Optimal. Leaf size=291 \[ -\frac {a^3 \cot ^5(c+d x)}{5 d}+\frac {a^3 \cot ^3(c+d x)}{3 d}-\frac {a^3 \cot (c+d x)}{d}-a^3 x+\frac {45 a^2 b \cos (c+d x)}{8 d}-\frac {3 a^2 b \cos (c+d x) \cot ^4(c+d x)}{4 d}+\frac {15 a^2 b \cos (c+d x) \cot ^2(c+d x)}{8 d}-\frac {45 a^2 b \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac {5 a b^2 \cot ^3(c+d x)}{2 d}+\frac {15 a b^2 \cot (c+d x)}{2 d}+\frac {3 a b^2 \cos ^2(c+d x) \cot ^3(c+d x)}{2 d}+\frac {15}{2} a b^2 x-\frac {5 b^3 \cos ^3(c+d x)}{6 d}-\frac {5 b^3 \cos (c+d x)}{2 d}-\frac {b^3 \cos ^3(c+d x) \cot ^2(c+d x)}{2 d}+\frac {5 b^3 \tanh ^{-1}(\cos (c+d x))}{2 d} \]
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Rubi [A] time = 0.23, antiderivative size = 291, normalized size of antiderivative = 1.00, number of steps used = 21, number of rules used = 10, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.476, Rules used = {2722, 2592, 288, 302, 206, 2591, 203, 321, 3473, 8} \[ \frac {45 a^2 b \cos (c+d x)}{8 d}-\frac {3 a^2 b \cos (c+d x) \cot ^4(c+d x)}{4 d}+\frac {15 a^2 b \cos (c+d x) \cot ^2(c+d x)}{8 d}-\frac {45 a^2 b \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac {a^3 \cot ^5(c+d x)}{5 d}+\frac {a^3 \cot ^3(c+d x)}{3 d}-\frac {a^3 \cot (c+d x)}{d}-a^3 x-\frac {5 a b^2 \cot ^3(c+d x)}{2 d}+\frac {15 a b^2 \cot (c+d x)}{2 d}+\frac {3 a b^2 \cos ^2(c+d x) \cot ^3(c+d x)}{2 d}+\frac {15}{2} a b^2 x-\frac {5 b^3 \cos ^3(c+d x)}{6 d}-\frac {5 b^3 \cos (c+d x)}{2 d}-\frac {b^3 \cos ^3(c+d x) \cot ^2(c+d x)}{2 d}+\frac {5 b^3 \tanh ^{-1}(\cos (c+d x))}{2 d} \]
Antiderivative was successfully verified.
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Rule 8
Rule 203
Rule 206
Rule 288
Rule 302
Rule 321
Rule 2591
Rule 2592
Rule 2722
Rule 3473
Rubi steps
\begin {align*} \int \cot ^6(c+d x) (a+b \sin (c+d x))^3 \, dx &=\int \left (b^3 \cos ^3(c+d x) \cot ^3(c+d x)+3 a b^2 \cos ^2(c+d x) \cot ^4(c+d x)+3 a^2 b \cos (c+d x) \cot ^5(c+d x)+a^3 \cot ^6(c+d x)\right ) \, dx\\ &=a^3 \int \cot ^6(c+d x) \, dx+\left (3 a^2 b\right ) \int \cos (c+d x) \cot ^5(c+d x) \, dx+\left (3 a b^2\right ) \int \cos ^2(c+d x) \cot ^4(c+d x) \, dx+b^3 \int \cos ^3(c+d x) \cot ^3(c+d x) \, dx\\ &=-\frac {a^3 \cot ^5(c+d x)}{5 d}-a^3 \int \cot ^4(c+d x) \, dx-\frac {\left (3 a^2 b\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (1-x^2\right )^3} \, dx,x,\cos (c+d x)\right )}{d}-\frac {\left (3 a b^2\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (1+x^2\right )^2} \, dx,x,\cot (c+d x)\right )}{d}-\frac {b^3 \operatorname {Subst}\left (\int \frac {x^6}{\left (1-x^2\right )^2} \, dx,x,\cos (c+d x)\right )}{d}\\ &=-\frac {b^3 \cos ^3(c+d x) \cot ^2(c+d x)}{2 d}+\frac {a^3 \cot ^3(c+d x)}{3 d}+\frac {3 a b^2 \cos ^2(c+d x) \cot ^3(c+d x)}{2 d}-\frac {3 a^2 b \cos (c+d x) \cot ^4(c+d x)}{4 d}-\frac {a^3 \cot ^5(c+d x)}{5 d}+a^3 \int \cot ^2(c+d x) \, dx+\frac {\left (15 a^2 b\right ) \operatorname {Subst}\left (\int \frac {x^4}{\left (1-x^2\right )^2} \, dx,x,\cos (c+d x)\right )}{4 d}-\frac {\left (15 a b^2\right ) \operatorname {Subst}\left (\int \frac {x^4}{1+x^2} \, dx,x,\cot (c+d x)\right )}{2 d}+\frac {\left (5 b^3\right ) \operatorname {Subst}\left (\int \frac {x^4}{1-x^2} \, dx,x,\cos (c+d x)\right )}{2 d}\\ &=-\frac {a^3 \cot (c+d x)}{d}+\frac {15 a^2 b \cos (c+d x) \cot ^2(c+d x)}{8 d}-\frac {b^3 \cos ^3(c+d x) \cot ^2(c+d x)}{2 d}+\frac {a^3 \cot ^3(c+d x)}{3 d}+\frac {3 a b^2 \cos ^2(c+d x) \cot ^3(c+d x)}{2 d}-\frac {3 a^2 b \cos (c+d x) \cot ^4(c+d x)}{4 d}-\frac {a^3 \cot ^5(c+d x)}{5 d}-a^3 \int 1 \, dx-\frac {\left (45 a^2 b\right ) \operatorname {Subst}\left (\int \frac {x^2}{1-x^2} \, dx,x,\cos (c+d x)\right )}{8 d}-\frac {\left (15 a b^2\right ) \operatorname {Subst}\left (\int \left (-1+x^2+\frac {1}{1+x^2}\right ) \, dx,x,\cot (c+d x)\right )}{2 d}+\frac {\left (5 b^3\right ) \operatorname {Subst}\left (\int \left (-1-x^2+\frac {1}{1-x^2}\right ) \, dx,x,\cos (c+d x)\right )}{2 d}\\ &=-a^3 x+\frac {45 a^2 b \cos (c+d x)}{8 d}-\frac {5 b^3 \cos (c+d x)}{2 d}-\frac {5 b^3 \cos ^3(c+d x)}{6 d}-\frac {a^3 \cot (c+d x)}{d}+\frac {15 a b^2 \cot (c+d x)}{2 d}+\frac {15 a^2 b \cos (c+d x) \cot ^2(c+d x)}{8 d}-\frac {b^3 \cos ^3(c+d x) \cot ^2(c+d x)}{2 d}+\frac {a^3 \cot ^3(c+d x)}{3 d}-\frac {5 a b^2 \cot ^3(c+d x)}{2 d}+\frac {3 a b^2 \cos ^2(c+d x) \cot ^3(c+d x)}{2 d}-\frac {3 a^2 b \cos (c+d x) \cot ^4(c+d x)}{4 d}-\frac {a^3 \cot ^5(c+d x)}{5 d}-\frac {\left (45 a^2 b\right ) \operatorname {Subst}\left (\int \frac {1}{1-x^2} \, dx,x,\cos (c+d x)\right )}{8 d}-\frac {\left (15 a b^2\right ) \operatorname {Subst}\left (\int \frac {1}{1+x^2} \, dx,x,\cot (c+d x)\right )}{2 d}+\frac {\left (5 b^3\right ) \operatorname {Subst}\left (\int \frac {1}{1-x^2} \, dx,x,\cos (c+d x)\right )}{2 d}\\ &=-a^3 x+\frac {15}{2} a b^2 x-\frac {45 a^2 b \tanh ^{-1}(\cos (c+d x))}{8 d}+\frac {5 b^3 \tanh ^{-1}(\cos (c+d x))}{2 d}+\frac {45 a^2 b \cos (c+d x)}{8 d}-\frac {5 b^3 \cos (c+d x)}{2 d}-\frac {5 b^3 \cos ^3(c+d x)}{6 d}-\frac {a^3 \cot (c+d x)}{d}+\frac {15 a b^2 \cot (c+d x)}{2 d}+\frac {15 a^2 b \cos (c+d x) \cot ^2(c+d x)}{8 d}-\frac {b^3 \cos ^3(c+d x) \cot ^2(c+d x)}{2 d}+\frac {a^3 \cot ^3(c+d x)}{3 d}-\frac {5 a b^2 \cot ^3(c+d x)}{2 d}+\frac {3 a b^2 \cos ^2(c+d x) \cot ^3(c+d x)}{2 d}-\frac {3 a^2 b \cos (c+d x) \cot ^4(c+d x)}{4 d}-\frac {a^3 \cot ^5(c+d x)}{5 d}\\ \end {align*}
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Mathematica [A] time = 2.57, size = 346, normalized size = 1.19 \[ \frac {-600 a \left (2 a^2-15 b^2\right ) (c+d x) \csc ^4(c+d x)+1200 b \left (4 b^2-9 a^2\right ) \left (\log \left (\cos \left (\frac {1}{2} (c+d x)\right )\right )-\log \left (\sin \left (\frac {1}{2} (c+d x)\right )\right )\right )+5 \cot (c+d x) \csc ^4(c+d x) \left (-80 a^3+12 b \left (60 a^2-29 b^2\right ) \sin (c+d x)+285 a b^2\right )+\csc ^5(c+d x) \left (5 \left (40 a^3-489 a b^2\right ) \cos (3 (c+d x))+\left (1065 a b^2-184 a^3\right ) \cos (5 (c+d x))+5 \left (-24 a^3 c \sin (5 (c+d x))-24 a^3 d x \sin (5 (c+d x))+60 a \left (2 a^2-15 b^2\right ) (c+d x) \sin (3 (c+d x))-306 a^2 b \sin (4 (c+d x))+36 a^2 b \sin (6 (c+d x))+180 a b^2 c \sin (5 (c+d x))+180 a b^2 d x \sin (5 (c+d x))-9 a b^2 \cos (7 (c+d x))+122 b^3 \sin (4 (c+d x))-22 b^3 \sin (6 (c+d x))-b^3 \sin (8 (c+d x))\right )\right )}{1920 d} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 412, normalized size = 1.42 \[ -\frac {360 \, a b^{2} \cos \left (d x + c\right )^{7} + 184 \, {\left (2 \, a^{3} - 15 \, a b^{2}\right )} \cos \left (d x + c\right )^{5} - 280 \, {\left (2 \, a^{3} - 15 \, a b^{2}\right )} \cos \left (d x + c\right )^{3} + 75 \, {\left ({\left (9 \, a^{2} b - 4 \, b^{3}\right )} \cos \left (d x + c\right )^{4} + 9 \, a^{2} b - 4 \, b^{3} - 2 \, {\left (9 \, a^{2} b - 4 \, b^{3}\right )} \cos \left (d x + c\right )^{2}\right )} \log \left (\frac {1}{2} \, \cos \left (d x + c\right ) + \frac {1}{2}\right ) \sin \left (d x + c\right ) - 75 \, {\left ({\left (9 \, a^{2} b - 4 \, b^{3}\right )} \cos \left (d x + c\right )^{4} + 9 \, a^{2} b - 4 \, b^{3} - 2 \, {\left (9 \, a^{2} b - 4 \, b^{3}\right )} \cos \left (d x + c\right )^{2}\right )} \log \left (-\frac {1}{2} \, \cos \left (d x + c\right ) + \frac {1}{2}\right ) \sin \left (d x + c\right ) + 120 \, {\left (2 \, a^{3} - 15 \, a b^{2}\right )} \cos \left (d x + c\right ) + 10 \, {\left (8 \, b^{3} \cos \left (d x + c\right )^{7} + 12 \, {\left (2 \, a^{3} - 15 \, a b^{2}\right )} d x \cos \left (d x + c\right )^{4} - 8 \, {\left (9 \, a^{2} b - 4 \, b^{3}\right )} \cos \left (d x + c\right )^{5} - 24 \, {\left (2 \, a^{3} - 15 \, a b^{2}\right )} d x \cos \left (d x + c\right )^{2} + 25 \, {\left (9 \, a^{2} b - 4 \, b^{3}\right )} \cos \left (d x + c\right )^{3} + 12 \, {\left (2 \, a^{3} - 15 \, a b^{2}\right )} d x - 15 \, {\left (9 \, a^{2} b - 4 \, b^{3}\right )} \cos \left (d x + c\right )\right )} \sin \left (d x + c\right )}{240 \, {\left (d \cos \left (d x + c\right )^{4} - 2 \, d \cos \left (d x + c\right )^{2} + d\right )} \sin \left (d x + c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 471, normalized size = 1.62 \[ \frac {6 \, a^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 45 \, a^{2} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{4} - 70 \, a^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} + 120 \, a b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 720 \, a^{2} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} + 120 \, b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} + 660 \, a^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) - 3240 \, a b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) - 480 \, {\left (2 \, a^{3} - 15 \, a b^{2}\right )} {\left (d x + c\right )} + 600 \, {\left (9 \, a^{2} b - 4 \, b^{3}\right )} \log \left ({\left | \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) \right |}\right ) - \frac {320 \, {\left (9 \, a b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} - 18 \, a^{2} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{4} + 18 \, b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{4} - 36 \, a^{2} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} + 24 \, b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} - 9 \, a b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) - 18 \, a^{2} b + 14 \, b^{3}\right )}}{{\left (\tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} + 1\right )}^{3}} - \frac {12330 \, a^{2} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} - 5480 \, b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 660 \, a^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{4} - 3240 \, a b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{4} - 720 \, a^{2} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} + 120 \, b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 70 \, a^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} + 120 \, a b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} + 45 \, a^{2} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 6 \, a^{3}}{\tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5}}}{960 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 415, normalized size = 1.43 \[ -\frac {a^{3} \left (\cot ^{5}\left (d x +c \right )\right )}{5 d}+\frac {a^{3} \left (\cot ^{3}\left (d x +c \right )\right )}{3 d}-\frac {a^{3} \cot \left (d x +c \right )}{d}-a^{3} x -\frac {a^{3} c}{d}-\frac {3 a^{2} b \left (\cos ^{7}\left (d x +c \right )\right )}{4 d \sin \left (d x +c \right )^{4}}+\frac {9 a^{2} b \left (\cos ^{7}\left (d x +c \right )\right )}{8 d \sin \left (d x +c \right )^{2}}+\frac {9 a^{2} b \left (\cos ^{5}\left (d x +c \right )\right )}{8 d}+\frac {15 a^{2} b \left (\cos ^{3}\left (d x +c \right )\right )}{8 d}+\frac {45 a^{2} b \cos \left (d x +c \right )}{8 d}+\frac {45 a^{2} b \ln \left (\csc \left (d x +c \right )-\cot \left (d x +c \right )\right )}{8 d}-\frac {a \,b^{2} \left (\cos ^{7}\left (d x +c \right )\right )}{d \sin \left (d x +c \right )^{3}}+\frac {4 a \,b^{2} \left (\cos ^{7}\left (d x +c \right )\right )}{d \sin \left (d x +c \right )}+\frac {4 a \,b^{2} \sin \left (d x +c \right ) \left (\cos ^{5}\left (d x +c \right )\right )}{d}+\frac {5 a \,b^{2} \sin \left (d x +c \right ) \left (\cos ^{3}\left (d x +c \right )\right )}{d}+\frac {15 a \,b^{2} \cos \left (d x +c \right ) \sin \left (d x +c \right )}{2 d}+\frac {15 a \,b^{2} x}{2}+\frac {15 a \,b^{2} c}{2 d}-\frac {b^{3} \left (\cos ^{7}\left (d x +c \right )\right )}{2 d \sin \left (d x +c \right )^{2}}-\frac {b^{3} \left (\cos ^{5}\left (d x +c \right )\right )}{2 d}-\frac {5 b^{3} \left (\cos ^{3}\left (d x +c \right )\right )}{6 d}-\frac {5 b^{3} \cos \left (d x +c \right )}{2 d}-\frac {5 b^{3} \ln \left (\csc \left (d x +c \right )-\cot \left (d x +c \right )\right )}{2 d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.89, size = 252, normalized size = 0.87 \[ -\frac {16 \, {\left (15 \, d x + 15 \, c + \frac {15 \, \tan \left (d x + c\right )^{4} - 5 \, \tan \left (d x + c\right )^{2} + 3}{\tan \left (d x + c\right )^{5}}\right )} a^{3} - 120 \, {\left (15 \, d x + 15 \, c + \frac {15 \, \tan \left (d x + c\right )^{4} + 10 \, \tan \left (d x + c\right )^{2} - 2}{\tan \left (d x + c\right )^{5} + \tan \left (d x + c\right )^{3}}\right )} a b^{2} + 20 \, {\left (4 \, \cos \left (d x + c\right )^{3} - \frac {6 \, \cos \left (d x + c\right )}{\cos \left (d x + c\right )^{2} - 1} + 24 \, \cos \left (d x + c\right ) - 15 \, \log \left (\cos \left (d x + c\right ) + 1\right ) + 15 \, \log \left (\cos \left (d x + c\right ) - 1\right )\right )} b^{3} + 45 \, a^{2} b {\left (\frac {2 \, {\left (9 \, \cos \left (d x + c\right )^{3} - 7 \, \cos \left (d x + c\right )\right )}}{\cos \left (d x + c\right )^{4} - 2 \, \cos \left (d x + c\right )^{2} + 1} - 16 \, \cos \left (d x + c\right ) + 15 \, \log \left (\cos \left (d x + c\right ) + 1\right ) - 15 \, \log \left (\cos \left (d x + c\right ) - 1\right )\right )}}{240 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.06, size = 507, normalized size = 1.74 \[ \frac {a^3\,{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^5}{160\,d}+\frac {{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{10}\,\left (12\,a\,b^2-22\,a^3\right )-{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^2\,\left (4\,a\,b^2-\frac {26\,a^3}{15}\right )+{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^4\,\left (96\,a\,b^2-\frac {78\,a^3}{5}\right )+{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^8\,\left (320\,a\,b^2-\frac {191\,a^3}{3}\right )+{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^6\,\left (408\,a\,b^2-\frac {296\,a^3}{5}\right )+{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^3\,\left (\frac {39\,a^2\,b}{2}-4\,b^3\right )+{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^9\,\left (216\,a^2\,b-196\,b^3\right )+{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^5\,\left (\frac {519\,a^2\,b}{2}-\frac {484\,b^3}{3}\right )+{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^7\,\left (\frac {909\,a^2\,b}{2}-268\,b^3\right )-\frac {a^3}{5}-\frac {3\,a^2\,b\,\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}{2}}{d\,\left (32\,{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^{11}+96\,{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^9+96\,{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^7+32\,{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^5\right )}+\frac {{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^3\,\left (\frac {a\,b^2}{8}-\frac {7\,a^3}{96}\right )}{d}-\frac {{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^2\,\left (\frac {3\,a^2\,b}{4}-\frac {b^3}{8}\right )}{d}+\frac {\ln \left (\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )\right )\,\left (\frac {45\,a^2\,b}{8}-\frac {5\,b^3}{2}\right )}{d}-\frac {\ln \left (\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )-\mathrm {i}\right )\,\left (\frac {a\,b^2\,15{}\mathrm {i}}{2}-a^3\,1{}\mathrm {i}\right )}{d}-\frac {\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )\,\left (\frac {27\,a\,b^2}{8}-\frac {11\,a^3}{16}\right )}{d}+\frac {3\,a^2\,b\,{\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )}^4}{64\,d}-\frac {a\,\ln \left (\mathrm {tan}\left (\frac {c}{2}+\frac {d\,x}{2}\right )+1{}\mathrm {i}\right )\,\left (2\,a^2-15\,b^2\right )\,1{}\mathrm {i}}{2\,d} \]
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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