )c - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 5 3 3 3 +--R (- 2a b c + (4a b + 2a b)c - 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 4a b c + (4a b + 2a )c + (8a b + 4a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c - 4a b - 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c - 2a b c + (8a b + 4a )c + (4a b + 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 4a b - 4a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 5 2 3 3 4 3 2 +--R - 2a c + (4a b + 2a )c + (- 2a b - 2a b )c +--R * +--R sin(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 4 2 2 4 4 2 2 4 +--R (- 4a c + (8a b + 4a )c - 4a b - 4a b )cos(x) - 4a c +--R + +--R 2 2 4 2 2 4 4 2 +--R (8a b + 4a )c - 4a b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 3 3 2 3 2 5 5 5 +--R (- 4a b c - 4a c + 8a b c + (4a b + 4a )c - 4a b + 4a b) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c - 4a b c + (8a b - 4a )c + (8a b - 4a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 4a b + 4a b + 8a )c - 4a b + 4a b + 8a b +--R * +--R cos(x) +--R + +--R 5 2 3 3 2 4 5 3 3 5 +--R - 4a c + 8a b c - 4a b c + (- 4a b + 4a )c + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 3 4 2 4 4 2 3 +--R (- 4a b c - 4a b c + (4a b + 4a b)c + 4a b + 4a b )cos(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 +--R - 4a c - 12a b c + (- 4a b + 4a )c + (12a b + 12a b)c +--R + +--R 2 4 4 2 +--R 8a b + 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 +--R - 8a c - 12a b c + (4a b + 8a )c + (12a b + 12a b)c +--R + +--R 2 4 4 2 +--R 4a b + 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 +--R - 4a c - 4a b c + (4a b + 4a )c + (4a b + 4a b)c +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 2a b c + (4a b + 2a )c + (4a b + 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 2a b c + (4a b + 2a )c + (4a b + 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 2 4 3 2 3 +--R - 2b c + (- 2b - 2a )c + (4b - 2a b)c +--R + +--R 4 2 2 4 2 5 2 3 4 6 4 2 +--R (4b + 2a b + 2a )c + (- 2b + 2a b + 4a b)c - 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R - 2c - 4b c + (2b - 2a )c + (8b - 4a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 4 2 +--R (2b + 4a )c + (- 4b + 4a b + 8a b)c - 2b + 2a b + 4a b +--R * +--R cos(x) +--R + +--R 6 5 2 4 3 2 3 4 2 2 4 2 +--R - 2c - 2b c + 4b c + (4b - 2a b)c + (- 2b - 2a b + 2a )c +--R + +--R 5 2 3 4 2 4 4 2 +--R (- 2b + 2a b + 4a b)c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 2 5 +--R - 2a b c - 4a b c + 2a b c + (4a b + 4a b )c + 2a b +--R + +--R 3 3 +--R 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 8a b c + (- 8a b + 2a )c + (4a b + 8a b)c +--R + +--R 4 3 2 5 3 3 +--R (10a b + 10a b )c + 4a b + 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c - 10a b c + (- 4a b + 4a )c + (8a b + 10a b)c +--R + +--R 4 3 2 5 3 3 +--R (8a b + 8a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 3 3 3 2 4 3 2 +--R - 2a c - 4a b c + 2a c + (4a b + 4a b)c + (2a b + 2a b )c +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R Type: Expression Integer +--E 251 + +--S 252 of 526 +m0848b:= a0848.2-r0848 +--R +--R +--R (241) +--R - +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R b\|- c + b + a \|c - b - a +--R * +--R x 2 x +--R log((c - b)tan(-) + 2a tan(-) + c + b) +--R 2 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x +--R (- c + b)\|- c + b + a \|c - b - a log(tan(-)) +--R 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|- c + b + a \|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 sin(x) +--R (c - b)\|- c + b + a \|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (c - b)tan(-) + a +--R | 2 2 2 2 +--R - 2a c\|c - b - a atanh(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R +------------+ +--R +--------------+ | 2 2 2 +--R | 2 2 2 ((c - b)sin(x) + a cos(x) + a)\|c - b - a +--R - 2a c\|- c + b + a atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b + a \|c - b - a +--R Type: Expression Integer +--E 252 + +--S 253 of 526 +d0848b:= D(m0848b,x) +--R +--R +--R (242) +--R 2 2 2 2 4 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 2 2 3 2 2 +--R (- b c - 2a c + b - 2a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 2 2 +--R (- c - b c + (b - 4a )c + b - 4a b)cos(x) - c + (b - 2a )c +--R + +--R 2 +--R - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 +--R (- a c - 4a b c - 3a b )cos(x) +--R + +--R 2 2 2 +--R (- 5a c - 12a b c - 7a b )cos(x) +--R + +--R 2 2 2 2 +--R (- 7a c - 12a b c - 5a b )cos(x) - 3a c - 4a b c - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 3 +--R (- b c - 2b c - b )cos(x) + (- c - 5b c - 7b c - 3b )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3c - 9b c - 9b c - 3b )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 3c - 7b c - 5b c - b )cos(x) - c - 2b c - b c +--R * +--R sin(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R (2a c - 2a b c)sin(x) +--R + +--R 2 2 3 3 2 2 3 4 +--R ((2b c - 4b c + 2b )cos(x) + 2c - 2b c - 2b c + 2b )sin(x) +--R + +--R 2 2 2 2 2 2 +--R (4a c - 4a b )cos(x) + (6a c + 2a b c - 8a b )cos(x) + 2a c +--R + +--R 2 +--R 2a b c - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R (4b c - 4b c)cos(x) + (4c + 4b c - 4b c - 4b )cos(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (6c + 2b c - 2b c - 6b )cos(x) + 2c + 2b c - 2b c - 2b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (2a c + 2a b c - 4a b )cos(x) + (6a c + 2a b c - 8a b )cos(x) +--R + +--R 2 2 2 2 +--R (6a c - 2a b c - 4a b )cos(x) + (2a c - 2a b c)cos(x) +--R * +--R sin(x) +--R + +--R 2 3 5 3 2 2 3 4 +--R (2b c - 2b )cos(x) + (2c + 6b c - 2b c - 6b )cos(x) +--R + +--R 3 2 2 3 3 3 2 2 3 2 +--R (6c + 6b c - 6b c - 6b )cos(x) + (6c + 2b c - 6b c - 2b )cos(x) +--R + +--R 3 2 +--R (2c - 2b c)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R 4a c sin(x) +--R + +--R 2 2 2 2 4 +--R ((- 2a c + 4a b c - 2a b )cos(x) + 2a c - 2a b )sin(x) +--R + +--R 2 2 3 2 2 +--R (- 2b c + 4a c + 2b + 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 2 +--R (- 2c - 2b c + (2b + 4a )c + 2b + 8a b)cos(x) - 2c + 2b c +--R + +--R 2 +--R 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 2 2 +--R (- 2a c - 6a b )cos(x) + (- 2a c - 8a b c - 6a b )cos(x) +--R + +--R 2 2 2 2 +--R (- 2a c - 8a b c + 2a b )cos(x) - 2a c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 3 2 4 +--R (- 2b c + (- 4b + 4a )c - 2b + 8a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- 2c - 10b c + (- 14b + 12a )c - 6b + 16a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6c - 18b c + (- 18b + 12a )c - 6b + 8a b)cos(x) +--R + +--R 3 2 2 2 3 3 2 2 +--R (- 6c - 14b c + (- 10b + 4a )c - 2b )cos(x) - 2c - 4b c - 2b c +--R * +--R sin(x) +--R + +--R 2 5 2 2 4 +--R (4a b c + 4a b )cos(x) + (4a c + 16a b c + 12a b )cos(x) +--R + +--R 2 2 3 +--R (12a c + 24a b c + 12a b )cos(x) +--R + +--R 2 2 2 2 +--R (12a c + 16a b c + 4a b )cos(x) + (4a c + 4a b c)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R (2a c + 2a b c)sin(x) +--R + +--R 2 3 3 2 2 3 4 +--R ((2b c - 2b )cos(x) + 2c + 2b c - 2b c - 2b )sin(x) +--R + +--R 2 2 2 2 2 +--R (4a c + 8a b c + 4a b )cos(x) + (6a c + 14a b c + 8a b )cos(x) +--R + +--R 2 2 +--R 2a c + 6a b c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R (4b c + 4b c)cos(x) + (4c + 12b c + 12b c + 4b )cos(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (6c + 14b c + 14b c + 6b )cos(x) + 2c + 6b c + 6b c + 2b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R (2a c + 6a b c + 4a b )cos(x) +--R + +--R 2 2 3 +--R (6a c + 14a b c + 8a b )cos(x) +--R + +--R 2 2 2 2 +--R (6a c + 10a b c + 4a b )cos(x) + (2a c + 2a b c)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 3 5 3 2 2 3 4 +--R (2b c + 4b c + 2b )cos(x) + (2c + 10b c + 14b c + 6b )cos(x) +--R + +--R 3 2 2 3 3 +--R (6c + 18b c + 18b c + 6b )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6c + 14b c + 10b c + 2b )cos(x) + (2c + 4b c + 2b c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 4 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 2 2 3 2 2 +--R (- b c - 2a c + b - 2a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 2 2 2 +--R (- c - b c + (b - 4a )c + b - 4a b)cos(x) - c + (b - 2a )c - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 2 2 +--R (- a c - 4a b c - 3a b )cos(x) + (- 5a c - 12a b c - 7a b )cos(x) +--R + +--R 2 2 2 2 +--R (- 7a c - 12a b c - 5a b )cos(x) - 3a c - 4a b c - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 3 +--R (- b c - 2b c - b )cos(x) + (- c - 5b c - 7b c - 3b )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3c - 9b c - 9b c - 3b )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 3c - 7b c - 5b c - b )cos(x) - c - 2b c - b c +--R * +--R sin(x) +--R / +--R 3 2 2 3 3 2 +--R (2a c - 2a b c - 2a b c + 2a b )cos(x) + 2a c - 2a b c +--R + +--R 2 3 +--R - 2a b c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (2b c + (- 2b + 4a )c - 2b c + 2b - 4a b )cos(x) +--R + +--R 4 2 2 2 4 2 2 4 3 +--R (2c + (- 4b + 8a )c + 2b - 8a b )cos(x) + 2c - 2b c +--R + +--R 2 2 2 3 2 2 +--R (- 2b + 4a )c + 2b c - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (2a c + 6a b c - 2a b c - 6a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (10a c + 14a b c - 10a b c - 14a b )cos(x) +--R + +--R 3 2 2 3 3 2 +--R (14a c + 10a b c - 14a b c - 10a b )cos(x) + 6a c + 2a b c +--R + +--R 2 3 +--R - 6a b c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (2b c + 2b c - 2b c - 2b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2c + 8b c + 4b c - 8b c - 6b )cos(x) +--R + +--R 4 3 3 4 2 +--R (6c + 12b c - 12b c - 6b )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (6c + 8b c - 4b c - 8b c - 2b )cos(x) + 2c + 2b c - 2b c +--R + +--R 3 +--R - 2b c +--R * +--R sin(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 2 2 4 +--R ((4a c - 4a b )cos(x) + 4a c - 4a b )sin(x) +--R + +--R 2 3 3 3 2 +--R (4a b c + 8a c - 4a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 3 +--R (4a c + 4a b c + (- 4a b + 16a )c - 4a b + 16a b)cos(x) +--R + +--R 3 2 3 3 +--R 4a c + (- 4a b + 8a )c + 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 3 +--R (4a c + 16a b c + 12a b )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (20a c + 48a b c + 28a b )cos(x) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (28a c + 48a b c + 20a b )cos(x) + 12a c + 16a b c + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 +--R (4a b c + 8a b c + 4a b )cos(x) +--R + +--R 3 2 2 3 3 +--R (4a c + 20a b c + 28a b c + 12a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (12a c + 36a b c + 36a b c + 12a b )cos(x) +--R + +--R 3 2 2 3 3 2 +--R (12a c + 28a b c + 20a b c + 4a b )cos(x) + 4a c + 8a b c +--R + +--R 2 +--R 4a b c +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 3 2 +--R (2a c + 2a b c - 2a b c - 2a b )cos(x) + 2a c + 2a b c +--R + +--R 2 3 +--R - 2a b c - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 2 3 2 4 2 2 2 +--R (2b c + (2b + 4a )c + (- 2b + 8a b)c - 2b + 4a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 8a c + (- 4b + 16a b)c - 2b + 8a b )cos(x) +--R + +--R 4 3 2 2 2 3 2 2 2 +--R 2c + 2b c + (- 2b + 4a )c + (- 2b + 8a b)c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (2a c + 10a b c + 14a b c + 6a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (10a c + 34a b c + 38a b c + 14a b )cos(x) +--R + +--R 3 2 2 3 3 2 +--R (14a c + 38a b c + 34a b c + 10a b )cos(x) + 6a c + 14a b c +--R + +--R 2 3 +--R 10a b c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (2b c + 6b c + 6b c + 2b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2c + 12b c + 24b c + 20b c + 6b )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (6c + 24b c + 36b c + 24b c + 6b )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (6c + 20b c + 24b c + 12b c + 2b )cos(x) + 2c + 6b c + 6b c +--R + +--R 3 +--R 2b c +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R Type: Expression Integer +--E 253 + +--S 254 of 526 +t0849:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x)) +--R +--R +--R C sin(x) + A +--R (243) ----------------------- +--R c sin(x) + b cos(x) + a +--R Type: Expression Integer +--E 254 + +--S 255 of 526 +r0849:= c*C*x/(b^2+c^2)+2*(A-a*c*C/(b^2+c^2))*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(1/2)-b*C*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) +--R +--R +--R (244) +--R +--------------+ +--R | 2 2 2 +--R - C b\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R x +--R (b - a)tan(-) - c +--------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c + 2C a c - 2A b )atan(-----------------) + C c x\|- c - b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression Integer +--E 255 + +--S 256 of 526 +a0849:= integrate(t0849,x) +--R +--R +--R (245) +--R [ +--R 2 2 +--R (- A c + C a c - A b ) +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R | 2 2 2 2 +--R C b\|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R C c x\|c + b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|c + b - a +--R , +--R +--R +--------------+ +--R | 2 2 2 2 +--R C b\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R +--------------+ +--R | 2 2 2 +--R C c x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 256 + +--S 257 of 526 +m0849a:= a0849.1-r0849 +--R +--R +--R (246) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (- A c + C a c - A b )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R C b\|- c - b + a \|c + b - a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R C b\|- c - b + a \|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|- c - b + a \|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2A c - 2C a c + 2A b )\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c + b )\|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 257 + +--S 258 of 526 +d0849a:= D(m0849a,x) +--R +--R +--R (247) +--R 3 2 2 2 3 2 2 3 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c +--R + +--R 5 4 2 3 +--R - A b + 2A a b - A a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- 2A a b + A a )c +--R + +--R 2 2 3 2 4 3 2 2 +--R (- C a b + 2C a b - C a )c + (A b - 2A a b + A a b )c +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R - A c + C a c - A b c +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 +--R (- 2A b + A a)c + (2C a b - C a )c + (- 3A b + 2A a b )c +--R + +--R 3 2 2 5 4 +--R (C a b - C a b )c - A b + A a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 +--R - 2A b c + 2C a b c + (- 3A b + A a b)c +--R + +--R 3 3 5 2 3 +--R (C a b - C a b)c - A b + A a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 2 2 3 +--R - A a c + C a c + (- 2A a b + A a b)c + (C a b - C a b)c +--R + +--R 4 2 3 +--R - A a b + A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 2 2 2 +--R 2A c - 2C a c + (4A b - 2A a b)c + (- 2C a b + 2C a b)c +--R + +--R 4 3 +--R (2A b - 2A a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 +--R (- 2A b + 2A a b )c +--R * +--R sin(x) +--R + +--R 5 4 2 3 2 2 2 +--R 2A c - 2C a c + (4A b - 2A a b)c + (- 2C a b + 2C a b)c +--R + +--R 4 3 +--R (2A b - 2A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 +--R 2A c - 2C a c + (2A b + 2A a b - 2A a )c +--R + +--R 2 3 2 3 2 2 +--R (- 2C a b + 2C a )c + (2A a b - 2A a b )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 3 2 2 3 3 +--R 2A b c - 2C a b c + (3A b - A a b)c + (- C a b + C a b)c +--R + +--R 5 2 3 +--R A b - A a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- 2A a b + A a )c +--R + +--R 2 2 3 2 4 3 2 2 +--R (- C a b + 2C a b - C a )c + (A b - 2A a b + A a b )c +--R * +--R cos(x) +--R + +--R 5 4 2 3 2 2 2 +--R - A c + C a c + (- 3A b + 2A a b)c + (2C a b - 2C a b)c +--R + +--R 4 3 +--R (- 2A b + 2A a b )c +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 3 2 2 5 4 +--R (A a c - C a c + A b c + (- C a b + C a b )c + A b - A a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 2 3 2 2 3 5 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c - A b +--R + +--R 4 2 3 +--R 2A a b - A a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 2 2 3 +--R - A a c + C a c + (- 2A a b + A a b)c + (C a b - C a b)c +--R + +--R 4 2 3 +--R - A a b + A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b - A a b + A a )c +--R + +--R 2 3 3 4 3 3 2 +--R (C a b - C a )c + (A b - 2A a b + A a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b - A a b +--R + +--R 2 4 3 3 +--R - A a b + A a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - A c + C a c + (- A b - A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 3 2 +--R (A b - 2A a b + A a b)c +--R + +--R 4 2 3 3 2 4 6 5 2 4 +--R (- C a b + C a b + C a b - C a b)c + A b - A a b - A a b +--R + +--R 3 3 +--R A a b +--R * +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + A a)c + (2C a b - C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + 2A a b + 2A a b - A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - C a b - 2C a b + C a )c +--R + +--R 5 4 2 3 3 2 +--R (- 2A b + A a b + 2A a b - A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 +--R - 2A b c + 2C a b c + (- 4A b + 2A a b)c +--R + +--R 3 3 2 5 2 3 +--R (2C a b - 2C a b)c + (- 2A b + 2A a b )c +--R * +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 2 +--R (- A a b + A a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 2 4 2 3 3 +--R 2A c - 2C a c + (4A b - 2A a )c + (- 2C a b + 2C a )c +--R + +--R 4 2 2 2 +--R (2A b - 2A a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + 4A a b + 2A a b - 2A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - 2C a b - 2C a b + 2C a )c +--R + +--R 5 4 2 3 3 2 +--R (- 2A b + 2A a b + 2A a b - 2A a b )c +--R * +--R sin(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2A c - 2C a c + (4A b - 2A a )c + (- 2C a b + 2C a )c +--R + +--R 4 2 2 2 +--R (2A b - 2A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2A c - 2C a c + (4A b - 2A a )c + (- 2C a b + 2C a )c +--R + +--R 4 2 2 2 +--R (2A b - 2A a b )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 3 2 3 3 3 2 +--R 2A b c - 2C a b c + (4A b - 2A a b)c + (- 2C a b + 2C a b)c +--R + +--R 5 2 3 +--R (2A b - 2A a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - A c + C a c + (- A b - A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 3 2 +--R (A b - 2A a b + A a b)c +--R + +--R 4 2 3 3 2 4 6 5 2 4 +--R (- C a b + C a b + C a b - C a b)c + A b - A a b - A a b +--R + +--R 3 3 +--R A a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- 3A b + A a b + A a )c +--R + +--R 2 2 3 3 4 3 2 2 3 2 +--R (2C a b - C a b - C a )c + (- 3A b + 2A a b + 2A a b - A a b)c +--R + +--R 4 2 3 3 2 4 6 5 2 4 3 3 +--R (C a b - C a b - C a b + C a b)c - A b + A a b + A a b - A a b +--R * +--R sin(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R A a c - C a c + (2A a b - A a )c + (- C a b + C a )c +--R + +--R 4 3 2 +--R (A a b - A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 2 +--R (- A a b + A a b )c +--R / +--R 2 2 4 4 3 2 2 2 2 +--R ((b - 2a b + a )c + (b - 2a b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 3a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (b - 3a b + 3a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 3 +--R (- b + a)c + (- 2b + 4a b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + 3a b - 3a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 3 3 +--R ((- b + a b)c + (- b + 2a b - a b)c - a b + 2a b - a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 6 +--R (- b + a )c + (- 2b + 2a b - a b + 2a b - a )c - b +--R + +--R 5 2 4 3 3 4 2 +--R 2a b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 2 5 2 4 3 3 +--R (- a b + a )c + (- 2a b + 3a b - a b)c - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c )sin(x) +--R + +--R 6 2 4 4 3 2 2 2 +--R (2c + (4a b - 2a )c + (- 2b + 4a b - 2a b )c )cos(x) +--R + +--R 6 2 2 4 4 3 2 2 2 +--R 2c + (4b - 4a b + 2a )c + (2b - 4a b + 2a b )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 4 2 3 2 +--R (2b c + (2b + 2a b - 2a b)c + (2a b - 2a b )c)cos(x) +--R + +--R 5 3 2 3 3 +--R (2b + 2a)c + (4b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 +--R (2b - 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 4 2 3 +--R 2a c + (4a b - 2a b)c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 2 2 +--R ((- b + a )c + (- b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (b + a)c + (2a b + a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + a b + a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 3 5 4 2 3 3 2 +--R (b + a)c + (2b - a b + a )c + (b - a b - a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 3 2 5 3 3 2 +--R ((b + a b)c + (b + 2a b - a b)c + a b - a b )cos(x) +--R + +--R 2 2 4 4 3 2 2 4 2 6 4 2 +--R ((b + 2a b + a )c + (2b + 2a b + a b - a )c + b - a b )cos(x) +--R + +--R 2 4 3 2 2 3 2 5 3 3 +--R (a b + a )c + (2a b + a b - a b)c + a b - a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 2a b + a )c + (2b - 4a b + a b + 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b - 2a b + 2a b - a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 6 3 4 4 3 +--R (b - 3a b + 2a b + a b - a b)c + b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 +--R (- b + a)c + (- 2b + 3a b - a b)c +--R + +--R 5 4 2 3 4 5 2 6 2 5 4 3 5 2 +--R (- b + 3a b - 3a b + 2a b - a )c + a b - 2a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b + a b)c + (- 2b + 2a b + a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (- b + a b + a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b + a )c + (- 2a b + 2a b + a b - a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- a b + a b + a b - a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (- 2b + 2a)c + (- 4b + 4a b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 3 +--R 2c + (2b + 2a b - 2a )c + (- 2b + 4a b - 2a b)c +--R + +--R 6 5 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 2 2 3 4 3 +--R 2c + (4b - 2a b)c + (2b - 4a b + 2a b + 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 2a b + 2a b + 2a b - 2a b )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 2 2 +--R (2b c + (4b - 2a b)c + (2b - 2a b )c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2b + 2a)c + (4b + 4a b - 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b - 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 2 +--R 2a c + (4a b - 2a )c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c)sin(x) +--R + +--R 6 3 2 3 4 +--R (b + a)c + (b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 2 5 4 3 +--R (- b + a b + 2a b - a b - a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 5 4 2 3 3 2 5 2 +--R (b + a)c + (2b + a b - a b)c + (b - a b - a b + 2a b - a )c +--R + +--R 6 3 4 5 2 +--R - a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b + a b)c + (2b + 2a b - a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (b + a b - a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b + 2a b + a )c + (2b + 4a b + a b - 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b + 2a b - 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 5 2 4 3 3 4 2 +--R (a b + a )c + (2a b + 2a b - a b - a )c + (a b + a b - a b - a b )c +--R Type: Expression Integer +--E 258 + +--S 259 of 526 +m0849b:= a0849.2-r0849 +--R +--R +--R (248) +--R +--------------+ +--R | 2 2 2 +--R C b\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +--R | 2 2 2 2 +--R C b\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2A c - 2C a c + 2A b )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression Integer +--E 259 + +--S 260 of 526 +d0849b:= D(m0849b,x) +--R +--R +--R (249) +--R 2 2 3 2 2 +--R ((- A b + A a)c + (C a b - C a )c - A b + A a b )sin(x) +--R + +--R 3 2 2 3 2 2 +--R ((- 2A c + 2C a c - 2A b c)cos(x) - 2A c + 2C a c - 2A b c)sin(x) +--R + +--R 2 2 3 2 2 +--R ((- 3A b + A a)c + (3C a b - C a )c - 3A b + A a b )cos(x) +--R + +--R 2 3 2 +--R (- 4A b c + 4C a b c - 4A b )cos(x) + (- A b - A a)c +--R + +--R 2 3 2 +--R (C a b + C a )c - A b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 3 2 2 2 +--R (4A c - 4C a c + 4A b c)sin(x) + (4A c - 4C a c + 4A b c)cos(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + 4A b c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 2 +--R ((3A b + A a)c + (- 3C a b - C a )c + 3A b + A a b )sin(x) +--R + +--R 3 2 2 3 2 2 +--R ((- 2A c + 2C a c - 2A b c)cos(x) - 2A c + 2C a c - 2A b c)sin(x) +--R + +--R 2 2 3 2 2 +--R ((A b + A a)c + (- C a b - C a )c + A b + A a b )cos(x) +--R + +--R 2 2 3 2 +--R (- A b - A a)c + (C a b + C a )c - A b - A a b +--R / +--R 2 2 2 4 3 2 2 2 +--R ((b - 2a b + a )c + b - 2a b + a b )sin(x) +--R + +--R 3 3 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)cos(x) + (- 2b + 2a)c +--R + +--R 3 2 +--R (- 2b + 2a b )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 2 4 2 2 +--R ((- 2b + 2a )c - 2b + 2a b )cos(x) + (- b + a )c - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)sin(x) +--R + +--R 4 2 2 4 2 2 +--R ((4c + 4b c )cos(x) + 4c + 4b c )sin(x) +--R + +--R 3 3 2 2 +--R ((2b + 2a)c + (2b + 2a b )c)cos(x) +--R + +--R 3 3 2 3 3 2 +--R ((4b + 4a)c + (4b + 4a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )sin(x) +--R + +--R 3 3 2 3 3 2 +--R (((2b + 2a)c + (2b + 2a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c) +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R ((b + 2a b + a )c + b + 2a b + a b )cos(x) +--R + +--R 2 2 2 4 3 2 2 2 2 2 +--R ((2b + 4a b + 2a )c + 2b + 4a b + 2a b )cos(x) + (b + 2a b + a )c +--R + +--R 4 3 2 2 +--R b + 2a b + a b +--R Type: Expression Integer +--E 260 + +--S 261 of 526 +t0850:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x))^2 +--R +--R +--R (250) +--R C sin(x) + A +--R --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R Type: Expression Integer +--E 261 + +--S 262 of 526 +r0850:= 2*(a*A-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(3/2)-(b*C-(A*c-a*C)*cos(x)+A*b*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (251) +--R 2 2 +--R ((- 2C c + 2A a c)sin(x) + (- 2C b c + 2A a b)cos(x) - 2C a c + 2A a ) +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (A b sin(x) + (- A c + C a)cos(x) + C b)\|- c - b + a +--R / +--R 3 2 2 2 3 2 2 2 3 +--R ((c + (b - a )c)sin(x) + (b c + b - a b)cos(x) + a c + a b - a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 262 + +--S 263 of 526 +a0850:= integrate(t0850,x) +--R +--R +--R (252) +--R [ +--R 2 2 +--R ((C b - C a)c + (- A a b + A a )c)sin(x) +--R + +--R 2 2 2 2 2 +--R ((C b - C a b)c - A a b + A a b)cos(x) + (C a b - C a )c - A a b +--R + +--R 3 +--R A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 2 2 +--R (A c + (C b - C a)c + A b - A a b)sin(x) +--R + +--R 2 2 2 2 +--R (A a c + C b - C a )cos(x) + A a c + C b - C a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 2 2 +--R ((2C b - 2C a)c + (- 2A a b + 2A a )c)sin(x) +--R + +--R 2 2 2 2 +--R ((2C b - 2C a b)c - 2A a b + 2A a b)cos(x) + (2C a b - 2C a )c +--R + +--R 2 3 +--R - 2A a b + 2A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 2 2 +--R (A c + (C b - C a)c + A b - A a b)sin(x) +--R + +--R 2 2 2 2 +--R (A a c + C b - C a )cos(x) + A a c + C b - C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 263 + +--S 264 of 526 +m0850a:= a0850.1-r0850 +--R +--R +--R (253) +--R +--------------+ +--R 2 | 2 2 2 +--R ((C b - C a)c - A a b + A a )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 | 2 2 2 2 +--R ((2C b - 2C a)c - 2A a b + 2A a )\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (A c + C b - C a)\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 3 2 2 3 | 2 2 2 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 264 + +--S 265 of 526 +d0850a:= D(m0850a,x) +--R +--R +--R (254) +--R 3 2 2 3 2 2 3 2 +--R ((- C b + 2C a b - C a b)c + A a b - 2A a b + A a b)sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + A a c + (C b - 2C a b + C a )c +--R + +--R 2 2 3 +--R (- A a b + 2A a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 +--R - C c + A a c +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (- 2C b + C a)c + (2A a b - A a )c + (- C b + C a b )c +--R + +--R 3 2 2 +--R A a b - A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 2C b c + 2A a b c + (- C b + C a b)c + A a b - A a b) +--R * +--R cos(x) +--R + +--R 3 2 2 2 2 2 2 3 +--R - C a c + A a c + (- C a b + C a b)c + A a b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 2 +--R (2C c - 2A a c + (2C b - 2C a b)c + (- 2A a b + 2A a b)c) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 +--R ((- 2C b + 2C a)c + (2A a b - 2A a )c )sin(x) +--R + +--R 4 3 2 2 2 2 +--R (2C c - 2A a c + (2C b - 2C a b)c + (- 2A a b + 2A a b)c) +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 2 3 +--R (2C c - 2A a c + (2C a b - 2C a )c + (- 2A a b + 2A a )c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 2 3 3 2 +--R (2C b c - 2A a b c + (C b - C a b)c - A a b + A a b)sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + A a c + (C b - 2C a b + C a )c +--R + +--R 2 2 3 +--R (- A a b + 2A a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 2 2 2 2 +--R - C c + A a c + (- 2C b + 2C a b)c + (2A a b - 2A a b)c +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 3 2 2 2 +--R (C a c - A a c + (C b - C a b )c - A a b + A a b )cos(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((- C b + 2C a b - C a b)c + A a b - 2A a b + A a b)cos(x) +--R + +--R 3 2 2 2 2 2 2 3 +--R - C a c + A a c + (- C a b + C a b)c + A a b - A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 5 4 2 3 2 3 2 +--R C c - A a c + (C a b - C a )c + (- A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 3 +--R (- C b + C a b + C a b - C a b)c + A a b - A a b +--R + +--R 3 2 4 +--R - A a b + A a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 2 3 2 +--R C c - A a c + (C a b - C a )c + (- A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 3 3 2 +--R (- C b + C a b + C a b - C a b)c + A a b - A a b - A a b +--R + +--R 4 +--R A a b +--R * +--R sin(x) +--R + +--R 4 2 3 +--R (2C b - C a)c + (- 2A a b + A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - C a b - 2C a b + C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A a b + A a b + 2A a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 +--R (2C b c - 2A a b c + (2C b - 2C a b)c + (- 2A a b + 2A a b)c) +--R * +--R cos(x) +--R + +--R 4 2 3 2 3 2 2 2 4 +--R C a c - A a c + (C a b - C a )c + (- A a b + A a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 2 3 2 3 2 +--R (- 2C c + 2A a c + (- 2C b + 2C a )c + (2A a b - 2A a )c ) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 +--R (2C b - 2C a)c + (- 2A a b + 2A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 2C a b - 2C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A a b + 2A a b + 2A a b - 2A a )c +--R * +--R sin(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R (- 2C c + 2A a c + (- 2C b + 2C a )c + (2A a b - 2A a )c ) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R (- 2C c + 2A a c + (- 2C b + 2C a )c + (2A a b - 2A a )c )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 3 2 2 3 3 +--R (- 2C b c + 2A a b c + (- 2C b + 2C a b)c + (2A a b - 2A a b)c) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 2 3 2 +--R C c - A a c + (C a b - C a )c + (- A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 3 3 2 +--R (- C b + C a b + C a b - C a b)c + A a b - A a b - A a b +--R + +--R 4 +--R A a b +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R C c - A a c + (2C b - C a b - C a )c +--R + +--R 2 2 3 2 4 3 2 2 3 +--R (- 2A a b + A a b + A a )c + (C b - C a b - C a b + C a b)c +--R + +--R 4 2 3 3 2 4 +--R - A a b + A a b + A a b - A a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 2 2 4 2 +--R (- C a c + A a c + (- C a b + C a )c + (A a b - A a )c)cos(x) +--R + +--R 4 2 3 2 3 2 2 2 4 +--R C a c - A a c + (C a b - C a )c + (- A a b + A a )c +--R / +--R 2 2 4 4 3 3 4 2 2 +--R ((b - 2a b + a )c + (b - 2a b + 2a b - a )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 4a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 +--R (- b + a)c + (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 +--R (- b + a b)c + (- b + 3a b - 2a b)c - a b + 2a b +--R + +--R 4 2 5 +--R - 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 5 +--R (- b + a )c + (- 2b + 2a b + 2a b - 2a )c - b + 2a b +--R + +--R 2 4 4 2 5 6 +--R - a b + a b - 2a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 4 2 5 2 4 4 2 +--R (- a b + a )c + (- 2a b + 3a b - a )c - a b + 2a b - 2a b +--R + +--R 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c )sin(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R (2c + (4a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c )cos(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R 2c + (4b - 4a b)c + (2b - 4a b + 4a b - 2a )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 +--R 2b c + (2b + 2a b - 4a b)c +--R + +--R 4 2 3 3 2 4 +--R (2a b - 2a b - 2a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 3 5 4 4 5 +--R ((2b + 2a)c + (4b - 4a )c + (2b - 2a b - 2a b + 2a )c)cos(x) +--R + +--R 5 2 2 3 3 4 2 3 3 2 4 +--R 2a c + (4a b - 2a b - 2a )c + (2a b - 2a b - 2a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- b + a )c + (- b + 2a b - a )c )sin(x) +--R + +--R 5 2 3 3 +--R (b + a)c + (2a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + a b + 2a b - 2a b - a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 +--R (b + a)c + (2b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + 2a b + a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 3 2 5 3 3 5 +--R ((b + a b)c + (b + 2a b - a b - 2a b)c + a b - 2a b + a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 2 4 +--R (b + 2a b + a )c + (2b + 2a b - 2a b - 2a )c + b - a b +--R + +--R 4 2 6 +--R - a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 4 2 5 3 3 5 +--R (a b + a )c + (2a b + a b - 2a b - a )c + a b - 2a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b + 2a b - a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b + 2a b + a b - 4a b + a b + 2a b - a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (b - 3a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 6 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c - b + 2a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R a b - 4a b + a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (2b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 2 5 3 4 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c - a b + 2a b + a b +--R + +--R 4 3 5 2 6 7 +--R - 4a b + a b + 2a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b - a b)c + (2b - 2a b - 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - a b - 2a b + 2a b + a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (a b - a )c + (2a b - 2a b - 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b - a b - 2a b + 2a b + a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (2b - 2a)c + (4b - 4a b - 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 2b - 2a b + 4a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a b)c +--R * +--R cos(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 4b + 2a b + 2a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 +--R (- 2b c + (- 4b + 4a b)c + (- 2b + 4a b - 2a b)c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- 2b - 2a)c + (- 4b - 4a b + 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 2b - 2a b + 4a b + 4a b - 2a b - 2a )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 5 2 +--R - 2a c + (- 4a b + 4a )c + (- 2a b + 4a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 2 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c)sin(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- b - 2a b + a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 2 5 4 3 6 +--R (b - a b - 2a b + 2a b + a b - a )c + b - 3a b + 3a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- 2b - a b + 2a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 3 4 5 2 7 +--R (- b + a b + 2a b - 2a b - a b + a )c + a b - 3a b + 3a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b - a b)c + (- 2b - 2a b + 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - a b + 2a b + 2a b - a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b - 2a b - a )c + (- 2b - 4a b + 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b - 2a b + a b + 4a b + a b - 2a b - a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b - a )c + (- 2a b - 2a b + 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- a b - a b + 2a b + 2a b - a b - a )c +--R Type: Expression Integer +--E 265 + +--S 266 of 526 +m0850b:= a0850.2-r0850 +--R +--R +--R (255) +--R 2 +--R ((2C b - 2C a)c - 2A a b + 2A a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 +--R ((2C b - 2C a)c - 2A a b + 2A a )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (A c + C b - C a)\|- c - b + a +--R / +--R +--------------+ +--R 2 3 2 2 3 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a +--R Type: Expression Integer +--E 266 + +--S 267 of 526 +d0850b:= D(m0850b,x) +--R +--R +--R (256) +--R 2 2 +--R ((- C b + C a)c + A a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + 2A a c)cos(x) - 2C c + 2A a c)sin(x) +--R + +--R 2 2 +--R ((- 3C b + C a)c + 3A a b - A a )cos(x) + (- 4C b c + 4A a b)cos(x) +--R + +--R 2 +--R (- C b - C a)c + A a b + A a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R (4C c - 4A a c)sin(x) + (4C c - 4A a c)cos(x) +--R + +--R 2 +--R (4C c - 4A a c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 +--R ((3C b + C a)c - 3A a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + 2A a c)cos(x) - 2C c + 2A a c)sin(x) +--R + +--R 2 2 2 +--R ((C b + C a)c - A a b - A a )cos(x) + (- C b - C a)c + A a b + A a +--R / +--R 2 2 2 4 3 3 4 2 +--R ((b - 2a b + a )c + b - 2a b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 +--R (- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )cos(x) +--R + +--R 2 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b + 2a )c - 2b + 4a b - 2a )cos(x) + (- b + a )c - b +--R + +--R 2 2 4 +--R 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)sin(x) +--R + +--R 4 2 2 2 4 2 2 2 +--R ((4c + (4b - 4a )c )cos(x) + 4c + (4b - 4a )c )sin(x) +--R + +--R 3 3 2 2 3 2 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 3 +--R ((4b + 4a)c + (4b + 4a b - 4a b - 4a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 3 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 3 4 2 +--R ((b + 2a b + a )c + b + 2a b - 2a b - a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R ((2b + 4a b + 2a )c + 2b + 4a b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R (b + 2a b + a )c + b + 2a b - 2a b - a +--R Type: Expression Integer +--E 267 + +--S 268 of 526 +t0851:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x))^3 +--R +--R +--R (257) +--R C sin(x) + A +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3b c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 3 3 2 2 +--R (3b c cos(x) + 6a b c cos(x) + 3a c)sin(x) + b cos(x) + 3a b cos(x) +--R + +--R 2 3 +--R 3a b cos(x) + a +--R Type: Expression Integer +--E 268 + +--S 269 of 526 +r0851:= (2*a^2*A+A*b^2+c*(A*c-3*a*C))*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(5/2)-1/2*(b*C-(A*c-a*C)*cos(x)+A*b*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x))^2-1/2*(a*b*C+(2*c^2*C-a*(3*A*c-a*C))*cos(x)+b*(3*a*A-2*c*C)*sin(x))/(a^2-b^2-c^2)^2/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (258) +--R 4 3 2 2 2 2 +--R (- 2A c + 6C a c + (- 2A b - 4A a )c )sin(x) +--R + +--R 3 2 3 2 3 +--R (- 4A b c + 12C a b c + (- 4A b - 8A a b)c)cos(x) - 4A a c +--R + +--R 2 2 2 3 +--R 12C a c + (- 4A a b - 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R (- 2A b c + 6C a b c - 2A b - 4A a b )cos(x) +--R + +--R 2 2 3 3 2 2 3 +--R (- 4A a b c + 12C a b c - 4A a b - 8A a b)cos(x) - 2A a c + 6C a c +--R + +--R 2 2 4 +--R - 2A a b - 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 2 2 +--R (2C b c - 3A a b c)sin(x) +--R + +--R 3 2 2 2 2 2 +--R (- 2C c + 3A a c + (2C b - C a )c - 3A a b )cos(x) + A b c +--R + +--R 3 2 +--R C a b c + A b - 4A a b +--R * +--R sin(x) +--R + +--R 2 2 2 +--R (- 2C b c + 3A a b c - C a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- A c - C a c + (- A b + 4A a )c - 2C a )cos(x) + C b c + C b +--R + +--R 2 +--R - 2C a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (4b - 4a )c + (2b - 4a b + 2a )c )sin(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (8b - 8a b)c + (4b - 8a b + 4a b)c)cos(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (8a b - 8a )c + (4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (4b - 4a b )c + 2b - 4a b + 2a b )cos(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (8a b - 8a b)c + 4a b - 8a b + 4a b)cos(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (4a b - 4a )c + 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 269 + +--S 270 of 526 +a0851:= integrate(t0851,x) +--R +--R +--R (259) +--R [ +--R 3 2 2 3 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 3 2 2 3 2 +--R (- 6C a b + 12C a b - 6C a b)c +--R + +--R 5 4 2 3 3 2 4 +--R (2A b - 4A a b + 6A a b - 8A a b + 4A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 3 2 2 3 4 2 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 2 3 3 2 4 5 +--R (2A a b - 4A a b + 6A a b - 8A a b + 4A a )c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 3 +--R (- A b + 2A a b - A a )c + (3C a b - 6C a b + 3C a )c +--R + +--R 2 2 3 4 2 +--R (- 2A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 3 2 6 5 2 4 +--R (- 3C a b + 6C a b - 3C a b )c + A b - 2A a b + 3A a b +--R + +--R 3 3 4 2 +--R - 4A a b + 2A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 +--R (2A a b - 4A a b + 2A a b)c +--R + +--R 2 3 3 2 4 5 2 4 3 3 +--R (- 6C a b + 12C a b - 6C a b)c + 2A a b - 4A a b + 6A a b +--R + +--R 4 2 5 +--R - 8A a b + 4A a b +--R * +--R cos(x) +--R + +--R 2 2 4 2 2 3 3 +--R (A b - 2A a b + A a )c + (- 3C a b + 6C a b - 3C a )c +--R + +--R 4 3 2 2 3 4 2 +--R (A b - 2A a b + 4A a b - 6A a b + 3A a )c +--R + +--R 3 2 4 5 2 4 3 3 4 2 5 +--R (- 3C a b + 6C a b - 3C a )c + A a b - 2A a b + 3A a b - 4A a b +--R + +--R 6 +--R 2A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 4 2 3 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 3 2 2 3 4 4 2 3 +--R (- 4C a b + 7C a b - 2C a b - C a )c - 3A a b + 6A a b +--R + +--R 3 2 +--R - 3A a b +--R * +--R cos(x) +--R + +--R 4 2 3 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- C a b - 2C a b + 7C a b - 4C a )c + A b - 2A a b +--R + +--R 2 3 3 2 4 +--R - 3A a b + 8A a b - 4A a b +--R * +--R sin(x) +--R + +--R 5 4 2 3 +--R A c + (- C b + C a)c + (3A a b - 4A a )c +--R + +--R 3 2 2 3 2 +--R (- 2C b + 7C a b - 7C a b + 2C a )c +--R + +--R 4 3 2 2 3 5 2 3 4 +--R (- A b + 3A a b - 8A a b + 6A a b)c - C b + 2C a b - C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 2 3 2 +--R (- A b - A a )c + (C a b - C a )c +--R + +--R 4 2 2 4 4 3 2 5 +--R (- A b - 3A a b + 4A a )c - 2C a b + 4C a b - 2C a +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R - A c + (C b - C a)c + (- A b - 3A a b + 3A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 6C a b + 7C a b - 3C a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c + C b - 2C a b - 2C a b +--R + +--R 3 2 4 5 +--R 4C a b + C a b - 2C a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 3 2 2 3 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 2 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 +--R (4A b - 8A a b + 12A a b - 16A a b + 8A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 3 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 2 2 3 4 2 +--R (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 +--R (4A a b - 8A a b + 12A a b - 16A a b + 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 3 +--R (- 2A b + 4A a b - 2A a )c + (6C a b - 12C a b + 6C a )c +--R + +--R 2 2 3 4 2 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 6 5 2 4 +--R (- 6C a b + 12C a b - 6C a b )c + 2A b - 4A a b + 6A a b +--R + +--R 3 3 4 2 +--R - 8A a b + 4A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 5 2 4 +--R (- 12C a b + 24C a b - 12C a b)c + 4A a b - 8A a b +--R + +--R 3 3 4 2 5 +--R 12A a b - 16A a b + 8A a b +--R * +--R cos(x) +--R + +--R 2 2 4 2 2 3 3 +--R (2A b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 3 2 2 3 4 2 +--R (2A b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 3 2 4 5 2 4 3 3 4 2 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b +--R + +--R 5 6 +--R - 8A a b + 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 4 2 3 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 3 2 2 3 4 4 2 3 +--R (- 4C a b + 7C a b - 2C a b - C a )c - 3A a b + 6A a b +--R + +--R 3 2 +--R - 3A a b +--R * +--R cos(x) +--R + +--R 4 2 3 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- C a b - 2C a b + 7C a b - 4C a )c + A b - 2A a b +--R + +--R 2 3 3 2 4 +--R - 3A a b + 8A a b - 4A a b +--R * +--R sin(x) +--R + +--R 5 4 2 3 +--R A c + (- C b + C a)c + (3A a b - 4A a )c +--R + +--R 3 2 2 3 2 +--R (- 2C b + 7C a b - 7C a b + 2C a )c +--R + +--R 4 3 2 2 3 5 2 3 4 +--R (- A b + 3A a b - 8A a b + 6A a b)c - C b + 2C a b - C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 2 3 2 +--R (- A b - A a )c + (C a b - C a )c +--R + +--R 4 2 2 4 4 3 2 5 +--R (- A b - 3A a b + 4A a )c - 2C a b + 4C a b - 2C a +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R - A c + (C b - C a)c + (- A b - 3A a b + 3A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 6C a b + 7C a b - 3C a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c + C b - 2C a b - 2C a b +--R + +--R 3 2 4 5 +--R 4C a b + C a b - 2C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 270 + +--S 271 of 526 +m0851a:= a0851.1-r0851 +--R +--R +--R (260) +--R 3 2 2 5 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 3 2 2 3 4 +--R (- 6C a b + 12C a b - 6C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (2A b - 4A a b + 6A a b - 8A a b + 4A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (2A a b - 4A a b + 6A a b - 8A a b + 4A a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 3 5 +--R (- A b + 2A a b - A a )c + (3C a b - 6C a b + 3C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (4A b - 8A a b + 2A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 3 2 3 +--R (- 15C a b + 30C a b - 15C a b )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (5A b - 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24C a b)c + 8A a b - 16A a b +--R + +--R 5 3 6 2 7 +--R 24A a b - 32A a b + 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 3 2 4 5 3 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (2A a b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 5 2 6 7 4 4 5 3 6 2 7 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b - 8A a b +--R + +--R 8 +--R 4A a +--R * +--R x +--R +------------+ (b - a)tan(-) - c +--R | 2 2 2 2 +--R \|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 2 5 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- 4C b + 4C a b + 3C a b - 2C a b - C a )c +--R + +--R 4 2 3 3 2 2 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R cos(x) +--R + +--R 6 2 5 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 5C a b + 6C a b + 3C a b - 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 2A a b + 3A a b - 4A a b + 2A a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 2 2 5 +--R A c + (- C b + C a)c + (- 4A b + 3A a b - 4A a )c +--R + +--R 3 2 2 3 4 +--R (4C b - C a b - 5C a b + 2C a )c +--R + +--R 4 3 2 2 3 3 +--R (- 5A b - 12A a b + 14A a b + 3A a b)c +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 7C b + 4C a b + 12C a b - 8C a b - C a b)c +--R + +--R 5 2 4 3 3 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b - 8A a b - A a )c + (9C a b - 8C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 8A a b - 27A a b + 32A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 14C a b + 8C a b + 24C a b - 16C a b - 2C a )c +--R + +--R 2 4 3 3 4 2 +--R (6A a b - 12A a b + 6A a b )c +--R * +--R cos(x) +--R + +--R 7 6 2 2 5 +--R - A c + (C b - C a)c + (- A b - 3A a b - A a )c +--R + +--R 2 2 3 4 2 2 3 4 3 +--R (- 2C a b + 9C a b - 7C a )c + (- 5A a b - 15A a b + 20A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (C b - 2C a b - 8C a b + 8C a b + 11C a b - 10C a )c +--R + +--R 3 3 4 2 5 +--R (3A a b - 6A a b + 3A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 5 +--R 2A b c + (- 4C b + 6C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b + 9A a b - 14A a b + 3A a )c +--R + +--R 4 2 2 3 4 3 +--R (4C b - 9C a b + 6C a b - C a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 4A b - 9A a b + 10A a b + 3A a b )c +--R + +--R 6 2 4 3 3 +--R (- 4C b + 12C a b - 8C a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 +--R 2A a c + (- 2C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 12A a b + 7A a b - 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (11C a b - 6C a b - 9C a b + 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 14A a b - 33A a b + 44A a b + 2A a b)c +--R + +--R 5 3 3 4 2 +--R (- 12C a b + 36C a b - 24C a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 5 +--R - 2A b c + (4C b - 6C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 9A a b + 2A a b - 3A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4C a b + 21C a b - 18C a b + C a )c +--R + +--R 4 2 3 3 2 4 2 +--R (- 3A a b - 6A a b - 39A a b + 48A a b)c +--R + +--R 2 4 4 2 5 +--R (- 12C a b + 36C a b - 24C a b)c +--R * +--R cos(x) +--R + +--R 6 2 5 3 2 3 4 +--R - 2A a c + (2C a b - 2C a )c + (- A b - 7A a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (C a b - 6C a b + 13C a b - 8C a )c +--R + +--R 5 4 2 3 4 5 2 +--R (- A b + 2A a b - 3A a b - 14A a b + 16A a )c +--R + +--R 3 3 5 6 +--R (- 4C a b + 12C a b - 8C a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 4 +--R A b c + (- 3C b + 5C a b - 2C a b)c +--R + +--R 3 2 2 3 3 +--R (6A a b - 10A a b + 3A a b)c +--R + +--R 4 2 3 3 2 4 2 +--R (3C a b - 6C a b + 4C a b - C a b)c +--R + +--R 6 2 4 3 3 7 2 5 3 4 +--R (- A b - 2A a b + 3A a b )c - C b + 3C a b - 2C a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b + 4A a b - A a )c + (- 3C a b + 4C a b - C a )c +--R + +--R 4 2 2 3 4 3 +--R (- A b + 9A a b - 16A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b + 4C a b - 12C a b + 8C a b - 2C a )c +--R + +--R 5 2 4 3 3 4 2 6 3 4 +--R (- 4A a b - 6A a b + 4A a b + 6A a b )c - 4C a b + 12C a b +--R + +--R 4 3 +--R - 8C a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- A b + A a )c + (4C b - 7C a b + 2C a b + C a )c +--R + +--R 4 3 2 2 4 3 +--R (- A b - 6A a b + 5A a b - 4A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2C b - 6C a b + 10C a b - 2C a b - 6C a b + 2C a )c +--R + +--R 5 3 3 4 2 5 2 5 4 3 +--R (- 3A a b - 18A a b + 18A a b + 3A a b)c - 6C a b + 18C a b +--R + +--R 5 2 +--R - 12C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (A b - 4A a b + A a )c + (3C a b - 4C a b + C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b - 4A a b - 9A a b + 12A a b - 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b - 8C a b + 16C a b - 12C a b + 2C a )c +--R + +--R 2 4 3 3 4 2 5 3 4 5 2 +--R (- 6A a b + 8A a b - 18A a b + 16A a b)c - 4C a b + 12C a b +--R + +--R 6 +--R - 8C a b +--R * +--R cos(x) +--R + +--R 2 5 3 2 3 4 +--R - A a c + (- C b + 2C a b - C a )c +--R + +--R 2 2 3 4 3 +--R (- A a b - 3A a b + 3A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- C b + 2C a b + 2C a b - 8C a b + 8C a b - 3C a )c +--R + +--R 3 3 4 2 5 6 4 3 6 7 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c - C a b + 3C a b - 2C a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 271 + +--S 272 of 526 +--d0851a:= D(m0851a,x) +--E 272 + +--S 273 of 526 +m0851b:= a0851.2-r0851 +--R +--R +--R (261) +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 12A a b - 16A a b + 8A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 12A a b - 16A a b + 8A a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 3 5 +--R (- 2A b + 4A a b - 2A a )c + (6C a b - 12C a b + 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (8A b - 16A a b + 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 3 +--R (- 30C a b + 60C a b - 30C a b )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (10A b - 20A a b + 30A a b - 40A a b + 20A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 60C a b + 120C a b - 60C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (20A a b - 40A a b + 60A a b - 80A a b + 40A a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 2 2 3 5 +--R (2A b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (2A b - 4A a b + 16A a b - 28A a b + 14A a )c +--R + +--R 3 2 4 5 3 +--R (- 30C a b + 60C a b - 30C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (10A a b - 20A a b + 30A a b - 40A a b + 20A a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 3 2 2 3 4 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 5 2 4 3 3 2 +--R (- 24C a b + 48C a b - 24C a b )c +--R + +--R 7 6 2 5 3 4 4 3 +--R (8A b - 16A a b + 24A a b - 32A a b + 16A a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 2 2 3 4 4 +--R (12C a b - 24C a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (20A a b - 40A a b + 12A a b + 16A a b - 8A a )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 72C a b + 144C a b - 72C a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 36A a b - 64A a b + 32A a b)c +--R + +--R 3 3 4 2 5 2 +--R (- 72C a b + 144C a b - 72C a b)c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a )c +--R + +--R 4 2 5 6 2 +--R (- 24C a b + 48C a b - 24C a )c +--R + +--R 3 4 4 3 5 2 6 7 +--R (8A a b - 16A a b + 24A a b - 32A a b + 16A a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (- 2A b + 4A a b - 2A a b )c +--R + +--R 4 2 3 3 2 3 +--R (6C a b - 12C a b + 6C a b )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 4A a b + 8A a b - 4A a b )c +--R + +--R 6 2 5 3 4 8 7 2 6 +--R (- 6C a b + 12C a b - 6C a b )c + 2A b - 4A a b + 6A a b +--R + +--R 3 5 4 4 +--R - 8A a b + 4A a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4A a b + 8A a b - 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 2 5 3 4 4 3 7 2 6 +--R (- 24C a b + 48C a b - 24C a b )c + 8A a b - 16A a b +--R + +--R 3 5 4 4 5 3 +--R 24A a b - 32A a b + 16A a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2A b - 4A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 4 5 3 +--R (- 6C a b + 12C a b - 12C a b + 6C a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 2A b - 4A a b + 16A a b - 28A a b + 10A a b + 8A a b +--R + +--R 6 +--R - 4A a +--R * +--R 2 +--R c +--R + +--R 3 4 4 3 5 2 2 6 3 5 +--R (- 36C a b + 72C a b - 36C a b )c + 12A a b - 24A a b +--R + +--R 4 4 5 3 6 2 +--R 36A a b - 48A a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a b)c +--R + +--R 4 3 5 2 6 3 5 4 4 +--R (- 24C a b + 48C a b - 24C a b)c + 8A a b - 16A a b +--R + +--R 5 3 6 2 7 +--R 24A a b - 32A a b + 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 3 2 4 5 3 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (2A a b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 5 2 6 7 4 4 5 3 6 2 7 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b - 8A a b +--R + +--R 8 +--R 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 12A a b - 16A a b + 8A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 12A a b - 16A a b + 8A a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 3 5 +--R (- 2A b + 4A a b - 2A a )c + (6C a b - 12C a b + 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (8A b - 16A a b + 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 3 +--R (- 30C a b + 60C a b - 30C a b )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (10A b - 20A a b + 30A a b - 40A a b + 20A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 60C a b + 120C a b - 60C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (20A a b - 40A a b + 60A a b - 80A a b + 40A a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 2 2 3 5 +--R (2A b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (2A b - 4A a b + 16A a b - 28A a b + 14A a )c +--R + +--R 3 2 4 5 3 +--R (- 30C a b + 60C a b - 30C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (10A a b - 20A a b + 30A a b - 40A a b + 20A a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 3 2 2 3 4 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 5 2 4 3 3 2 +--R (- 24C a b + 48C a b - 24C a b )c +--R + +--R 7 6 2 5 3 4 4 3 +--R (8A b - 16A a b + 24A a b - 32A a b + 16A a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 2 2 3 4 4 +--R (12C a b - 24C a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (20A a b - 40A a b + 12A a b + 16A a b - 8A a )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 72C a b + 144C a b - 72C a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 36A a b - 64A a b + 32A a b)c +--R + +--R 3 3 4 2 5 2 +--R (- 72C a b + 144C a b - 72C a b)c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a )c +--R + +--R 4 2 5 6 2 +--R (- 24C a b + 48C a b - 24C a )c +--R + +--R 3 4 4 3 5 2 6 7 +--R (8A a b - 16A a b + 24A a b - 32A a b + 16A a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (- 2A b + 4A a b - 2A a b )c +--R + +--R 4 2 3 3 2 3 +--R (6C a b - 12C a b + 6C a b )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 4A a b + 8A a b - 4A a b )c +--R + +--R 6 2 5 3 4 8 7 2 6 +--R (- 6C a b + 12C a b - 6C a b )c + 2A b - 4A a b + 6A a b +--R + +--R 3 5 4 4 +--R - 8A a b + 4A a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4A a b + 8A a b - 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 2 5 3 4 4 3 7 2 6 +--R (- 24C a b + 48C a b - 24C a b )c + 8A a b - 16A a b +--R + +--R 3 5 4 4 5 3 +--R 24A a b - 32A a b + 16A a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2A b - 4A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 4 5 3 +--R (- 6C a b + 12C a b - 12C a b + 6C a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 2A b - 4A a b + 16A a b - 28A a b + 10A a b + 8A a b +--R + +--R 6 +--R - 4A a +--R * +--R 2 +--R c +--R + +--R 3 4 4 3 5 2 2 6 3 5 +--R (- 36C a b + 72C a b - 36C a b )c + 12A a b - 24A a b +--R + +--R 4 4 5 3 6 2 +--R 36A a b - 48A a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a b)c +--R + +--R 4 3 5 2 6 3 5 4 4 +--R (- 24C a b + 48C a b - 24C a b)c + 8A a b - 16A a b +--R + +--R 5 3 6 2 7 +--R 24A a b - 32A a b + 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 3 2 4 5 3 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (2A a b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 5 2 6 7 4 4 5 3 6 2 7 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b - 8A a b +--R + +--R 8 +--R 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 2 5 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- 4C b + 4C a b + 3C a b - 2C a b - C a )c +--R + +--R 4 2 3 3 2 2 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R cos(x) +--R + +--R 6 2 5 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 5C a b + 6C a b + 3C a b - 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 2A a b + 3A a b - 4A a b + 2A a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 2 2 5 +--R A c + (- C b + C a)c + (- 4A b + 3A a b - 4A a )c +--R + +--R 3 2 2 3 4 +--R (4C b - C a b - 5C a b + 2C a )c +--R + +--R 4 3 2 2 3 3 +--R (- 5A b - 12A a b + 14A a b + 3A a b)c +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 7C b + 4C a b + 12C a b - 8C a b - C a b)c +--R + +--R 5 2 4 3 3 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b - 8A a b - A a )c + (9C a b - 8C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 8A a b - 27A a b + 32A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 14C a b + 8C a b + 24C a b - 16C a b - 2C a )c +--R + +--R 2 4 3 3 4 2 +--R (6A a b - 12A a b + 6A a b )c +--R * +--R cos(x) +--R + +--R 7 6 2 2 5 +--R - A c + (C b - C a)c + (- A b - 3A a b - A a )c +--R + +--R 2 2 3 4 2 2 3 4 3 +--R (- 2C a b + 9C a b - 7C a )c + (- 5A a b - 15A a b + 20A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (C b - 2C a b - 8C a b + 8C a b + 11C a b - 10C a )c +--R + +--R 3 3 4 2 5 +--R (3A a b - 6A a b + 3A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 5 +--R 2A b c + (- 4C b + 6C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b + 9A a b - 14A a b + 3A a )c +--R + +--R 4 2 2 3 4 3 +--R (4C b - 9C a b + 6C a b - C a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 4A b - 9A a b + 10A a b + 3A a b )c +--R + +--R 6 2 4 3 3 +--R (- 4C b + 12C a b - 8C a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 +--R 2A a c + (- 2C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 12A a b + 7A a b - 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (11C a b - 6C a b - 9C a b + 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 14A a b - 33A a b + 44A a b + 2A a b)c +--R + +--R 5 3 3 4 2 +--R (- 12C a b + 36C a b - 24C a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 5 +--R - 2A b c + (4C b - 6C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 9A a b + 2A a b - 3A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4C a b + 21C a b - 18C a b + C a )c +--R + +--R 4 2 3 3 2 4 2 +--R (- 3A a b - 6A a b - 39A a b + 48A a b)c +--R + +--R 2 4 4 2 5 +--R (- 12C a b + 36C a b - 24C a b)c +--R * +--R cos(x) +--R + +--R 6 2 5 3 2 3 4 +--R - 2A a c + (2C a b - 2C a )c + (- A b - 7A a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (C a b - 6C a b + 13C a b - 8C a )c +--R + +--R 5 4 2 3 4 5 2 +--R (- A b + 2A a b - 3A a b - 14A a b + 16A a )c +--R + +--R 3 3 5 6 +--R (- 4C a b + 12C a b - 8C a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 4 +--R A b c + (- 3C b + 5C a b - 2C a b)c +--R + +--R 3 2 2 3 3 +--R (6A a b - 10A a b + 3A a b)c +--R + +--R 4 2 3 3 2 4 2 +--R (3C a b - 6C a b + 4C a b - C a b)c +--R + +--R 6 2 4 3 3 7 2 5 3 4 +--R (- A b - 2A a b + 3A a b )c - C b + 3C a b - 2C a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b + 4A a b - A a )c + (- 3C a b + 4C a b - C a )c +--R + +--R 4 2 2 3 4 3 +--R (- A b + 9A a b - 16A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b + 4C a b - 12C a b + 8C a b - 2C a )c +--R + +--R 5 2 4 3 3 4 2 6 3 4 +--R (- 4A a b - 6A a b + 4A a b + 6A a b )c - 4C a b + 12C a b +--R + +--R 4 3 +--R - 8C a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- A b + A a )c + (4C b - 7C a b + 2C a b + C a )c +--R + +--R 4 3 2 2 4 3 +--R (- A b - 6A a b + 5A a b - 4A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2C b - 6C a b + 10C a b - 2C a b - 6C a b + 2C a )c +--R + +--R 5 3 3 4 2 5 2 5 4 3 +--R (- 3A a b - 18A a b + 18A a b + 3A a b)c - 6C a b + 18C a b +--R + +--R 5 2 +--R - 12C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (A b - 4A a b + A a )c + (3C a b - 4C a b + C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b - 4A a b - 9A a b + 12A a b - 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b - 8C a b + 16C a b - 12C a b + 2C a )c +--R + +--R 2 4 3 3 4 2 5 3 4 5 2 +--R (- 6A a b + 8A a b - 18A a b + 16A a b)c - 4C a b + 12C a b +--R + +--R 6 +--R - 8C a b +--R * +--R cos(x) +--R + +--R 2 5 3 2 3 4 +--R - A a c + (- C b + 2C a b - C a )c +--R + +--R 2 2 3 4 3 +--R (- A a b - 3A a b + 3A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- C b + 2C a b + 2C a b - 8C a b + 8C a b - 3C a )c +--R + +--R 3 3 4 2 5 6 4 3 6 7 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c - C a b + 3C a b - 2C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 273 + +--S 274 of 526 +--d0851b:= D(m0851b,x) +--E 274 + +--S 275 of 526 +t0852:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x)) +--R +--R +--R B cos(x) + A +--R (262) ----------------------- +--R c sin(x) + b cos(x) + a +--R Type: Expression Integer +--E 275 + +--S 276 of 526 +r0852:= b*B*x/(b^2+c^2)+2*(A-a*b*B/(b^2+c^2))*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(1/2)+B*c*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) +--R +--R +--R (263) +--R +--------------+ +--R | 2 2 2 +--R B c\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R x +--R (b - a)tan(-) - c +--------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c - 2A b + 2B a b)atan(-----------------) + B b x\|- c - b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression Integer +--E 276 + +--S 277 of 526 +a0852:= integrate(t0852,x) +--R +--R +--R (264) +--R [ +--R 2 2 +--R (- A c - A b + B a b) +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R | 2 2 2 2 +--R - B c\|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R B b x\|c + b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|c + b - a +--R , +--R +--R +--------------+ +--R | 2 2 2 2 +--R - B c\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R +--------------+ +--R | 2 2 2 +--R B b x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 277 + +--S 278 of 526 +m0852a:= a0852.1-r0852 +--R +--R +--R (265) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (- A c - A b + B a b)\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - B c\|- c - b + a \|c + b - a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R - B c\|- c - b + a \|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|- c - b + a \|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2A c + 2A b - 2B a b)\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c + b )\|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 278 + +--S 279 of 526 +d0852a:= D(m0852a,x) +--R +--R +--R (266) +--R 3 2 2 2 5 4 +--R (- A b + 2A a b - A a b)c - A b + (B + 2A)a b +--R + +--R 2 3 3 2 +--R (- 2B - A)a b + B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 +--R - A c + ((B - 2A)a b + A a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 2 3 +--R - A c + (- A b + B a b)c +--R * +--R sin(x) +--R + +--R 4 3 2 2 2 5 +--R (- 2A b + A a)c + (- 3A b + (2B + 2A)a b - B a b)c - A b +--R + +--R 4 2 3 +--R (B + A)a b - B a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 2 5 4 +--R - 2A b c + (- 3A b + 2B a b + A a b)c - A b + B a b +--R + +--R 2 3 3 2 +--R A a b - B a b +--R * +--R cos(x) +--R + +--R 4 2 2 2 4 2 3 +--R - A a c + (- 2A a b + (B + A)a b)c - A a b + (B + A)a b +--R + +--R 3 2 +--R - B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 +--R 2A c + (4A b + (- 2B - 2A)a b)c +--R + +--R 4 3 2 2 +--R (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 +--R ((- 2A b + 2A a)c + (- 2A b + (2B + 2A)a b - 2B a b)c )sin(x) +--R + +--R 5 2 3 +--R 2A c + (4A b + (- 2B - 2A)a b)c +--R + +--R 4 3 2 2 +--R (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 +--R 2A c + (2A b + (- 2B + 2A)a b - 2A a )c +--R + +--R 3 2 2 3 +--R (2A a b + (- 2B - 2A)a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 5 4 2 3 +--R 2A b c + (3A b - 2B a b - A a b)c + A b - B a b - A a b +--R + +--R 3 2 +--R B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 +--R - A c + ((B - 2A)a b + A a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 2 3 +--R - A c + (- 3A b + (B + 2A)a b)c +--R + +--R 4 3 2 2 +--R (- 2A b + (2B + 2A)a b - 2B a b )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 5 4 2 3 2 +--R (A a c + (A b - B a b)c + A b + (- B - A)a b + B a b )cos(x) +--R + +--R 3 2 2 2 5 4 +--R (- A b + 2A a b - A a b)c - A b + (B + 2A)a b +--R + +--R 2 3 3 2 +--R (- 2B - A)a b + B a b +--R * +--R cos(x) +--R + +--R 4 2 2 2 4 2 3 3 2 +--R - A a c + (- 2A a b + (B + A)a b)c - A a b + (B + A)a b - B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 6 2 2 4 +--R - A c + (- A b + (B - A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 +--R (A b - 2A a b + B a b + (- B + A)a b)c + A b +--R + +--R 5 2 4 3 3 4 2 +--R (- B - A)a b + (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 2 2 4 +--R - A c + (- A b + (B - A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 5 +--R (A b - 2A a b + B a b + (- B + A)a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R sin(x) +--R + +--R 5 +--R (- 2A b + A a)c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 2A)a b + (- B + 2A)a b - A a )c +--R + +--R 5 4 2 3 3 2 4 +--R (- 2A b + (2B + A)a b + (- B + 2A)a b + (- 2B - A)a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 2 2 3 +--R - 2A b c + (- 4A b + 2B a b + 2A a b)c +--R + +--R 5 4 2 3 3 2 +--R (- 2A b + 2B a b + 2A a b - 2B a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 3 +--R - A a c + (- 2A a b + B a b + A a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 2 4 +--R 2A c + (4A b - 2B a b - 2A a )c +--R + +--R 4 3 2 2 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 5 +--R (- 2A b + 2A a)c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 4A)a b + (- 2B + 2A)a b - 2A a )c +--R + +--R 5 4 2 3 3 2 +--R - 2A b + (2B + 2A)a b + (- 2B + 2A)a b + (- 2B - 2A)a b +--R + +--R 4 +--R 2B a b +--R * +--R c +--R * +--R sin(x) +--R + +--R 6 2 2 4 +--R 2A c + (4A b - 2B a b - 2A a )c +--R + +--R 4 3 2 2 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 4 +--R 2A c + (4A b - 2B a b - 2A a )c +--R + +--R 4 3 2 2 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 +--R 2A b c + (4A b - 2B a b - 2A a b)c +--R + +--R 5 4 2 3 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 4 +--R - A c + (- A b + (B - A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 5 +--R (A b - 2A a b + B a b + (- B + A)a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 2 2 4 +--R - A c + (- 3A b + (B + A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 +--R (- 3A b + (2B + 2A)a b + (- B + 2A)a b + (- B - A)a b)c - A b +--R + +--R 5 2 4 3 3 4 2 +--R (B + A)a b + (- B + A)a b + (- B - A)a b + B a b +--R * +--R sin(x) +--R + +--R 5 2 2 3 3 +--R A a c + (2A a b - B a b - A a )c +--R + +--R 4 2 3 3 2 4 +--R (A a b - B a b - A a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 3 +--R - A a c + (- 2A a b + B a b + A a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R / +--R 2 2 4 4 3 2 2 2 2 +--R ((b - 2a b + a )c + (b - 2a b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 3a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (b - 3a b + 3a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 3 +--R (- b + a)c + (- 2b + 4a b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + 3a b - 3a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 3 3 +--R ((- b + a b)c + (- b + 2a b - a b)c - a b + 2a b - a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 6 +--R (- b + a )c + (- 2b + 2a b - a b + 2a b - a )c - b +--R + +--R 5 2 4 3 3 4 2 +--R 2a b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 2 5 2 4 3 3 +--R (- a b + a )c + (- 2a b + 3a b - a b)c - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c )sin(x) +--R + +--R 6 2 4 4 3 2 2 2 +--R (2c + (4a b - 2a )c + (- 2b + 4a b - 2a b )c )cos(x) +--R + +--R 6 2 2 4 4 3 2 2 2 +--R 2c + (4b - 4a b + 2a )c + (2b - 4a b + 2a b )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 4 2 3 2 +--R (2b c + (2b + 2a b - 2a b)c + (2a b - 2a b )c)cos(x) +--R + +--R 5 3 2 3 3 +--R (2b + 2a)c + (4b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 +--R (2b - 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 4 2 3 +--R 2a c + (4a b - 2a b)c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 2 2 +--R ((- b + a )c + (- b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (b + a)c + (2a b + a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + a b + a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 3 5 4 2 3 3 2 +--R (b + a)c + (2b - a b + a )c + (b - a b - a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 3 2 5 3 3 2 +--R ((b + a b)c + (b + 2a b - a b)c + a b - a b )cos(x) +--R + +--R 2 2 4 4 3 2 2 4 2 6 4 2 +--R ((b + 2a b + a )c + (2b + 2a b + a b - a )c + b - a b )cos(x) +--R + +--R 2 4 3 2 2 3 2 5 3 3 +--R (a b + a )c + (2a b + a b - a b)c + a b - a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 2a b + a )c + (2b - 4a b + a b + 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b - 2a b + 2a b - a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 6 3 4 4 3 +--R (b - 3a b + 2a b + a b - a b)c + b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 +--R (- b + a)c + (- 2b + 3a b - a b)c +--R + +--R 5 4 2 3 4 5 2 6 2 5 4 3 5 2 +--R (- b + 3a b - 3a b + 2a b - a )c + a b - 2a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b + a b)c + (- 2b + 2a b + a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (- b + a b + a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b + a )c + (- 2a b + 2a b + a b - a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- a b + a b + a b - a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (- 2b + 2a)c + (- 4b + 4a b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 3 +--R 2c + (2b + 2a b - 2a )c + (- 2b + 4a b - 2a b)c +--R + +--R 6 5 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 2 2 3 4 3 +--R 2c + (4b - 2a b)c + (2b - 4a b + 2a b + 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 2a b + 2a b + 2a b - 2a b )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 2 2 +--R (2b c + (4b - 2a b)c + (2b - 2a b )c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2b + 2a)c + (4b + 4a b - 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b - 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 2 +--R 2a c + (4a b - 2a )c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c)sin(x) +--R + +--R 6 3 2 3 4 +--R (b + a)c + (b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 2 5 4 3 +--R (- b + a b + 2a b - a b - a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 5 4 2 3 3 2 5 2 +--R (b + a)c + (2b + a b - a b)c + (b - a b - a b + 2a b - a )c +--R + +--R 6 3 4 5 2 +--R - a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b + a b)c + (2b + 2a b - a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (b + a b - a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b + 2a b + a )c + (2b + 4a b + a b - 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b + 2a b - 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 5 2 4 3 3 4 2 +--R (a b + a )c + (2a b + 2a b - a b - a )c + (a b + a b - a b - a b )c +--R Type: Expression Integer +--E 279 + +--S 280 of 526 +m0852b:= a0852.2-r0852 +--R +--R +--R (267) +--R +--------------+ +--R | 2 2 2 +--R - B c\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +--R | 2 2 2 2 +--R - B c\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2A c + 2A b - 2B a b)atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression Integer +--E 280 + +--S 281 of 526 +d0852b:= D(m0852b,x) +--R +--R +--R (268) +--R 2 3 2 2 2 +--R ((- A b + A a)c - A b + (B + A)a b - B a b)sin(x) +--R + +--R 3 2 3 +--R (- 2A c + (- 2A b + 2B a b)c)cos(x) - 2A c +--R + +--R 2 +--R (- 2A b + 2B a b)c +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 +--R ((- 3A b + A a)c - 3A b + (3B + A)a b - B a b)cos(x) +--R + +--R 2 3 2 2 3 +--R (- 4A b c - 4A b + 4B a b )cos(x) + (- A b - A a)c - A b +--R + +--R 2 2 +--R (B - A)a b + B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 +--R (4A c + (4A b - 4B a b)c)sin(x) +--R + +--R 3 2 2 3 2 +--R (4A c + (4A b - 4B a b)c)cos(x) + (4A c + (4A b - 4B a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 +--R ((3A b + A a)c + 3A b + (- 3B + A)a b - B a b)sin(x) +--R + +--R 3 2 3 2 +--R ((- 2A c + (- 2A b + 2B a b)c)cos(x) - 2A c + (- 2A b + 2B a b)c) +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 +--R ((A b + A a)c + A b + (- B + A)a b - B a b)cos(x) + (- A b - A a)c +--R + +--R 3 2 2 +--R - A b + (B - A)a b + B a b +--R / +--R 2 2 2 4 3 2 2 2 +--R ((b - 2a b + a )c + b - 2a b + a b )sin(x) +--R + +--R 3 3 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)cos(x) + (- 2b + 2a)c +--R + +--R 3 2 +--R (- 2b + 2a b )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 2 4 2 2 +--R ((- 2b + 2a )c - 2b + 2a b )cos(x) + (- b + a )c - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)sin(x) +--R + +--R 4 2 2 4 2 2 +--R ((4c + 4b c )cos(x) + 4c + 4b c )sin(x) +--R + +--R 3 3 2 2 +--R ((2b + 2a)c + (2b + 2a b )c)cos(x) +--R + +--R 3 3 2 3 3 2 +--R ((4b + 4a)c + (4b + 4a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )sin(x) +--R + +--R 3 3 2 3 3 2 +--R (((2b + 2a)c + (2b + 2a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c) +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R ((b + 2a b + a )c + b + 2a b + a b )cos(x) +--R + +--R 2 2 2 4 3 2 2 2 2 2 +--R ((2b + 4a b + 2a )c + 2b + 4a b + 2a b )cos(x) + (b + 2a b + a )c +--R + +--R 4 3 2 2 +--R b + 2a b + a b +--R Type: Expression Integer +--E 281 + +--S 282 of 526 +t0853:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x))^2 +--R +--R +--R (269) +--R B cos(x) + A +--R --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R Type: Expression Integer +--E 282 + +--S 283 of 526 +r0853:= 2*(a*A-b*B)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(3/2)+(B*c+A*c*cos(x)-(A*b-a*B)*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (270) +--R 2 2 +--R ((- 2B b + 2A a)c sin(x) + (- 2B b + 2A a b)cos(x) - 2B a b + 2A a ) +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((A b - B a)sin(x) - A c cos(x) - B c)\|- c - b + a +--R / +--R 3 2 2 2 3 2 2 2 3 +--R ((c + (b - a )c)sin(x) + (b c + b - a b)cos(x) + a c + a b - a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 283 + +--S 284 of 526 +a0853:= integrate(t0853,x) +--R +--R +--R (271) +--R [ +--R 2 2 +--R (B b + (- B - A)a b + A a )c sin(x) +--R + +--R 3 2 2 2 2 3 +--R (B b + (- B - A)a b + A a b)cos(x) + B a b + (- B - A)a b + A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 2 2 2 +--R ((- B + A)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R (- B b + A a)c cos(x) + (- B b + A a)c +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a )c sin(x) +--R + +--R 3 2 2 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a b)cos(x) + 2B a b + (- 2B - 2A)a b +--R + +--R 3 +--R 2A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 2 2 2 +--R ((- B + A)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R (- B b + A a)c cos(x) + (- B b + A a)c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 284 + +--S 285 of 526 +m0853a:= a0853.1-r0853 +--R +--R +--R (272) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (B b + (- B - A)a b + A a )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a )\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B + A)c\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 3 2 2 3 | 2 2 2 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 285 + +--S 286 of 526 +d0853a:= D(m0853a,x) +--R +--R +--R (273) +--R 4 3 2 2 3 2 +--R (- B b + (2B + A)a b + (- B - 2A)a b + A a b)sin(x) +--R + +--R 3 +--R (- B b + A a)c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 3 +--R (- B b + A a)c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 +--R (- 2B b + (B + 2A)a b - A a )c - B b + (B + A)a b +--R + +--R 2 2 +--R - A a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 3 2 2 3 +--R ((- 2B b + 2A a b)c - B b + A a b + B a b - A a b)cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- B a b + A a )c - B a b + (B + A)a b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 2 +--R ((2B b - 2A a)c + (2B b + (- 2B - 2A)a b + 2A a b)c)sin(x) +--R + +--R 2 2 2 +--R (- 2B b + (2B + 2A)a b - 2A a )c sin(x) +--R + +--R 3 3 2 2 2 +--R ((2B b - 2A a)c + (2B b + (- 2B - 2A)a b + 2A a b)c)cos(x) +--R + +--R 3 2 2 3 +--R ((2B b - 2A a)c + (2B a b + (- 2B - 2A)a b + 2A a )c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 3 2 2 3 2 +--R ((2B b - 2A a b)c + B b - A a b - B a b + A a b)sin(x) +--R + +--R 3 +--R (- B b + A a)c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 3 3 2 2 +--R (- B b + A a)c + (- 2B b + (2B + 2A)a b - 2A a b)c +--R * +--R sin(x) +--R + +--R 2 2 4 3 2 2 2 +--R ((B a b - A a )c + B b + (- B - A)a b + A a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (- B b + (2B + A)a b + (- B - 2A)a b + A a b)cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- B a b + A a )c - B a b + (B + A)a b - A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 4 2 2 3 2 5 +--R (B b - A a)c + (B a b + (- B - A)a b + A a )c - B b +--R + +--R 4 2 3 3 2 4 +--R (B + A)a b + (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 5 +--R (B b - A a)c + (B a b + (- B - A)a b + A a )c - B b +--R + +--R 4 2 3 3 2 4 +--R (B + A)a b + (B - A)a b + (- B - A)a b + A a b +--R * +--R sin(x) +--R + +--R 2 2 3 +--R (2B b + (- B - 2A)a b + A a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- B - 2A)a b + (- 2B + A)a b + (B + 2A)a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 4 3 2 2 3 +--R ((2B b - 2A a b)c + (2B b - 2A a b - 2B a b + 2A a b)c)cos(x) +--R + +--R 2 3 3 2 2 3 4 +--R (B a b - A a )c + (B a b - A a b - B a b + A a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 2 2 +--R ((- 2B b + 2A a)c + (- 2B b + 2A a b + 2B a b - 2A a )c )sin(x) +--R + +--R 2 2 3 +--R (2B b + (- 2B - 2A)a b + 2A a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- 2B - 2A)a b + (- 2B + 2A)a b + (2B + 2A)a b - 2A a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 3 2 2 +--R ((- 2B b + 2A a)c + (- 2B b + 2A a b + 2B a b - 2A a )c )cos(x) +--R + +--R 4 3 2 2 3 2 +--R ((- 2B b + 2A a)c + (- 2B b + 2A a b + 2B a b - 2A a )c )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 3 2 2 3 2 +--R ((- 2B b + 2A a b)c + (- 2B b + 2A a b + 2B a b - 2A a b)c)sin(x) +--R + +--R 4 2 2 3 2 5 +--R (B b - A a)c + (B a b + (- B - A)a b + A a )c - B b +--R + +--R 4 2 3 3 2 4 +--R (B + A)a b + (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 2 +--R (B b - A a)c + (2B b + (- B - 2A)a b + (- B + A)a b + A a )c +--R + +--R 5 4 2 3 3 2 4 +--R B b + (- B - A)a b + (- B + A)a b + (B + A)a b - A a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 2 3 4 2 +--R ((- B a b + A a )c + (- B a b + A a b + B a b - A a )c)cos(x) +--R + +--R 2 3 3 2 2 3 4 +--R (B a b - A a )c + (B a b - A a b - B a b + A a )c +--R / +--R 2 2 4 4 3 3 4 2 2 +--R ((b - 2a b + a )c + (b - 2a b + 2a b - a )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 4a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 +--R (- b + a)c + (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 +--R (- b + a b)c + (- b + 3a b - 2a b)c - a b + 2a b +--R + +--R 4 2 5 +--R - 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 5 +--R (- b + a )c + (- 2b + 2a b + 2a b - 2a )c - b + 2a b +--R + +--R 2 4 4 2 5 6 +--R - a b + a b - 2a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 4 2 5 2 4 4 2 +--R (- a b + a )c + (- 2a b + 3a b - a )c - a b + 2a b - 2a b +--R + +--R 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c )sin(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R (2c + (4a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c )cos(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R 2c + (4b - 4a b)c + (2b - 4a b + 4a b - 2a )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 +--R 2b c + (2b + 2a b - 4a b)c +--R + +--R 4 2 3 3 2 4 +--R (2a b - 2a b - 2a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 3 5 4 4 5 +--R ((2b + 2a)c + (4b - 4a )c + (2b - 2a b - 2a b + 2a )c)cos(x) +--R + +--R 5 2 2 3 3 4 2 3 3 2 4 +--R 2a c + (4a b - 2a b - 2a )c + (2a b - 2a b - 2a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- b + a )c + (- b + 2a b - a )c )sin(x) +--R + +--R 5 2 3 3 +--R (b + a)c + (2a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + a b + 2a b - 2a b - a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 +--R (b + a)c + (2b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + 2a b + a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 3 2 5 3 3 5 +--R ((b + a b)c + (b + 2a b - a b - 2a b)c + a b - 2a b + a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 2 4 +--R (b + 2a b + a )c + (2b + 2a b - 2a b - 2a )c + b - a b +--R + +--R 4 2 6 +--R - a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 4 2 5 3 3 5 +--R (a b + a )c + (2a b + a b - 2a b - a )c + a b - 2a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b + 2a b - a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b + 2a b + a b - 4a b + a b + 2a b - a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (b - 3a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 6 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c - b + 2a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R a b - 4a b + a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (2b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 2 5 3 4 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c - a b + 2a b + a b +--R + +--R 4 3 5 2 6 7 +--R - 4a b + a b + 2a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b - a b)c + (2b - 2a b - 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - a b - 2a b + 2a b + a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (a b - a )c + (2a b - 2a b - 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b - a b - 2a b + 2a b + a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (2b - 2a)c + (4b - 4a b - 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 2b - 2a b + 4a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a b)c +--R * +--R cos(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 4b + 2a b + 2a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 +--R (- 2b c + (- 4b + 4a b)c + (- 2b + 4a b - 2a b)c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- 2b - 2a)c + (- 4b - 4a b + 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 2b - 2a b + 4a b + 4a b - 2a b - 2a )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 5 2 +--R - 2a c + (- 4a b + 4a )c + (- 2a b + 4a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 2 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c)sin(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- b - 2a b + a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 2 5 4 3 6 +--R (b - a b - 2a b + 2a b + a b - a )c + b - 3a b + 3a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- 2b - a b + 2a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 3 4 5 2 7 +--R (- b + a b + 2a b - 2a b - a b + a )c + a b - 3a b + 3a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b - a b)c + (- 2b - 2a b + 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - a b + 2a b + 2a b - a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b - 2a b - a )c + (- 2b - 4a b + 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b - 2a b + a b + 4a b + a b - 2a b - a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b - a )c + (- 2a b - 2a b + 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- a b - a b + 2a b + 2a b - a b - a )c +--R Type: Expression Integer +--E 286 + +--S 287 of 526 +m0853b:= a0853.2-r0853 +--R +--R +--R (274) +--R 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (- B + A)c\|- c - b + a +--R / +--R +--------------+ +--R 2 3 2 2 3 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a +--R Type: Expression Integer +--E 287 + +--S 288 of 526 +d0853b:= D(m0853b,x) +--R +--R +--R (275) +--R 2 2 2 +--R (- B b + (B + A)a b - A a )sin(x) +--R + +--R ((- 2B b + 2A a)c cos(x) + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 2 +--R (- 3B b + (B + 3A)a b - A a )cos(x) + (- 4B b + 4A a b)cos(x) +--R + +--R 2 2 +--R - B b + (- B + A)a b + A a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 +--R (4B b - 4A a)c sin(x) + (4B b - 4A a)c cos(x) +--R + +--R (4B b - 4A a)c cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 +--R (3B b + (B - 3A)a b - A a )sin(x) +--R + +--R ((- 2B b + 2A a)c cos(x) + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 2 2 +--R (B b + (B - A)a b - A a )cos(x) - B b + (- B + A)a b + A a +--R / +--R 2 2 2 4 3 3 4 2 +--R ((b - 2a b + a )c + b - 2a b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 +--R (- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )cos(x) +--R + +--R 2 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b + 2a )c - 2b + 4a b - 2a )cos(x) + (- b + a )c - b +--R + +--R 2 2 4 +--R 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)sin(x) +--R + +--R 4 2 2 2 4 2 2 2 +--R ((4c + (4b - 4a )c )cos(x) + 4c + (4b - 4a )c )sin(x) +--R + +--R 3 3 2 2 3 2 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 3 +--R ((4b + 4a)c + (4b + 4a b - 4a b - 4a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 3 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 3 4 2 +--R ((b + 2a b + a )c + b + 2a b - 2a b - a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R ((2b + 4a b + 2a )c + 2b + 4a b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R (b + 2a b + a )c + b + 2a b - 2a b - a +--R Type: Expression Integer +--E 288 + +--S 289 of 526 +t0854:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x))^3 +--R +--R +--R (276) +--R B cos(x) + A +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3b c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 3 3 2 2 +--R (3b c cos(x) + 6a b c cos(x) + 3a c)sin(x) + b cos(x) + 3a b cos(x) +--R + +--R 2 3 +--R 3a b cos(x) + a +--R Type: Expression Integer +--E 289 + +--S 290 of 526 +r0854:= (2*a^2*A+b*(A*b-3*a*B)+A*c^2)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(5/2)+1/2*(B*c+A*c*cos(x)-(A*b-a*B)*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x))^2+1/2*(a*B*c+(3*a*A-2*b*B)*c*cos(x)+(2*b^2*B-a*(3*A*b-a*B))*sin(x))/(a^2-b^2-c^2)^2/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (277) +--R 4 2 2 2 2 +--R (- 2A c + (- 2A b + 6B a b - 4A a )c )sin(x) +--R + +--R 3 3 2 2 3 +--R (- 4A b c + (- 4A b + 12B a b - 8A a b)c)cos(x) - 4A a c +--R + +--R 2 2 3 +--R (- 4A a b + 12B a b - 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 4 3 2 2 2 +--R (- 2A b c - 2A b + 6B a b - 4A a b )cos(x) +--R + +--R 2 3 2 2 3 2 2 2 2 +--R (- 4A a b c - 4A a b + 12B a b - 8A a b)cos(x) - 2A a c - 2A a b +--R + +--R 3 4 +--R 6B a b - 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 2 2 2 +--R (2B b - 3A a b + B a )c sin(x) +--R + +--R 2 3 2 2 2 +--R ((- 2B b + 3A a)c + 2B b - 3A a b + B a b)cos(x) + A b c +--R + +--R 3 2 2 3 +--R A b + B a b - 4A a b + 2B a +--R * +--R sin(x) +--R + +--R 2 2 +--R (- 2B b + 3A a b)c cos(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b - B a b + 4A a )c)cos(x) - B c + (- B b + 2B a )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (4b - 4a )c + (2b - 4a b + 2a )c )sin(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (8b - 8a b)c + (4b - 8a b + 4a b)c)cos(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (8a b - 8a )c + (4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (4b - 4a b )c + 2b - 4a b + 2a b )cos(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (8a b - 8a b)c + 4a b - 8a b + 4a b)cos(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (4a b - 4a )c + 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 290 + +--S 291 of 526 +a0854:= integrate(t0854,x) +--R +--R +--R (278) +--R [ +--R 3 2 2 3 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 5 4 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 6A)a b +--R + +--R 3 2 4 +--R (- 6B - 8A)a b + 4A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 3 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 4 2 3 3 2 4 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b +--R + +--R 5 +--R 4A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 2 2 4 +--R (- A b + 2A a b - A a )c +--R + +--R 3 2 2 3 4 2 6 +--R (3B a b + (- 6B - 2A)a b + (3B + 4A)a b - 2A a )c + A b +--R + +--R 5 2 4 3 3 4 2 +--R (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b + 2A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 5 2 4 +--R (2A a b - 4A a b + 2A a b)c + 2A a b + (- 6B - 4A)a b +--R + +--R 3 3 4 2 5 +--R (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R cos(x) +--R + +--R 2 2 4 +--R (A b - 2A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 +--R (A b + (- 3B - 2A)a b + (6B + 4A)a b + (- 3B - 6A)a b + 3A a )c +--R + +--R 2 4 3 3 4 2 5 6 +--R A a b + (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b + 2A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 4 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 2 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 5 4 2 3 3 2 +--R 2B b + (- 4B - 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8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 3 2 2 3 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 3 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 2 2 4 +--R (- 2A b + 4A a b - 2A a )c +--R + +--R 3 2 2 3 4 2 6 +--R (6B a b + (- 12B - 4A)a b + (6B + 8A)a b - 4A a )c + 2A b +--R + +--R 5 2 4 3 3 4 2 +--R (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 5 2 4 +--R (4A a b - 8A a b + 4A a b)c + 4A a b + (- 12B - 8A)a b +--R + +--R 3 3 4 2 5 +--R (24B + 12A)a b + (- 12B - 16A)a b + 8A a b +--R * +--R cos(x) +--R + +--R 2 2 4 +--R (2A b - 4A a b + 2A a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 4 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 2 4 3 3 4 2 5 6 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 4 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 2 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 5 4 2 3 3 2 +--R 2B b + (- 4B - 3A)a b + (3B + 6A)a b + (- 2B - 3A)a b +--R + +--R 4 +--R B a b +--R * +--R cos(x) +--R + +--R 4 +--R (2B - 2A)a c +--R + +--R 3 2 2 3 2 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 5 4 2 3 3 2 +--R A b + (B - 2A)a b + (- 2B - 3A)a b + (3B + 8A)a b +--R + +--R 4 5 +--R (- 4B - 4A)a b + 2B a +--R * +--R sin(x) +--R + +--R 5 2 2 3 +--R (- B + A)c + (- 2B b + (B + 3A)a b + (2B - 4A)a )c +--R + +--R 4 3 2 2 +--R (- B - A)b + (7B + 3A)a b + (- 7B - 8A)a b +--R + +--R 3 4 +--R (2B + 6A)a b - B a +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 +--R (- A b + 2B a b - A a )c +--R + +--R 4 3 2 2 3 4 +--R (- A b + 5B a b - 3A a b - 5B a b + 4A a )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 +--R (B - A)c + ((2B - A)b + (B - 3A)a b + (- 2B + 3A)a )c +--R + +--R 4 3 2 2 3 +--R B b + (- 2B - 3A)a b + (7B + 5A)a b + (- 7B - 6A)a b +--R + +--R 4 +--R (B + 4A)a +--R * +--R c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 291 + +--S 292 of 526 +m0854a:= a0854.1-r0854 +--R +--R +--R (279) +--R 3 2 2 5 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 5 4 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 6A)a b +--R + +--R 3 2 4 +--R (- 6B - 8A)a b + 4A a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 4 2 3 3 2 4 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b +--R + +--R 5 +--R 4A a +--R * +--R 3 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- A b + 2A a b - A a )c +--R + +--R 4 3 2 2 3 +--R 4A b + (3B - 8A)a b + (- 6B + 2A)a b + (3B + 4A)a b +--R + +--R 4 +--R - 2A a +--R * +--R 4 +--R c +--R + +--R 6 5 2 4 +--R 5A b + (- 15B - 10A)a b + (30B + 15A)a b +--R + +--R 3 3 4 2 +--R (- 15B - 20A)a b + 10A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (10A a b - 20A a b + 10A a b)c +--R + +--R 5 2 4 3 3 +--R 10A a b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 4 2 5 +--R (- 30B - 40A)a b + 20A a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 2 2 6 +--R (A b - 2A a b + A a )c +--R + +--R 4 3 2 2 3 +--R A b + (- 3B - 2A)a b + (6B + 8A)a b + (- 3B - 14A)a b +--R + +--R 4 +--R 7A a +--R * +--R 4 +--R c +--R + +--R 2 4 3 3 4 2 +--R 5A a b + (- 15B - 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a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R 3 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2A b + 4A a b - 2A a )c +--R + +--R 4 3 2 2 3 +--R 8A b + (6B - 16A)a b + (- 12B + 4A)a b + (6B + 8A)a b +--R + +--R 4 +--R - 4A a +--R * +--R 4 +--R c +--R + +--R 6 5 2 4 +--R 10A b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 3 3 4 2 +--R (- 30B - 40A)a b + 20A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 5 2 4 3 3 +--R 20A a b + (- 60B - 40A)a b + (120B + 60A)a b +--R + +--R 4 2 5 +--R (- 60B - 80A)a b + 40A a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 2 2 6 +--R (2A b - 4A a b + 2A a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b + (- 6B - 28A)a b +--R + +--R 4 +--R 14A a +--R * +--R 4 +--R c +--R + +--R 2 4 3 3 4 2 +--R 10A a b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 5 6 +--R (- 30B - 40A)a b + 20A a +--R * +--R 2 +--R c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (12B - 8A)a b + (- 24B - 4A)a b +--R + +--R 3 2 4 +--R (12B + 16A)a b - 8A a b +--R * +--R 3 +--R c +--R + +--R 7 6 2 5 +--R 8A b + (- 24B - 16A)a b + (48B + 24A)a b +--R + +--R 3 4 4 3 +--R (- 24B - 32A)a b + 16A a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 +--R 20A a b + (12B - 40A)a b + (- 24B + 12A)a b +--R + +--R 4 5 +--R (12B + 16A)a b - 8A a +--R * +--R 3 +--R c +--R + +--R 6 2 5 3 4 +--R 24A a b + (- 72B - 48A)a b + (144B + 72A)a b +--R + +--R 4 3 5 2 +--R (- 72B - 96A)a b + 48A a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 36A)a b +--R + +--R 3 2 4 +--R (- 12B - 64A)a b + 32A a b +--R * +--R 3 +--R c +--R + +--R 2 5 3 4 4 3 +--R 24A a b + (- 72B - 48A)a b + (144B + 72A)a b +--R + +--R 5 2 6 +--R (- 72B - 96A)a b + 48A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 20A)a b +--R + +--R 4 5 +--R (- 12B - 32A)a b + 16A a +--R * +--R 3 +--R c +--R + +--R 3 4 4 3 5 2 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b +--R + +--R 6 7 +--R (- 24B - 32A)a b + 16A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (- 2A b + 4A a b - 2A a b )c +--R + +--R 5 2 4 3 3 4 2 2 8 +--R (6B a b + (- 12B - 4A)a b + (6B + 8A)a b - 4A a b )c + 2A b +--R + +--R 7 2 6 3 5 4 4 +--R (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4A a b + 8A a b - 4A a b)c +--R + +--R 5 2 4 3 3 4 2 +--R 4A a b + (12B - 8A)a b + (- 24B - 4A)a b + (12B + 16A)a b +--R + +--R 5 +--R - 8A a b +--R * +--R 2 +--R c +--R + +--R 7 2 6 3 5 4 4 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b + (- 24B - 32A)a b +--R + +--R 5 3 +--R 16A a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2A b - 4A a b + 4A a b - 2A a )c +--R + +--R 6 5 2 4 3 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b - 28A a b +--R + +--R 4 2 5 6 +--R (- 12B + 10A)a b + (6B + 8A)a b - 4A a +--R * +--R 2 +--R c +--R + +--R 2 6 3 5 4 4 +--R 12A a b + (- 36B - 24A)a b + (72B + 36A)a b +--R + +--R 5 3 6 2 +--R (- 36B - 48A)a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 5 2 4 3 3 +--R 4A a b + (- 12B - 8A)a b + (24B + 20A)a b +--R + +--R 4 2 5 +--R (- 12B - 32A)a b + 16A a b +--R * +--R 2 +--R c +--R + +--R 3 5 4 4 5 3 6 2 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b + (- 24B - 32A)a b +--R + +--R 7 +--R 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2A a b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 6 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R x +--R +------------+ (b - a)tan(-) - c +--R | 2 2 2 2 +--R \|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 4 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 5 4 2 3 3 2 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 +--R - B a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 6 +--R (2B - 2A)a c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 5 4 2 3 3 2 +--R A b + (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b +--R + +--R 4 +--R 2A a b +--R * +--R 2 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 2 5 +--R (- B + A)c + ((2B - 4A)b + (B + 3A)a b + (2B - 4A)a )c +--R + +--R 4 3 2 2 +--R (13B - 5A)b + (- B - 12A)a b + (- 12B + 14A)a b +--R + +--R 3 +--R 3A a b +--R * +--R 3 +--R c +--R + +--R 6 5 2 4 3 3 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 2 +--R - B a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (10B - 8A)a b - A a )c +--R + +--R 4 3 2 2 +--R - A b + (29B - 8A)a b + (- 8B - 27A)a b +--R + +--R 3 4 +--R (- 21B + 32A)a b + 4A a +--R * +--R 3 +--R c +--R + +--R 5 2 4 3 3 +--R - 4B a b + (8B + 6A)a b + (- 6B - 12A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 7 2 2 5 +--R (B - A)c + ((2B - A)b + (B - 3A)a b + (2B - A)a )c +--R + +--R 4 3 2 2 3 +--R - B b + 2B a b + (16B - 5A)a b + (- 9B - 15A)a b +--R + +--R 4 +--R (- 8B + 20A)a +--R * +--R 3 +--R c +--R + +--R 2 4 3 3 4 2 5 +--R - 2B a b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 6 +--R - B a +--R * +--R c +--R * +--R 2 +--R sin(x) +--R + +--R 6 +--R (- 2B + 2A)b c +--R + +--R 3 2 2 3 4 +--R ((- 4B - 2A)b + (6B + 9A)a b + (2B - 14A)a b + 3A a )c +--R + +--R 5 4 2 3 +--R (10B - 4A)b - 9A a b + (- 11B + 10A)a b +--R + +--R 3 2 4 +--R (2B + 3A)a b - B a b +--R * +--R 2 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 6 +--R (- 2B + 2A)a c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 12A)a b + (2B + 7A)a b + (4B - 8A)a )c +--R + +--R 5 4 2 3 +--R A b + (33B - 14A)a b + (- 6B - 33A)a b +--R + +--R 3 2 4 +--R (- 27B + 44A)a b + 2A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 6 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 4 +--R ((8B - 2A)b + (- 6B - 9A)a b + (10B + 2A)a b - 3A a )c +--R + +--R 5 4 2 3 +--R 2B b + (- 4B - 3A)a b + (39B - 6A)a b +--R + +--R 3 2 4 +--R (- 14B - 39A)a b + (- 23B + 48A)a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2B - 2A)a c + (- A b + 6B a b + (- 2B - 7A)a b + 4A a )c +--R + +--R 5 4 2 3 3 2 +--R - A b + (3B + 2A)a b + (- 6B - 3A)a b + 15B a b +--R + +--R 4 5 +--R (- 4B - 14A)a b + (- 8B + 16A)a +--R * +--R 2 +--R c +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- B + A)b c + (- 4B b + (5B + 6A)a b - 10A a b + 3A a b)c +--R + +--R 6 5 2 4 3 3 4 2 +--R ((B - A)b + 3B a b + (- 5B - 2A)a b + (2B + 3A)a b - B a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (- 2B + 4A)a b - A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 3B a b + (4B + 9A)a b + (3B - 16A)a b + 4A a )c +--R + +--R 5 2 4 3 3 +--R (8B - 4A)a b + (4B - 6A)a b + (- 14B + 4A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + 2B a b + (- 2B + A)a )c +--R + +--R 4 3 2 2 3 +--R (4B - A)b + (- 3B - 6A)a b + (4B + 5A)a b - 3B a b +--R + +--R 4 +--R (4B - 4A)a +--R * +--R 3 +--R c +--R + +--R 6 5 2 4 3 3 +--R 2B b + (- 4B - 3A)a b + 19B a b + (- 4B - 18A)a b +--R + +--R 4 2 5 6 +--R (- 14B + 18A)a b + (2B + 3A)a b - B a +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (A b + (2B - 4A)a b + A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b + (7B - 4A)a b + (- 4B - 9A)a b + (B + 12A)a b - 4A a )c +--R + +--R 5 2 4 3 3 4 2 +--R 4B a b + (- 8B - 6A)a b + (18B + 8A)a b + (- 8B - 18A)a b +--R + +--R 5 +--R (- 6B + 16A)a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 5 +--R (B b - 2B a b + (2B - A)a )c +--R + +--R 4 3 2 2 3 4 3 +--R (B b - 2B a b + (2B - A)a b + (3B - 3A)a b + (- 3B + 3A)a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2B a b + (- 4B - 3A)a b + (6B + 5A)a b + (- 3B - 6A)a b +--R + +--R 6 +--R (- B + 4A)a +--R * +--R c +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 292 + +--S 293 of 526 +--d0854a:= D(m0854a,x) +--E 293 + +--S 294 of 526 +m0854b:= a0854.2-r0854 +--R +--R +--R (280) +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R 3 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2A b + 4A a b - 2A a )c +--R + +--R 4 3 2 2 3 +--R 8A b + (6B - 16A)a b + (- 12B + 4A)a b + (6B + 8A)a b +--R + +--R 4 +--R - 4A a +--R * +--R 4 +--R c +--R + +--R 6 5 2 4 +--R 10A b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 3 3 4 2 +--R (- 30B - 40A)a b + 20A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 5 2 4 3 3 +--R 20A a b + (- 60B - 40A)a b + (120B + 60A)a b +--R + +--R 4 2 5 +--R (- 60B - 80A)a b + 40A a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 2 2 6 +--R (2A b - 4A a b + 2A a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b + (- 6B - 28A)a b +--R + +--R 4 +--R 14A a +--R * +--R 4 +--R c +--R + +--R 2 4 3 3 4 2 +--R 10A a b + (- 30B - 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4A a b + 4A a b - 2A a )c +--R + +--R 6 5 2 4 3 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b - 28A a b +--R + +--R 4 2 5 6 +--R (- 12B + 10A)a b + (6B + 8A)a b - 4A a +--R * +--R 2 +--R c +--R + +--R 2 6 3 5 4 4 +--R 12A a b + (- 36B - 24A)a b + (72B + 36A)a b +--R + +--R 5 3 6 2 +--R (- 36B - 48A)a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 5 2 4 3 3 +--R 4A a b + (- 12B - 8A)a b + (24B + 20A)a b +--R + +--R 4 2 5 +--R (- 12B - 32A)a b + 16A a b +--R * +--R 2 +--R c +--R + +--R 3 5 4 4 5 3 6 2 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b + (- 24B - 32A)a b +--R + +--R 7 +--R 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2A a b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 6 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R 3 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2A b + 4A a b - 2A a )c +--R + +--R 4 3 2 2 3 +--R 8A b + (6B - 16A)a b + (- 12B + 4A)a b + (6B + 8A)a b +--R + +--R 4 +--R - 4A a +--R * +--R 4 +--R c +--R + +--R 6 5 2 4 +--R 10A b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 3 3 4 2 +--R (- 30B - 40A)a b + 20A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 5 2 4 3 3 +--R 20A a b + (- 60B - 40A)a b + (120B + 60A)a b +--R + +--R 4 2 5 +--R (- 60B - 80A)a b + 40A a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 2 2 6 +--R (2A b - 4A a b + 2A a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b + (- 6B - 28A)a b +--R + +--R 4 +--R 14A a +--R * +--R 4 +--R c +--R + +--R 2 4 3 3 4 2 +--R 10A a b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 5 6 +--R (- 30B - 40A)a b + 20A a +--R * +--R 2 +--R c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (12B - 8A)a b + (- 24B - 4A)a b +--R + +--R 3 2 4 +--R (12B + 16A)a b - 8A a b +--R * +--R 3 +--R c +--R + +--R 7 6 2 5 +--R 8A b + (- 24B - 16A)a b + (48B + 24A)a b +--R + +--R 3 4 4 3 +--R (- 24B - 32A)a b + 16A a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 +--R 20A a b + (12B - 40A)a b + (- 24B + 12A)a b +--R + +--R 4 5 +--R (12B + 16A)a b - 8A a +--R * +--R 3 +--R c +--R + +--R 6 2 5 3 4 +--R 24A a b + (- 72B - 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16A)a b + (48B + 24A)a b + (- 24B - 32A)a b +--R + +--R 7 +--R 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2A a b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 6 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 4 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 5 4 2 3 3 2 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 +--R - B a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 6 +--R (2B - 2A)a c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 5 4 2 3 3 2 +--R A b + (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b +--R + +--R 4 +--R 2A a b +--R * +--R 2 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 2 5 +--R (- B + A)c + ((2B - 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2A)b + (6B + 9A)a b + (2B - 14A)a b + 3A a )c +--R + +--R 5 4 2 3 +--R (10B - 4A)b - 9A a b + (- 11B + 10A)a b +--R + +--R 3 2 4 +--R (2B + 3A)a b - B a b +--R * +--R 2 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 6 +--R (- 2B + 2A)a c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 12A)a b + (2B + 7A)a b + (4B - 8A)a )c +--R + +--R 5 4 2 3 +--R A b + (33B - 14A)a b + (- 6B - 33A)a b +--R + +--R 3 2 4 +--R (- 27B + 44A)a b + 2A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 6 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 4 +--R ((8B - 2A)b + (- 6B - 9A)a b + (10B + 2A)a b - 3A a )c +--R + +--R 5 4 2 3 +--R 2B b + (- 4B - 3A)a b + (39B - 6A)a b +--R + +--R 3 2 4 +--R (- 14B - 39A)a b + (- 23B + 48A)a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2B - 2A)a c + (- A b + 6B a b + (- 2B - 7A)a b + 4A a )c +--R + +--R 5 4 2 3 3 2 +--R - A b + (3B + 2A)a b + (- 6B - 3A)a b + 15B a b +--R + +--R 4 5 +--R (- 4B - 14A)a b + (- 8B + 16A)a +--R * +--R 2 +--R c +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- B + A)b c + (- 4B b + (5B + 6A)a b - 10A a b + 3A a b)c +--R + +--R 6 5 2 4 3 3 4 2 +--R ((B - A)b + 3B a b + (- 5B - 2A)a b + (2B + 3A)a b - B a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (- 2B + 4A)a b - A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 3B a b + (4B + 9A)a b + (3B - 16A)a b + 4A a )c +--R + +--R 5 2 4 3 3 +--R (8B - 4A)a b + (4B - 6A)a b + (- 14B + 4A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + 2B a b + (- 2B + A)a )c +--R + +--R 4 3 2 2 3 +--R (4B - A)b + (- 3B - 6A)a b + (4B + 5A)a b - 3B a b +--R + +--R 4 +--R (4B - 4A)a +--R * +--R 3 +--R c +--R + +--R 6 5 2 4 3 3 +--R 2B b + (- 4B - 3A)a b + 19B a b + (- 4B - 18A)a b +--R + +--R 4 2 5 6 +--R (- 14B + 18A)a b + (2B + 3A)a b - B a +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (A b + (2B - 4A)a b + A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b + (7B - 4A)a b + (- 4B - 9A)a b + (B + 12A)a b - 4A a )c +--R + +--R 5 2 4 3 3 4 2 +--R 4B a b + (- 8B - 6A)a b + (18B + 8A)a b + (- 8B - 18A)a b +--R + +--R 5 +--R (- 6B + 16A)a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 5 +--R (B b - 2B a b + (2B - A)a )c +--R + +--R 4 3 2 2 3 4 3 +--R (B b - 2B a b + (2B - A)a b + (3B - 3A)a b + (- 3B + 3A)a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2B a b + (- 4B - 3A)a b + (6B + 5A)a b + (- 3B - 6A)a b +--R + +--R 6 +--R (- B + 4A)a +--R * +--R c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 294 + +--S 295 of 526 +--d0854b:= D(m0854b,x) +--E 295 + +--S 296 of 526 +t0855:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)) +--R +--R +--R C sin(x) + B cos(x) + A +--R (281) ----------------------- +--R c sin(x) + b cos(x) + a +--R Type: Expression Integer +--E 296 + +--S 297 of 526 +r0855:= (b*B+c*C)*x/(b^2+c^2)+2*(A-a*(b*B+c*C)/(b^2+c^2))*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(1/2)+(B*c-b*C)*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) +--R +--R +--R (282) +--R +--------------+ +--R | 2 2 2 +--R (B c - C b)\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (- 2A c + 2C a c - 2A b + 2B a b)atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (C c + B b)x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression Integer +--E 297 + +--S 298 of 526 +a0855:= integrate(t0855,x) +--R +--R +--R (283) +--R [ +--R 2 2 +--R (- A c + C a c - A b + B a b) +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R | 2 2 2 2 +--R (- B c + C b)\|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R (B c - C b)\|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R (C c + B b)x\|c + b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|c + b - a +--R , +--R +--R +--------------+ +--R | 2 2 2 2 +--R (- B c + C b)\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R (B c - C b)\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R +--------------+ +--R | 2 2 2 +--R (C c + B b)x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 298 + +--S 299 of 526 +m0855a:= a0855.1-r0855 +--R +--R +--R (284) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (- A c + C a c - A b + B a b)\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B c + C b)\|- c - b + a \|c + b - a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R (- B c + C b)\|- c - b + a \|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (B c - C b)\|- c - b + a \|c + b - a +--R * +--R - 2c sin(x) - 2b cos(x) - 2a +--R log(----------------------------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2A c - 2C a c + 2A b - 2B a b)\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c + b )\|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 299 + +--S 300 of 526 +d0855a:= D(m0855a,x) +--R +--R +--R (285) +--R 3 2 2 2 3 2 2 3 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c +--R + +--R 5 4 2 3 3 2 +--R - A b + (B + 2A)a b + (- 2B - A)a b + B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + ((B - 2A)a b + A a )c +--R + +--R 2 2 3 2 +--R (- C a b + 2C a b - C a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- A b + B a b)c +--R * +--R sin(x) +--R + +--R 4 2 3 +--R (- 2A b + A a)c + (2C a b - C a )c +--R + +--R 3 2 2 2 3 2 2 +--R (- 3A b + (2B + 2A)a b - B a b)c + (C a b - C a b )c +--R + +--R 5 4 2 3 +--R - A b + (B + A)a b - B a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 2 +--R - 2A b c + 2C a b c + (- 3A b + 2B a b + A a b)c +--R + +--R 3 3 5 4 2 3 3 2 +--R (C a b - C a b)c - A b + B a b + A a b - B a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 +--R - A a c + C a c + (- 2A a b + (B + A)a b)c +--R + +--R 2 2 3 4 2 3 3 2 +--R (C a b - C a b)c - A a b + (B + A)a b - B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 +--R 2A c - 2C a c + (4A b + (- 2B - 2A)a b)c +--R + +--R 2 2 2 4 3 2 2 +--R (- 2C a b + 2C a b)c + (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 2 +--R (- 2A b + (2B + 2A)a b - 2B a b)c +--R * +--R sin(x) +--R + +--R 5 4 2 3 +--R 2A c - 2C a c + (4A b + (- 2B - 2A)a b)c +--R + +--R 2 2 2 4 3 2 2 +--R (- 2C a b + 2C a b)c + (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 +--R 2A c - 2C a c + (2A b + (- 2B + 2A)a b - 2A a )c +--R + +--R 2 3 2 3 2 2 3 +--R (- 2C a b + 2C a )c + (2A a b + (- 2B - 2A)a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 3 2 2 2 +--R 2A b c - 2C a b c + (3A b - 2B a b - A a b)c +--R + +--R 3 3 5 4 2 3 3 2 +--R (- C a b + C a b)c + A b - B a b - A a b + B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + ((B - 2A)a b + A a )c +--R + +--R 2 2 3 2 +--R (- C a b + 2C a b - C a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- 3A b + (B + 2A)a b)c +--R + +--R 2 2 2 4 3 2 2 +--R (2C a b - 2C a b)c + (- 2A b + (2B + 2A)a b - 2B a b )c +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 3 2 2 5 +--R A a c - C a c + (A b - B a b)c + (- C a b + C a b )c + A b +--R + +--R 4 2 3 +--R (- B - A)a b + B a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 2 3 2 2 3 5 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c - A b +--R + +--R 4 2 3 3 2 +--R (B + 2A)a b + (- 2B - A)a b + B a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 2 2 3 +--R - A a c + C a c + (- 2A a b + (B + A)a b)c + (C a b - C a b)c +--R + +--R 4 2 3 3 2 +--R - A a b + (B + A)a b - B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b + (B - A)a b + A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (C a b - C a )c + (A b - 2A a b + B a b + (- B + A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b + (B - A)a b + A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (C a b - C a )c + (A b - 2A a b + B a b + (- B + A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + A a)c + (2C a b - C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 2A)a b + (- B + 2A)a b - A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - C a b - 2C a b + C a )c +--R + +--R 5 4 2 3 3 2 4 +--R (- 2A b + (2B + A)a b + (- B + 2A)a b + (- 2B - A)a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 2 3 +--R - 2A b c + 2C a b c + (- 4A b + 2B a b + 2A a b)c +--R + +--R 3 3 2 5 4 2 3 3 2 +--R (2C a b - 2C a b)c + (- 2A b + 2B a b + 2A a b - 2B a b )c +--R * +--R cos(x) +--R + +--R 5 2 4 2 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + B a b + A a )c + (C a b - C a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 2 4 +--R 2A c - 2C a c + (4A b - 2B a b - 2A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (- 2C a b + 2C a )c + (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 4A)a b + (- 2B + 2A)a b - 2A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - 2C a b - 2C a b + 2C a )c +--R + +--R 5 4 2 3 3 2 +--R - 2A b + (2B + 2A)a b + (- 2B + 2A)a b + (- 2B - 2A)a b +--R + +--R 4 +--R 2B a b +--R * +--R c +--R * +--R sin(x) +--R + +--R 6 5 2 2 4 +--R 2A c - 2C a c + (4A b - 2B a b - 2A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (- 2C a b + 2C a )c + (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 +--R 2A c - 2C a c + (4A b - 2B a b - 2A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (- 2C a b + 2C a )c + (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 3 2 2 3 +--R 2A b c - 2C a b c + (4A b - 2B a b - 2A a b)c +--R + +--R 3 3 2 5 4 2 3 3 2 +--R (- 2C a b + 2C a b)c + (2A b - 2B a b - 2A a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b + (B - A)a b + A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (C a b - C a )c + (A b - 2A a b + B a b + (- B + A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- 3A b + (B + A)a b + A a )c +--R + +--R 2 2 3 3 +--R (2C a b - C a b - C a )c +--R + +--R 4 3 2 2 3 2 +--R (- 3A b + (2B + 2A)a b + (- B + 2A)a b + (- B - A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (C a b - C a b - C a b + C a b)c - A b + (B + A)a b +--R + +--R 2 4 3 3 4 2 +--R (- B + A)a b + (- B - A)a b + B a b +--R * +--R sin(x) +--R + +--R 5 2 4 2 2 3 3 2 2 4 2 +--R A a c - C a c + (2A a b - B a b - A a )c + (- C a b + C a )c +--R + +--R 4 2 3 3 2 4 +--R (A a b - B a b - A a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 2 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + B a b + A a )c + (C a b - C a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R / +--R 2 2 4 4 3 2 2 2 2 +--R ((b - 2a b + a )c + (b - 2a b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 3a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (b - 3a b + 3a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 3 +--R (- b + a)c + (- 2b + 4a b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + 3a b - 3a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 3 3 +--R ((- b + a b)c + (- b + 2a b - a b)c - a b + 2a b - a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 6 +--R (- b + a )c + (- 2b + 2a b - a b + 2a b - a )c - b +--R + +--R 5 2 4 3 3 4 2 +--R 2a b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 2 5 2 4 3 3 +--R (- a b + a )c + (- 2a b + 3a b - a b)c - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c )sin(x) +--R + +--R 6 2 4 4 3 2 2 2 +--R (2c + (4a b - 2a )c + (- 2b + 4a b - 2a b )c )cos(x) +--R + +--R 6 2 2 4 4 3 2 2 2 +--R 2c + (4b - 4a b + 2a )c + (2b - 4a b + 2a b )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 4 2 3 2 +--R (2b c + (2b + 2a b - 2a b)c + (2a b - 2a b )c)cos(x) +--R + +--R 5 3 2 3 3 +--R (2b + 2a)c + (4b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 +--R (2b - 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 4 2 3 +--R 2a c + (4a b - 2a b)c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 2 2 +--R ((- b + a )c + (- b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (b + a)c + (2a b + a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + a b + a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 3 5 4 2 3 3 2 +--R (b + a)c + (2b - a b + a )c + (b - a b - a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 3 2 5 3 3 2 +--R ((b + a b)c + (b + 2a b - a b)c + a b - a b )cos(x) +--R + +--R 2 2 4 4 3 2 2 4 2 6 4 2 +--R ((b + 2a b + a )c + (2b + 2a b + a b - a )c + b - a b )cos(x) +--R + +--R 2 4 3 2 2 3 2 5 3 3 +--R (a b + a )c + (2a b + a b - a b)c + a b - a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 2a b + a )c + (2b - 4a b + a b + 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b - 2a b + 2a b - a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 6 3 4 4 3 +--R (b - 3a b + 2a b + a b - a b)c + b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 +--R (- b + a)c + (- 2b + 3a b - a b)c +--R + +--R 5 4 2 3 4 5 2 6 2 5 4 3 5 2 +--R (- b + 3a b - 3a b + 2a b - a )c + a b - 2a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b + a b)c + (- 2b + 2a b + a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (- b + a b + a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b + a )c + (- 2a b + 2a b + a b - a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- a b + a b + a b - a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (- 2b + 2a)c + (- 4b + 4a b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 3 +--R 2c + (2b + 2a b - 2a )c + (- 2b + 4a b - 2a b)c +--R + +--R 6 5 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 2 2 3 4 3 +--R 2c + (4b - 2a b)c + (2b - 4a b + 2a b + 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 2a b + 2a b + 2a b - 2a b )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 2 2 +--R (2b c + (4b - 2a b)c + (2b - 2a b )c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2b + 2a)c + (4b + 4a b - 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b - 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 2 +--R 2a c + (4a b - 2a )c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c)sin(x) +--R + +--R 6 3 2 3 4 +--R (b + a)c + (b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 2 5 4 3 +--R (- b + a b + 2a b - a b - a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 5 4 2 3 3 2 5 2 +--R (b + a)c + (2b + a b - a b)c + (b - a b - a b + 2a b - a )c +--R + +--R 6 3 4 5 2 +--R - a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b + a b)c + (2b + 2a b - a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (b + a b - a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b + 2a b + a )c + (2b + 4a b + a b - 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b + 2a b - 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 5 2 4 3 3 4 2 +--R (a b + a )c + (2a b + 2a b - a b - a )c + (a b + a b - a b - a b )c +--R Type: Expression Integer +--E 300 + +--S 301 of 526 +m0855b:= a0855.2-r0855 +--R +--R +--R (286) +--R +--------------+ +--R | 2 2 2 +--R (- B c + C b)\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +--R | 2 2 2 2 +--R (- B c + C b)\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R (B c - C b)\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2A c - 2C a c + 2A b - 2B a b)atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression Integer +--E 301 + +--S 302 of 526 +d0855b:= D(m0855b,x) +--R +--R +--R (287) +--R 2 2 3 2 2 +--R ((- A b + A a)c + (C a b - C a )c - A b + (B + A)a b - B a b) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c + 2C a c + (- 2A b + 2B a b)c)cos(x) - 2A c + 2C a c +--R + +--R 2 +--R (- 2A b + 2B a b)c +--R * +--R sin(x) +--R + +--R 2 2 3 2 +--R (- 3A b + A a)c + (3C a b - C a )c - 3A b + (3B + A)a b +--R + +--R 2 +--R - B a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 2 2 +--R (- 4A b c + 4C a b c - 4A b + 4B a b )cos(x) + (- A b - A a)c +--R + +--R 2 3 2 2 +--R (C a b + C a )c - A b + (B - A)a b + B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 +--R (4A c - 4C a c + (4A b - 4B a b)c)sin(x) +--R + +--R 3 2 2 2 +--R (4A c - 4C a c + (4A b - 4B a b)c)cos(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + (4A b - 4B a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 2 +--R ((3A b + A a)c + (- 3C a b - C a )c + 3A b + (- 3B + A)a b - B a b) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c + 2C a c + (- 2A b + 2B a b)c)cos(x) - 2A c + 2C a c +--R + +--R 2 +--R (- 2A b + 2B a b)c +--R * +--R sin(x) +--R + +--R 2 2 3 2 2 2 +--R ((A b + A a)c + (- C a b - C a )c + A b + (- B + A)a b - B a b)cos(x) +--R + +--R 2 2 3 2 2 +--R (- A b - A a)c + (C a b + C a )c - A b + (B - A)a b + B a b +--R / +--R 2 2 2 4 3 2 2 2 +--R ((b - 2a b + a )c + b - 2a b + a b )sin(x) +--R + +--R 3 3 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)cos(x) + (- 2b + 2a)c +--R + +--R 3 2 +--R (- 2b + 2a b )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 2 4 2 2 +--R ((- 2b + 2a )c - 2b + 2a b )cos(x) + (- b + a )c - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)sin(x) +--R + +--R 4 2 2 4 2 2 +--R ((4c + 4b c )cos(x) + 4c + 4b c )sin(x) +--R + +--R 3 3 2 2 +--R ((2b + 2a)c + (2b + 2a b )c)cos(x) +--R + +--R 3 3 2 3 3 2 +--R ((4b + 4a)c + (4b + 4a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )sin(x) +--R + +--R 3 3 2 3 3 2 +--R (((2b + 2a)c + (2b + 2a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c) +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R ((b + 2a b + a )c + b + 2a b + a b )cos(x) +--R + +--R 2 2 2 4 3 2 2 2 2 2 +--R ((2b + 4a b + 2a )c + 2b + 4a b + 2a b )cos(x) + (b + 2a b + a )c +--R + +--R 4 3 2 2 +--R b + 2a b + a b +--R Type: Expression Integer +--E 302 + +--S 303 of 526 +t0856:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2 +--R +--R +--R (288) +--R C sin(x) + B cos(x) + A +--R --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R Type: Expression Integer +--E 303 + +--S 304 of 526 +r0856:= 2*(a*A-b*B-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(3/2)+(B*c-b*C+(A*c-a*C)*cos(x)-(A*b-a*B)*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (289) +--R 2 +--R (- 2C c + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 +--R (- 2C b c - 2B b + 2A a b)cos(x) - 2C a c - 2B a b + 2A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((A b - B a)sin(x) + (- A c + C a)cos(x) - B c + C b)\|- c - b + a +--R / +--R 3 2 2 2 3 2 2 2 3 +--R ((c + (b - a )c)sin(x) + (b c + b - a b)cos(x) + a c + a b - a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 304 + +--S 305 of 526 +a0856:= integrate(t0856,x) +--R +--R +--R (290) +--R [ +--R 2 2 2 +--R ((C b - C a)c + (B b + (- B - A)a b + A a )c)sin(x) +--R + +--R 2 3 2 2 +--R ((C b - C a b)c + B b + (- B - A)a b + A a b)cos(x) +--R + +--R 2 2 2 3 +--R (C a b - C a )c + B a b + (- B - A)a b + A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 2 2 2 +--R ((- B + A)c + (C b - C a)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R 2 2 2 2 +--R ((- B b + A a)c + C b - C a )cos(x) + (- B b + A a)c + C b - C a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 2 2 2 +--R ((2C b - 2C a)c + (2B b + (- 2B - 2A)a b + 2A a )c)sin(x) +--R + +--R 2 3 2 2 +--R ((2C b - 2C a b)c + 2B b + (- 2B - 2A)a b + 2A a b)cos(x) +--R + +--R 2 2 2 3 +--R (2C a b - 2C a )c + 2B a b + (- 2B - 2A)a b + 2A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 2 2 2 +--R ((- B + A)c + (C b - C a)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R 2 2 2 2 +--R ((- B b + A a)c + C b - C a )cos(x) + (- B b + A a)c + C b - C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 305 + +--S 306 of 526 +m0856a:= a0856.1-r0856 +--R +--R +--R (291) +--R +--------------+ +--R 2 2 | 2 2 2 +--R ((C b - C a)c + B b + (- B - A)a b + A a )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R ((2C b - 2C a)c + 2B b + (- 2B - 2A)a b + 2A a )\|c + b - a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R ((- B + A)c + C b - C a)\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 3 2 2 3 | 2 2 2 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a \|c + b - a +--R Type: Expression Integer +--E 306 + +--S 307 of 526 +d0856a:= D(m0856a,x) +--R +--R +--R (292) +--R 3 2 2 4 3 +--R (- C b + 2C a b - C a b)c - B b + (2B + A)a b +--R + +--R 2 2 3 +--R (- B - 2A)a b + A a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + (- B b + A a)c + (C b - 2C a b + C a )c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 +--R - C c + (- B b + A a)c +--R * +--R sin(x) +--R + +--R 3 2 2 2 +--R (- 2C b + C a)c + (- 2B b + (B + 2A)a b - A a )c +--R + +--R 3 2 4 3 2 2 +--R (- C b + C a b )c - B b + (B + A)a b - A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 4 +--R - 2C b c + (- 2B b + 2A a b)c + (- C b + C a b)c - B b +--R + +--R 3 2 2 3 +--R A a b + B a b - A a b +--R * +--R cos(x) +--R + +--R 3 2 2 2 2 3 +--R - C a c + (- B a b + A a )c + (- C a b + C a b)c - B a b +--R + +--R 2 2 3 +--R (B + A)a b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 +--R 2C c + (2B b - 2A a)c + (2C b - 2C a b)c +--R + +--R 3 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 2 +--R ((- 2C b + 2C a)c + (- 2B b + (2B + 2A)a b - 2A a )c )sin(x) +--R + +--R 4 3 2 2 +--R 2C c + (2B b - 2A a)c + (2C b - 2C a b)c +--R + +--R 3 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R 2C c + (2B b - 2A a)c + (2C a b - 2C a )c +--R + +--R 2 2 3 +--R (2B a b + (- 2B - 2A)a b + 2A a )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 +--R 2C b c + (2B b - 2A a b)c + (C b - C a b)c + B b - A a b +--R + +--R 2 2 3 +--R - B a b + A a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + (- B b + A a)c + (C b - 2C a b + C a )c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 2 2 +--R - C c + (- B b + A a)c + (- 2C b + 2C a b)c +--R + +--R 3 2 2 +--R (- 2B b + (2B + 2A)a b - 2A a b)c +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 4 +--R C a c + (B a b - A a )c + (C b - C a b )c + B b +--R + +--R 3 2 2 +--R (- B - A)a b + A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 4 3 +--R (- C b + 2C a b - C a b)c - B b + (2B + A)a b +--R + +--R 2 2 3 +--R (- B - 2A)a b + A a b +--R * +--R cos(x) +--R + +--R 3 2 2 2 2 3 +--R - C a c + (- B a b + A a )c + (- C a b + C a b)c - B a b +--R + +--R 2 2 3 +--R (B + A)a b - A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 5 4 2 3 +--R C c + (B b - A a)c + (C a b - C a )c +--R + +--R 2 2 3 2 +--R (B a b + (- B - A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (- C b + C a b + C a b - C a b)c - B b + (B + A)a b +--R + +--R 2 3 3 2 4 +--R (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R C c + (B b - A a)c + (C a b - C a )c +--R + +--R 2 2 3 2 +--R (B a b + (- B - A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (- C b + C a b + C a b - C a b)c - B b + (B + A)a b +--R + +--R 2 3 3 2 4 +--R (B - A)a b + (- B - A)a b + A a b +--R * +--R sin(x) +--R + +--R 4 2 2 3 +--R (2C b - C a)c + (2B b + (- B - 2A)a b + A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - C a b - 2C a b + C a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- B - 2A)a b + (- 2B + A)a b + (B + 2A)a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 3 3 2 2 +--R 2C b c + (2B b - 2A a b)c + (2C b - 2C a b)c +--R + +--R 4 3 2 2 3 +--R (2B b - 2A a b - 2B a b + 2A a b)c +--R * +--R cos(x) +--R + +--R 4 2 3 2 3 2 +--R C a c + (B a b - A a )c + (C a b - C a )c +--R + +--R 3 2 2 3 4 +--R (B a b - A a b - B a b + A a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 2 3 +--R - 2C c + (- 2B b + 2A a)c + (- 2C b + 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2B b + 2A a b + 2B a b - 2A a )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 3 +--R (2C b - 2C a)c + (2B b + (- 2B - 2A)a b + 2A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 2C a b - 2C a b + 2C a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- 2B - 2A)a b + (- 2B + 2A)a b + (2B + 2A)a b - 2A a )c +--R * +--R sin(x) +--R + +--R 5 4 2 2 3 +--R - 2C c + (- 2B b + 2A a)c + (- 2C b + 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2B b + 2A a b + 2B a b - 2A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 +--R - 2C c + (- 2B b + 2A a)c + (- 2C b + 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2B b + 2A a b + 2B a b - 2A a )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 2 +--R - 2C b c + (- 2B b + 2A a b)c + (- 2C b + 2C a b)c +--R + +--R 4 3 2 2 3 +--R (- 2B b + 2A a b + 2B a b - 2A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R C c + (B b - A a)c + (C a b - C a )c +--R + +--R 2 2 3 2 +--R (B a b + (- B - A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (- C b + C a b + C a b - C a b)c - B b + (B + A)a b +--R + +--R 2 3 3 2 4 +--R (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R C c + (B b - A a)c + (2C b - C a b - C a )c +--R + +--R 3 2 2 3 2 +--R (2B b + (- B - 2A)a b + (- B + A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (C b - C a b - C a b + C a b)c + B b + (- B - A)a b +--R + +--R 2 3 3 2 4 +--R (- B + A)a b + (B + A)a b - A a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 +--R - C a c + (- B a b + A a )c + (- C a b + C a )c +--R + +--R 3 2 2 3 4 +--R (- B a b + A a b + B a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 3 2 3 2 +--R C a c + (B a b - A a )c + (C a b - C a )c +--R + +--R 3 2 2 3 4 +--R (B a b - A a b - B a b + A a )c +--R / +--R 2 2 4 4 3 3 4 2 2 +--R ((b - 2a b + a )c + (b - 2a b + 2a b - a )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 4a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 +--R (- b + a)c + (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 +--R (- b + a b)c + (- b + 3a b - 2a b)c - a b + 2a b +--R + +--R 4 2 5 +--R - 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 5 +--R (- b + a )c + (- 2b + 2a b + 2a b - 2a )c - b + 2a b +--R + +--R 2 4 4 2 5 6 +--R - a b + a b - 2a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 4 2 5 2 4 4 2 +--R (- a b + a )c + (- 2a b + 3a b - a )c - a b + 2a b - 2a b +--R + +--R 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c )sin(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R (2c + (4a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c )cos(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R 2c + (4b - 4a b)c + (2b - 4a b + 4a b - 2a )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 +--R 2b c + (2b + 2a b - 4a b)c +--R + +--R 4 2 3 3 2 4 +--R (2a b - 2a b - 2a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 3 5 4 4 5 +--R ((2b + 2a)c + (4b - 4a )c + (2b - 2a b - 2a b + 2a )c)cos(x) +--R + +--R 5 2 2 3 3 4 2 3 3 2 4 +--R 2a c + (4a b - 2a b - 2a )c + (2a b - 2a b - 2a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- b + a )c + (- b + 2a b - a )c )sin(x) +--R + +--R 5 2 3 3 +--R (b + a)c + (2a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + a b + 2a b - 2a b - a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 +--R (b + a)c + (2b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + 2a b + a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 3 2 5 3 3 5 +--R ((b + a b)c + (b + 2a b - a b - 2a b)c + a b - 2a b + a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 2 4 +--R (b + 2a b + a )c + (2b + 2a b - 2a b - 2a )c + b - a b +--R + +--R 4 2 6 +--R - a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 4 2 5 3 3 5 +--R (a b + a )c + (2a b + a b - 2a b - a )c + a b - 2a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b + 2a b - a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b + 2a b + a b - 4a b + a b + 2a b - a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (b - 3a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 6 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c - b + 2a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R a b - 4a b + a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (2b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 2 5 3 4 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c - a b + 2a b + a b +--R + +--R 4 3 5 2 6 7 +--R - 4a b + a b + 2a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b - a b)c + (2b - 2a b - 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - a b - 2a b + 2a b + a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (a b - a )c + (2a b - 2a b - 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b - a b - 2a b + 2a b + a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (2b - 2a)c + (4b - 4a b - 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 2b - 2a b + 4a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a b)c +--R * +--R cos(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 4b + 2a b + 2a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 +--R (- 2b c + (- 4b + 4a b)c + (- 2b + 4a b - 2a b)c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- 2b - 2a)c + (- 4b - 4a b + 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 2b - 2a b + 4a b + 4a b - 2a b - 2a )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 5 2 +--R - 2a c + (- 4a b + 4a )c + (- 2a b + 4a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 2 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c)sin(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- b - 2a b + a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 2 5 4 3 6 +--R (b - a b - 2a b + 2a b + a b - a )c + b - 3a b + 3a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- 2b - a b + 2a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 3 4 5 2 7 +--R (- b + a b + 2a b - 2a b - a b + a )c + a b - 3a b + 3a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b - a b)c + (- 2b - 2a b + 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - a b + 2a b + 2a b - a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b - 2a b - a )c + (- 2b - 4a b + 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b - 2a b + a b + 4a b + a b - 2a b - a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b - a )c + (- 2a b - 2a b + 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- a b - a b + 2a b + 2a b - a b - a )c +--R Type: Expression Integer +--E 307 + +--S 308 of 526 +m0856b:= a0856.2-r0856 +--R +--R +--R (293) +--R 2 2 +--R ((2C b - 2C a)c + 2B b + (- 2B - 2A)a b + 2A a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R ((2C b - 2C a)c + 2B b + (- 2B - 2A)a b + 2A a )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((- B + A)c + C b - C a)\|- c - b + a +--R / +--R +--------------+ +--R 2 3 2 2 3 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a +--R Type: Expression Integer +--E 308 + +--S 309 of 526 +d0856b:= D(m0856b,x) +--R +--R +--R (294) +--R 2 2 2 +--R ((- C b + C a)c - B b + (B + A)a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + (- 2B b + 2A a)c)cos(x) - 2C c + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 +--R ((- 3C b + C a)c - 3B b + (B + 3A)a b - A a )cos(x) +--R + +--R 2 2 +--R (- 4C b c - 4B b + 4A a b)cos(x) + (- C b - C a)c - B b +--R + +--R 2 +--R (- B + A)a b + A a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R (4C c + (4B b - 4A a)c)sin(x) + (4C c + (4B b - 4A a)c)cos(x) +--R + +--R 2 +--R (4C c + (4B b - 4A a)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 +--R ((3C b + C a)c + 3B b + (B - 3A)a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + (- 2B b + 2A a)c)cos(x) - 2C c + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 2 +--R ((C b + C a)c + B b + (B - A)a b - A a )cos(x) + (- C b - C a)c - B b +--R + +--R 2 +--R (- B + A)a b + A a +--R / +--R 2 2 2 4 3 3 4 2 +--R ((b - 2a b + a )c + b - 2a b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 +--R (- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )cos(x) +--R + +--R 2 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b + 2a )c - 2b + 4a b - 2a )cos(x) + (- b + a )c - b +--R + +--R 2 2 4 +--R 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)sin(x) +--R + +--R 4 2 2 2 4 2 2 2 +--R ((4c + (4b - 4a )c )cos(x) + 4c + (4b - 4a )c )sin(x) +--R + +--R 3 3 2 2 3 2 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 3 +--R ((4b + 4a)c + (4b + 4a b - 4a b - 4a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 3 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 3 4 2 +--R ((b + 2a b + a )c + b + 2a b - 2a b - a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R ((2b + 4a b + 2a )c + 2b + 4a b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R (b + 2a b + a )c + b + 2a b - 2a b - a +--R Type: Expression Integer +--E 309 + +--S 310 of 526 +t0857:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3 +--R +--R +--R (295) +--R C sin(x) + B cos(x) + A +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3b c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 3 3 2 2 +--R (3b c cos(x) + 6a b c cos(x) + 3a c)sin(x) + b cos(x) + 3a b cos(x) +--R + +--R 2 3 +--R 3a b cos(x) + a +--R Type: Expression Integer +--E 310 + +--S 311 of 526 +r0857:= -(b*(A*b-a*B)+c*(A*c-a*C)+2*a*(a*A-b*B-c*C))*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(3/2)/(-a^2+b^2+c^2)+1/2*(B*c-b*C-(-A*c+a*C)*cos(x)+(-A*b+a*B)*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x))^2+1/2*((A*b-a*B)*c-b*(A*c-a*C)-(a*(A*c-a*C)+2*c*(a*A-b*B-c*C))*cos(x)+(a*(A*b-a*B)+2*b*(a*A-b*B-c*C))*sin(x))/(a^2-b^2-c^2)/(-a^2+b^2+c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (296) +--R 4 3 2 2 2 2 +--R (- 2A c + 6C a c + (- 2A b + 6B a b - 4A a )c )sin(x) +--R + +--R 3 2 3 2 2 +--R (- 4A b c + 12C a b c + (- 4A b + 12B a b - 8A a b)c)cos(x) +--R + +--R 3 2 2 2 2 3 +--R - 4A a c + 12C a c + (- 4A a b + 12B a b - 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R (- 2A b c + 6C a b c - 2A b + 6B a b - 4A a b )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4A a b c + 12C a b c - 4A a b + 12B a b - 8A a b)cos(x) +--R + +--R 2 2 3 2 2 3 4 +--R - 2A a c + 6C a c - 2A a b + 6B a b - 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 2 2 2 2 +--R (2C b c + (2B b - 3A a b + B a )c)sin(x) +--R + +--R 3 2 2 2 3 +--R - 2C c + (- 2B b + 3A a)c + (2C b - C a )c + 2B b +--R + +--R 2 2 +--R - 3A a b + B a b +--R * +--R cos(x) +--R + +--R 2 3 2 2 3 +--R A b c + C a b c + A b + B a b - 4A a b + 2B a +--R * +--R sin(x) +--R + +--R 2 2 2 2 +--R (- 2C b c + (- 2B b + 3A a b)c - C a b)cos(x) +--R + +--R 3 2 2 2 3 3 +--R (- A c - C a c + (- A b - B a b + 4A a )c - 2C a )cos(x) - B c +--R + +--R 2 2 2 3 2 +--R C b c + (- B b + 2B a )c + C b - 2C a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (4b - 4a )c + (2b - 4a b + 2a )c )sin(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (8b - 8a b)c + (4b - 8a b + 4a b)c)cos(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (8a b - 8a )c + (4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (4b - 4a b )c + 2b - 4a b + 2a b )cos(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (8a b - 8a b)c + 4a b - 8a b + 4a b)cos(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (4a b - 4a )c + 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression Integer +--E 311 + +--S 312 of 526 +a0857:= integrate(t0857,x) +--R +--R +--R (297) +--R [ +--R 3 2 2 3 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 3 2 2 3 2 +--R (- 6C a b + 12C a b - 6C a b)c +--R + +--R 5 4 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 6A)a b +--R + +--R 3 2 4 +--R (- 6B - 8A)a b + 4A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 3 2 2 3 4 2 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 2 3 3 2 4 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b +--R + +--R 5 +--R 4A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 3 +--R (- A b + 2A a b - A a )c + (3C a b - 6C a b + 3C a )c +--R + +--R 3 2 2 3 4 2 +--R (3B a b + (- 6B - 2A)a b + (3B + 4A)a b - 2A a )c +--R + +--R 4 2 3 3 2 6 5 +--R (- 3C a b + 6C a b - 3C a b )c + A b + (- 3B - 2A)a b +--R + +--R 2 4 3 3 4 2 +--R (6B + 3A)a b + (- 3B - 4A)a b + 2A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 +--R (2A a b - 4A a b + 2A a b)c +--R + +--R 2 3 3 2 4 5 2 4 +--R (- 6C a b + 12C a b - 6C a b)c + 2A a b + (- 6B - 4A)a b +--R + +--R 3 3 4 2 5 +--R (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R cos(x) +--R + +--R 2 2 4 2 2 3 3 +--R (A b - 2A a b + A a )c + (- 3C a b + 6C a b - 3C a )c +--R + +--R 4 3 2 2 3 4 2 +--R (A b + (- 3B - 2A)a b + (6B + 4A)a b + (- 3B - 6A)a b + 3A a )c +--R + +--R 3 2 4 5 2 4 3 3 +--R (- 3C a b + 6C a b - 3C a )c + A a b + (- 3B - 2A)a b +--R + +--R 4 2 5 6 +--R (6B + 3A)a b + (- 3B - 4A)a b + 2A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 4 2 3 +--R (2B - 2A)b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 3 2 2 3 4 5 +--R (- 4C a b + 7C a b - 2C a b - C a )c + 2B b +--R + +--R 4 2 3 3 2 4 +--R (- 4B - 3A)a b + (3B + 6A)a b + (- 2B - 3A)a b + B a b +--R * +--R cos(x) +--R + +--R 4 2 3 +--R (2B - 2A)a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 3 2 2 3 4 5