Optimal. Leaf size=218 \[ \frac {2 \cot ^9(c+d x)}{9 a^2 d}+\frac {4 \cot ^7(c+d x)}{7 a^2 d}+\frac {2 \cot ^5(c+d x)}{5 a^2 d}-\frac {9 \tanh ^{-1}(\cos (c+d x))}{256 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}+\frac {3 \cot (c+d x) \csc ^7(c+d x)}{80 a^2 d}+\frac {9 \cot (c+d x) \csc ^5(c+d x)}{160 a^2 d}-\frac {3 \cot (c+d x) \csc ^3(c+d x)}{128 a^2 d}-\frac {9 \cot (c+d x) \csc (c+d x)}{256 a^2 d} \]
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Rubi [A] time = 0.49, antiderivative size = 218, normalized size of antiderivative = 1.00, number of steps used = 17, number of rules used = 7, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.241, Rules used = {2875, 2873, 2611, 3768, 3770, 2607, 270} \[ \frac {2 \cot ^9(c+d x)}{9 a^2 d}+\frac {4 \cot ^7(c+d x)}{7 a^2 d}+\frac {2 \cot ^5(c+d x)}{5 a^2 d}-\frac {9 \tanh ^{-1}(\cos (c+d x))}{256 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}+\frac {3 \cot (c+d x) \csc ^7(c+d x)}{80 a^2 d}+\frac {9 \cot (c+d x) \csc ^5(c+d x)}{160 a^2 d}-\frac {3 \cot (c+d x) \csc ^3(c+d x)}{128 a^2 d}-\frac {9 \cot (c+d x) \csc (c+d x)}{256 a^2 d} \]
Antiderivative was successfully verified.
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Rule 270
Rule 2607
Rule 2611
Rule 2873
Rule 2875
Rule 3768
Rule 3770
Rubi steps
\begin {align*} \int \frac {\cot ^8(c+d x) \csc ^3(c+d x)}{(a+a \sin (c+d x))^2} \, dx &=\frac {\int \cot ^4(c+d x) \csc ^7(c+d x) (a-a \sin (c+d x))^2 \, dx}{a^4}\\ &=\frac {\int \left (a^2 \cot ^4(c+d x) \csc ^5(c+d x)-2 a^2 \cot ^4(c+d x) \csc ^6(c+d x)+a^2 \cot ^4(c+d x) \csc ^7(c+d x)\right ) \, dx}{a^4}\\ &=\frac {\int \cot ^4(c+d x) \csc ^5(c+d x) \, dx}{a^2}+\frac {\int \cot ^4(c+d x) \csc ^7(c+d x) \, dx}{a^2}-\frac {2 \int \cot ^4(c+d x) \csc ^6(c+d x) \, dx}{a^2}\\ &=-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}-\frac {3 \int \cot ^2(c+d x) \csc ^7(c+d x) \, dx}{10 a^2}-\frac {3 \int \cot ^2(c+d x) \csc ^5(c+d x) \, dx}{8 a^2}-\frac {2 \operatorname {Subst}\left (\int x^4 \left (1+x^2\right )^2 \, dx,x,-\cot (c+d x)\right )}{a^2 d}\\ &=\frac {\cot (c+d x) \csc ^5(c+d x)}{16 a^2 d}-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}+\frac {3 \cot (c+d x) \csc ^7(c+d x)}{80 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}+\frac {3 \int \csc ^7(c+d x) \, dx}{80 a^2}+\frac {\int \csc ^5(c+d x) \, dx}{16 a^2}-\frac {2 \operatorname {Subst}\left (\int \left (x^4+2 x^6+x^8\right ) \, dx,x,-\cot (c+d x)\right )}{a^2 d}\\ &=\frac {2 \cot ^5(c+d x)}{5 a^2 d}+\frac {4 \cot ^7(c+d x)}{7 a^2 d}+\frac {2 \cot ^9(c+d x)}{9 a^2 d}-\frac {\cot (c+d x) \csc ^3(c+d x)}{64 a^2 d}+\frac {9 \cot (c+d x) \csc ^5(c+d x)}{160 a^2 d}-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}+\frac {3 \cot (c+d x) \csc ^7(c+d x)}{80 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}+\frac {\int \csc ^5(c+d x) \, dx}{32 a^2}+\frac {3 \int \csc ^3(c+d x) \, dx}{64 a^2}\\ &=\frac {2 \cot ^5(c+d x)}{5 a^2 d}+\frac {4 \cot ^7(c+d x)}{7 a^2 d}+\frac {2 \cot ^9(c+d x)}{9 a^2 d}-\frac {3 \cot (c+d x) \csc (c+d x)}{128 a^2 d}-\frac {3 \cot (c+d x) \csc ^3(c+d x)}{128 a^2 d}+\frac {9 \cot (c+d x) \csc ^5(c+d x)}{160 a^2 d}-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}+\frac {3 \cot (c+d x) \csc ^7(c+d x)}{80 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}+\frac {3 \int \csc (c+d x) \, dx}{128 a^2}+\frac {3 \int \csc ^3(c+d x) \, dx}{128 a^2}\\ &=-\frac {3 \tanh ^{-1}(\cos (c+d x))}{128 a^2 d}+\frac {2 \cot ^5(c+d x)}{5 a^2 d}+\frac {4 \cot ^7(c+d x)}{7 a^2 d}+\frac {2 \cot ^9(c+d x)}{9 a^2 d}-\frac {9 \cot (c+d x) \csc (c+d x)}{256 a^2 d}-\frac {3 \cot (c+d x) \csc ^3(c+d x)}{128 a^2 d}+\frac {9 \cot (c+d x) \csc ^5(c+d x)}{160 a^2 d}-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}+\frac {3 \cot (c+d x) \csc ^7(c+d x)}{80 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}+\frac {3 \int \csc (c+d x) \, dx}{256 a^2}\\ &=-\frac {9 \tanh ^{-1}(\cos (c+d x))}{256 a^2 d}+\frac {2 \cot ^5(c+d x)}{5 a^2 d}+\frac {4 \cot ^7(c+d x)}{7 a^2 d}+\frac {2 \cot ^9(c+d x)}{9 a^2 d}-\frac {9 \cot (c+d x) \csc (c+d x)}{256 a^2 d}-\frac {3 \cot (c+d x) \csc ^3(c+d x)}{128 a^2 d}+\frac {9 \cot (c+d x) \csc ^5(c+d x)}{160 a^2 d}-\frac {\cot ^3(c+d x) \csc ^5(c+d x)}{8 a^2 d}+\frac {3 \cot (c+d x) \csc ^7(c+d x)}{80 a^2 d}-\frac {\cot ^3(c+d x) \csc ^7(c+d x)}{10 a^2 d}\\ \end {align*}
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Mathematica [A] time = 1.81, size = 353, normalized size = 1.62 \[ \frac {\csc ^{10}(c+d x) \left (1720320 \sin (2 (c+d x))+1228800 \sin (4 (c+d x))+184320 \sin (6 (c+d x))-40960 \sin (8 (c+d x))+4096 \sin (10 (c+d x))-3219300 \cos (c+d x)-1237320 \cos (3 (c+d x))+278712 \cos (5 (c+d x))+54810 \cos (7 (c+d x))-5670 \cos (9 (c+d x))+357210 \log \left (\sin \left (\frac {1}{2} (c+d x)\right )\right )+595350 \cos (2 (c+d x)) \log \left (\cos \left (\frac {1}{2} (c+d x)\right )\right )-340200 \cos (4 (c+d x)) \log \left (\cos \left (\frac {1}{2} (c+d x)\right )\right )+127575 \cos (6 (c+d x)) \log \left (\cos \left (\frac {1}{2} (c+d x)\right )\right )-28350 \cos (8 (c+d x)) \log \left (\cos \left (\frac {1}{2} (c+d x)\right )\right )+2835 \cos (10 (c+d x)) \log \left (\cos \left (\frac {1}{2} (c+d x)\right )\right )-357210 \log \left (\cos \left (\frac {1}{2} (c+d x)\right )\right )-595350 \cos (2 (c+d x)) \log \left (\sin \left (\frac {1}{2} (c+d x)\right )\right )+340200 \cos (4 (c+d x)) \log \left (\sin \left (\frac {1}{2} (c+d x)\right )\right )-127575 \cos (6 (c+d x)) \log \left (\sin \left (\frac {1}{2} (c+d x)\right )\right )+28350 \cos (8 (c+d x)) \log \left (\sin \left (\frac {1}{2} (c+d x)\right )\right )-2835 \cos (10 (c+d x)) \log \left (\sin \left (\frac {1}{2} (c+d x)\right )\right )\right )}{41287680 a^2 d} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 294, normalized size = 1.35 \[ \frac {5670 \, \cos \left (d x + c\right )^{9} - 26460 \, \cos \left (d x + c\right )^{7} + 16128 \, \cos \left (d x + c\right )^{5} + 26460 \, \cos \left (d x + c\right )^{3} - 2835 \, {\left (\cos \left (d x + c\right )^{10} - 5 \, \cos \left (d x + c\right )^{8} + 10 \, \cos \left (d x + c\right )^{6} - 10 \, \cos \left (d x + c\right )^{4} + 5 \, \cos \left (d x + c\right )^{2} - 1\right )} \log \left (\frac {1}{2} \, \cos \left (d x + c\right ) + \frac {1}{2}\right ) + 2835 \, {\left (\cos \left (d x + c\right )^{10} - 5 \, \cos \left (d x + c\right )^{8} + 10 \, \cos \left (d x + c\right )^{6} - 10 \, \cos \left (d x + c\right )^{4} + 5 \, \cos \left (d x + c\right )^{2} - 1\right )} \log \left (-\frac {1}{2} \, \cos \left (d x + c\right ) + \frac {1}{2}\right ) - 1024 \, {\left (8 \, \cos \left (d x + c\right )^{9} - 36 \, \cos \left (d x + c\right )^{7} + 63 \, \cos \left (d x + c\right )^{5}\right )} \sin \left (d x + c\right ) - 5670 \, \cos \left (d x + c\right )}{161280 \, {\left (a^{2} d \cos \left (d x + c\right )^{10} - 5 \, a^{2} d \cos \left (d x + c\right )^{8} + 10 \, a^{2} d \cos \left (d x + c\right )^{6} - 10 \, a^{2} d \cos \left (d x + c\right )^{4} + 5 \, a^{2} d \cos \left (d x + c\right )^{2} - a^{2} d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 331, normalized size = 1.52 \[ \frac {\frac {45360 \, \log \left ({\left | \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) \right |}\right )}{a^{2}} - \frac {132858 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{10} - 30240 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 1260 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{8} + 6720 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 7560 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{6} + 4032 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} - 630 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{4} - 720 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} + 945 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} - 560 \, \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 126}{a^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{10}} + \frac {126 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{10} - 560 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 945 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{8} - 720 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 630 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{6} + 4032 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} - 7560 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{4} + 6720 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} + 1260 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} - 30240 \, a^{18} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )}{a^{20}}}{1290240 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.75, size = 398, normalized size = 1.83 \[ \frac {\tan ^{10}\left (\frac {d x}{2}+\frac {c}{2}\right )}{10240 d \,a^{2}}-\frac {\tan ^{9}\left (\frac {d x}{2}+\frac {c}{2}\right )}{2304 d \,a^{2}}+\frac {3 \left (\tan ^{8}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}{4096 d \,a^{2}}-\frac {\tan ^{7}\left (\frac {d x}{2}+\frac {c}{2}\right )}{1792 d \,a^{2}}-\frac {\tan ^{6}\left (\frac {d x}{2}+\frac {c}{2}\right )}{2048 d \,a^{2}}+\frac {\tan ^{5}\left (\frac {d x}{2}+\frac {c}{2}\right )}{320 a^{2} d}-\frac {3 \left (\tan ^{4}\left (\frac {d x}{2}+\frac {c}{2}\right )\right )}{512 a^{2} d}+\frac {\tan ^{3}\left (\frac {d x}{2}+\frac {c}{2}\right )}{192 d \,a^{2}}+\frac {\tan ^{2}\left (\frac {d x}{2}+\frac {c}{2}\right )}{1024 a^{2} d}-\frac {3 \tan \left (\frac {d x}{2}+\frac {c}{2}\right )}{128 d \,a^{2}}+\frac {1}{2048 d \,a^{2} \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{6}}+\frac {3}{128 d \,a^{2} \tan \left (\frac {d x}{2}+\frac {c}{2}\right )}+\frac {9 \ln \left (\tan \left (\frac {d x}{2}+\frac {c}{2}\right )\right )}{256 d \,a^{2}}-\frac {1}{320 a^{2} d \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{5}}+\frac {1}{1792 d \,a^{2} \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{7}}-\frac {1}{1024 a^{2} d \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{2}}+\frac {1}{2304 d \,a^{2} \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{9}}-\frac {3}{4096 d \,a^{2} \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{8}}+\frac {3}{512 a^{2} d \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{4}}-\frac {1}{192 a^{2} d \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{3}}-\frac {1}{10240 d \,a^{2} \tan \left (\frac {d x}{2}+\frac {c}{2}\right )^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.43, size = 435, normalized size = 2.00 \[ -\frac {\frac {\frac {30240 \, \sin \left (d x + c\right )}{\cos \left (d x + c\right ) + 1} - \frac {1260 \, \sin \left (d x + c\right )^{2}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{2}} - \frac {6720 \, \sin \left (d x + c\right )^{3}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{3}} + \frac {7560 \, \sin \left (d x + c\right )^{4}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{4}} - \frac {4032 \, \sin \left (d x + c\right )^{5}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{5}} + \frac {630 \, \sin \left (d x + c\right )^{6}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{6}} + \frac {720 \, \sin \left (d x + c\right )^{7}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{7}} - \frac {945 \, \sin \left (d x + c\right )^{8}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{8}} + \frac {560 \, \sin \left (d x + c\right )^{9}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{9}} - \frac {126 \, \sin \left (d x + c\right )^{10}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{10}}}{a^{2}} - \frac {45360 \, \log \left (\frac {\sin \left (d x + c\right )}{\cos \left (d x + c\right ) + 1}\right )}{a^{2}} - \frac {{\left (\frac {560 \, \sin \left (d x + c\right )}{\cos \left (d x + c\right ) + 1} - \frac {945 \, \sin \left (d x + c\right )^{2}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{2}} + \frac {720 \, \sin \left (d x + c\right )^{3}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{3}} + \frac {630 \, \sin \left (d x + c\right )^{4}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{4}} - \frac {4032 \, \sin \left (d x + c\right )^{5}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{5}} + \frac {7560 \, \sin \left (d x + c\right )^{6}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{6}} - \frac {6720 \, \sin \left (d x + c\right )^{7}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{7}} - \frac {1260 \, \sin \left (d x + c\right )^{8}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{8}} + \frac {30240 \, \sin \left (d x + c\right )^{9}}{{\left (\cos \left (d x + c\right ) + 1\right )}^{9}} - 126\right )} {\left (\cos \left (d x + c\right ) + 1\right )}^{10}}{a^{2} \sin \left (d x + c\right )^{10}}}{1290240 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 14.34, size = 531, normalized size = 2.44 \[ \frac {126\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{20}-126\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{20}-560\,\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{19}+560\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{19}\,\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )+945\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^2\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{18}-720\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^3\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{17}-630\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^4\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{16}+4032\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^5\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{15}-7560\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^6\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{14}+6720\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^7\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{13}+1260\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^8\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{12}-30240\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^9\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{11}+30240\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{11}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^9-1260\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{12}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^8-6720\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{13}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^7+7560\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{14}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^6-4032\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{15}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^5+630\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{16}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^4+720\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{17}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^3-945\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{18}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^2+45360\,\ln \left (\frac {\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}\right )\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{10}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{10}}{1290240\,a^2\,d\,{\cos \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{10}\,{\sin \left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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