Optimal. Leaf size=290 \[ a^4 A x+\frac {\left (8 a^4 B+24 a^2 b^2 B+3 b^4 B+16 a^3 b (2 A+C)+4 a b^3 (4 A+3 C)\right ) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac {\left (95 a^3 b B+80 a b^3 B+12 a^4 C+4 b^4 (5 A+4 C)+2 a^2 b^2 (85 A+56 C)\right ) \tan (c+d x)}{30 d}+\frac {b \left (130 a^2 b B+45 b^3 B+24 a^3 C+4 a b^2 (40 A+29 C)\right ) \sec (c+d x) \tan (c+d x)}{120 d}+\frac {\left (20 A b^2+35 a b B+12 a^2 C+16 b^2 C\right ) (a+b \sec (c+d x))^2 \tan (c+d x)}{60 d}+\frac {(5 b B+4 a C) (a+b \sec (c+d x))^3 \tan (c+d x)}{20 d}+\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.39, antiderivative size = 290, normalized size of antiderivative = 1.00, number of steps
used = 8, number of rules used = 5, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.152, Rules used = {4141, 4133,
3855, 3852, 8} \begin {gather*} a^4 A x+\frac {\tan (c+d x) \left (12 a^2 C+35 a b B+20 A b^2+16 b^2 C\right ) (a+b \sec (c+d x))^2}{60 d}+\frac {b \tan (c+d x) \sec (c+d x) \left (24 a^3 C+130 a^2 b B+4 a b^2 (40 A+29 C)+45 b^3 B\right )}{120 d}+\frac {\tan (c+d x) \left (12 a^4 C+95 a^3 b B+2 a^2 b^2 (85 A+56 C)+80 a b^3 B+4 b^4 (5 A+4 C)\right )}{30 d}+\frac {\left (8 a^4 B+16 a^3 b (2 A+C)+24 a^2 b^2 B+4 a b^3 (4 A+3 C)+3 b^4 B\right ) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac {(4 a C+5 b B) \tan (c+d x) (a+b \sec (c+d x))^3}{20 d}+\frac {C \tan (c+d x) (a+b \sec (c+d x))^4}{5 d} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 8
Rule 3852
Rule 3855
Rule 4133
Rule 4141
Rubi steps
\begin {align*} \int (a+b \sec (c+d x))^4 \left (A+B \sec (c+d x)+C \sec ^2(c+d x)\right ) \, dx &=\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d}+\frac {1}{5} \int (a+b \sec (c+d x))^3 \left (5 a A+(5 A b+5 a B+4 b C) \sec (c+d x)+(5 b B+4 a C) \sec ^2(c+d x)\right ) \, dx\\ &=\frac {(5 b B+4 a C) (a+b \sec (c+d x))^3 \tan (c+d x)}{20 d}+\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d}+\frac {1}{20} \int (a+b \sec (c+d x))^2 \left (20 a^2 A+\left (40 a A b+20 a^2 B+15 b^2 B+28 a b C\right ) \sec (c+d x)+\left (20 A b^2+35 a b B+12 a^2 C+16 b^2 C\right ) \sec ^2(c+d x)\right ) \, dx\\ &=\frac {\left (20 A b^2+35 a b B+12 a^2 C+16 b^2 C\right ) (a+b \sec (c+d x))^2 \tan (c+d x)}{60 d}+\frac {(5 b B+4 a C) (a+b \sec (c+d x))^3 \tan (c+d x)}{20 d}+\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d}+\frac {1}{60} \int (a+b \sec (c+d x)) \left (60 a^3 A+\left (60 a^3 B+115 a b^2 B+36 a^2 b (5 A+3 C)+8 b^3 (5 A+4 C)\right ) \sec (c+d x)+\left (130 a^2 b B+45 b^3 B+24 a^3 C+4 a b^2 (40 A+29 C)\right ) \sec ^2(c+d x)\right ) \, dx\\ &=\frac {b \left (130 a^2 b B+45 b^3 B+24 a^3 C+4 a b^2 (40 A+29 C)\right ) \sec (c+d x) \tan (c+d x)}{120 d}+\frac {\left (20 A b^2+35 a b B+12 a^2 C+16 b^2 C\right ) (a+b \sec (c+d x))^2 \tan (c+d x)}{60 d}+\frac {(5 b B+4 a C) (a+b \sec (c+d x))^3 \tan (c+d x)}{20 d}+\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d}+\frac {1}{120} \int \left (120 a^4 A+15 \left (8 a^4 B+24 a^2 b^2 B+3 b^4 B+16 a^3 b (2 A+C)+4 a b^3 (4 A+3 C)\right ) \sec (c+d x)+4 \left (95 a^3 b B+80 a b^3 B+12 a^4 C+4 b^4 (5 A+4 C)+2 a^2 b^2 (85 A+56 C)\right ) \sec ^2(c+d x)\right ) \, dx\\ &=a^4 A x+\frac {b \left (130 a^2 b B+45 b^3 B+24 a^3 C+4 a b^2 (40 A+29 C)\right ) \sec (c+d x) \tan (c+d x)}{120 d}+\frac {\left (20 A b^2+35 a b B+12 a^2 C+16 b^2 C\right ) (a+b \sec (c+d x))^2 \tan (c+d x)}{60 d}+\frac {(5 b B+4 a C) (a+b \sec (c+d x))^3 \tan (c+d x)}{20 d}+\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d}+\frac {1}{8} \left (8 a^4 B+24 a^2 b^2 B+3 b^4 B+16 a^3 b (2 A+C)+4 a b^3 (4 A+3 C)\right ) \int \sec (c+d x) \, dx+\frac {1}{30} \left (95 a^3 b B+80 a b^3 B+12 a^4 C+4 b^4 (5 A+4 C)+2 a^2 b^2 (85 A+56 C)\right ) \int \sec ^2(c+d x) \, dx\\ &=a^4 A x+\frac {\left (8 a^4 B+24 a^2 b^2 B+3 b^4 B+16 a^3 b (2 A+C)+4 a b^3 (4 A+3 C)\right ) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac {b \left (130 a^2 b B+45 b^3 B+24 a^3 C+4 a b^2 (40 A+29 C)\right ) \sec (c+d x) \tan (c+d x)}{120 d}+\frac {\left (20 A b^2+35 a b B+12 a^2 C+16 b^2 C\right ) (a+b \sec (c+d x))^2 \tan (c+d x)}{60 d}+\frac {(5 b B+4 a C) (a+b \sec (c+d x))^3 \tan (c+d x)}{20 d}+\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d}-\frac {\left (95 a^3 b B+80 a b^3 B+12 a^4 C+4 b^4 (5 A+4 C)+2 a^2 b^2 (85 A+56 C)\right ) \text {Subst}(\int 1 \, dx,x,-\tan (c+d x))}{30 d}\\ &=a^4 A x+\frac {\left (8 a^4 B+24 a^2 b^2 B+3 b^4 B+16 a^3 b (2 A+C)+4 a b^3 (4 A+3 C)\right ) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac {\left (95 a^3 b B+80 a b^3 B+12 a^4 C+4 b^4 (5 A+4 C)+2 a^2 b^2 (85 A+56 C)\right ) \tan (c+d x)}{30 d}+\frac {b \left (130 a^2 b B+45 b^3 B+24 a^3 C+4 a b^2 (40 A+29 C)\right ) \sec (c+d x) \tan (c+d x)}{120 d}+\frac {\left (20 A b^2+35 a b B+12 a^2 C+16 b^2 C\right ) (a+b \sec (c+d x))^2 \tan (c+d x)}{60 d}+\frac {(5 b B+4 a C) (a+b \sec (c+d x))^3 \tan (c+d x)}{20 d}+\frac {C (a+b \sec (c+d x))^4 \tan (c+d x)}{5 d}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(690\) vs. \(2(290)=580\).
time = 4.16, size = 690, normalized size = 2.38 \begin {gather*} \frac {\left (C+B \cos (c+d x)+A \cos ^2(c+d x)\right ) \sec ^5(c+d x) \left (600 a^4 A (c+d x) \cos (c+d x)+300 a^4 A (c+d x) \cos (3 (c+d x))+60 a^4 A c \cos (5 (c+d x))+60 a^4 A d x \cos (5 (c+d x))-120 \left (8 a^4 B+24 a^2 b^2 B+3 b^4 B+16 a^3 b (2 A+C)+4 a b^3 (4 A+3 C)\right ) \cos ^5(c+d x) \left (\log \left (\cos \left (\frac {1}{2} (c+d x)\right )-\sin \left (\frac {1}{2} (c+d x)\right )\right )-\log \left (\cos \left (\frac {1}{2} (c+d x)\right )+\sin \left (\frac {1}{2} (c+d x)\right )\right )\right )+720 a^2 A b^2 \sin (c+d x)+160 A b^4 \sin (c+d x)+480 a^3 b B \sin (c+d x)+640 a b^3 B \sin (c+d x)+120 a^4 C \sin (c+d x)+960 a^2 b^2 C \sin (c+d x)+320 b^4 C \sin (c+d x)+480 a A b^3 \sin (2 (c+d x))+720 a^2 b^2 B \sin (2 (c+d x))+210 b^4 B \sin (2 (c+d x))+480 a^3 b C \sin (2 (c+d x))+840 a b^3 C \sin (2 (c+d x))+1080 a^2 A b^2 \sin (3 (c+d x))+200 A b^4 \sin (3 (c+d x))+720 a^3 b B \sin (3 (c+d x))+800 a b^3 B \sin (3 (c+d x))+180 a^4 C \sin (3 (c+d x))+1200 a^2 b^2 C \sin (3 (c+d x))+160 b^4 C \sin (3 (c+d x))+240 a A b^3 \sin (4 (c+d x))+360 a^2 b^2 B \sin (4 (c+d x))+45 b^4 B \sin (4 (c+d x))+240 a^3 b C \sin (4 (c+d x))+180 a b^3 C \sin (4 (c+d x))+360 a^2 A b^2 \sin (5 (c+d x))+40 A b^4 \sin (5 (c+d x))+240 a^3 b B \sin (5 (c+d x))+160 a b^3 B \sin (5 (c+d x))+60 a^4 C \sin (5 (c+d x))+240 a^2 b^2 C \sin (5 (c+d x))+32 b^4 C \sin (5 (c+d x))\right )}{480 d (A+2 C+2 B \cos (c+d x)+A \cos (2 (c+d x)))} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.14, size = 421, normalized size = 1.45 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 497, normalized size = 1.71 \begin {gather*} \frac {240 \, {\left (d x + c\right )} A a^{4} + 480 \, {\left (\tan \left (d x + c\right )^{3} + 3 \, \tan \left (d x + c\right )\right )} C a^{2} b^{2} + 320 \, {\left (\tan \left (d x + c\right )^{3} + 3 \, \tan \left (d x + c\right )\right )} B a b^{3} + 80 \, {\left (\tan \left (d x + c\right )^{3} + 3 \, \tan \left (d x + c\right )\right )} A b^{4} + 16 \, {\left (3 \, \tan \left (d x + c\right )^{5} + 10 \, \tan \left (d x + c\right )^{3} + 15 \, \tan \left (d x + c\right )\right )} C b^{4} - 60 \, C a b^{3} {\left (\frac {2 \, {\left (3 \, \sin \left (d x + c\right )^{3} - 5 \, \sin \left (d x + c\right )\right )}}{\sin \left (d x + c\right )^{4} - 2 \, \sin \left (d x + c\right )^{2} + 1} - 3 \, \log \left (\sin \left (d x + c\right ) + 1\right ) + 3 \, \log \left (\sin \left (d x + c\right ) - 1\right )\right )} - 15 \, B b^{4} {\left (\frac {2 \, {\left (3 \, \sin \left (d x + c\right )^{3} - 5 \, \sin \left (d x + c\right )\right )}}{\sin \left (d x + c\right )^{4} - 2 \, \sin \left (d x + c\right )^{2} + 1} - 3 \, \log \left (\sin \left (d x + c\right ) + 1\right ) + 3 \, \log \left (\sin \left (d x + c\right ) - 1\right )\right )} - 240 \, C a^{3} b {\left (\frac {2 \, \sin \left (d x + c\right )}{\sin \left (d x + c\right )^{2} - 1} - \log \left (\sin \left (d x + c\right ) + 1\right ) + \log \left (\sin \left (d x + c\right ) - 1\right )\right )} - 360 \, B a^{2} b^{2} {\left (\frac {2 \, \sin \left (d x + c\right )}{\sin \left (d x + c\right )^{2} - 1} - \log \left (\sin \left (d x + c\right ) + 1\right ) + \log \left (\sin \left (d x + c\right ) - 1\right )\right )} - 240 \, A a b^{3} {\left (\frac {2 \, \sin \left (d x + c\right )}{\sin \left (d x + c\right )^{2} - 1} - \log \left (\sin \left (d x + c\right ) + 1\right ) + \log \left (\sin \left (d x + c\right ) - 1\right )\right )} + 240 \, B a^{4} \log \left (\sec \left (d x + c\right ) + \tan \left (d x + c\right )\right ) + 960 \, A a^{3} b \log \left (\sec \left (d x + c\right ) + \tan \left (d x + c\right )\right ) + 240 \, C a^{4} \tan \left (d x + c\right ) + 960 \, B a^{3} b \tan \left (d x + c\right ) + 1440 \, A a^{2} b^{2} \tan \left (d x + c\right )}{240 \, d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 5.04, size = 340, normalized size = 1.17 \begin {gather*} \frac {240 \, A a^{4} d x \cos \left (d x + c\right )^{5} + 15 \, {\left (8 \, B a^{4} + 16 \, {\left (2 \, A + C\right )} a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left (4 \, A + 3 \, C\right )} a b^{3} + 3 \, B b^{4}\right )} \cos \left (d x + c\right )^{5} \log \left (\sin \left (d x + c\right ) + 1\right ) - 15 \, {\left (8 \, B a^{4} + 16 \, {\left (2 \, A + C\right )} a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left (4 \, A + 3 \, C\right )} a b^{3} + 3 \, B b^{4}\right )} \cos \left (d x + c\right )^{5} \log \left (-\sin \left (d x + c\right ) + 1\right ) + 2 \, {\left (24 \, C b^{4} + 8 \, {\left (15 \, C a^{4} + 60 \, B a^{3} b + 30 \, {\left (3 \, A + 2 \, C\right )} a^{2} b^{2} + 40 \, B a b^{3} + 2 \, {\left (5 \, A + 4 \, C\right )} b^{4}\right )} \cos \left (d x + c\right )^{4} + 15 \, {\left (16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 4 \, {\left (4 \, A + 3 \, C\right )} a b^{3} + 3 \, B b^{4}\right )} \cos \left (d x + c\right )^{3} + 8 \, {\left (30 \, C a^{2} b^{2} + 20 \, B a b^{3} + {\left (5 \, A + 4 \, C\right )} b^{4}\right )} \cos \left (d x + c\right )^{2} + 30 \, {\left (4 \, C a b^{3} + B b^{4}\right )} \cos \left (d x + c\right )\right )} \sin \left (d x + c\right )}{240 \, d \cos \left (d x + c\right )^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a + b \sec {\left (c + d x \right )}\right )^{4} \left (A + B \sec {\left (c + d x \right )} + C \sec ^{2}{\left (c + d x \right )}\right )\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1140 vs.
\(2 (278) = 556\).
time = 0.54, size = 1140, normalized size = 3.93 \begin {gather*} \frac {120 \, {\left (d x + c\right )} A a^{4} + 15 \, {\left (8 \, B a^{4} + 32 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 12 \, C a b^{3} + 3 \, B b^{4}\right )} \log \left ({\left | \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 1 \right |}\right ) - 15 \, {\left (8 \, B a^{4} + 32 \, A a^{3} b + 16 \, C a^{3} b + 24 \, B a^{2} b^{2} + 16 \, A a b^{3} + 12 \, C a b^{3} + 3 \, B b^{4}\right )} \log \left ({\left | \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) - 1 \right |}\right ) - \frac {2 \, {\left (120 \, C a^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 480 \, B a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} - 240 \, C a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 720 \, A a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} - 360 \, B a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 720 \, C a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} - 240 \, A a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 480 \, B a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} - 300 \, C a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 120 \, A b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} - 75 \, B b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} + 120 \, C b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{9} - 480 \, C a^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 1920 \, B a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} + 480 \, C a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 2880 \, A a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} + 720 \, B a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 1920 \, C a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} + 480 \, A a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 1280 \, B a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} + 120 \, C a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 320 \, A b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} + 30 \, B b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} - 160 \, C b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{7} + 720 \, C a^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 2880 \, B a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 4320 \, A a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 2400 \, C a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 1600 \, B a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 400 \, A b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} + 464 \, C b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{5} - 480 \, C a^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 1920 \, B a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 480 \, C a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 2880 \, A a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 720 \, B a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 1920 \, C a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 480 \, A a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 1280 \, B a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 120 \, C a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 320 \, A b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 30 \, B b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} - 160 \, C b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{3} + 120 \, C a^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 480 \, B a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 240 \, C a^{3} b \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 720 \, A a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 360 \, B a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 720 \, C a^{2} b^{2} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 240 \, A a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 480 \, B a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 300 \, C a b^{3} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 120 \, A b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 75 \, B b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right ) + 120 \, C b^{4} \tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )\right )}}{{\left (\tan \left (\frac {1}{2} \, d x + \frac {1}{2} \, c\right )^{2} - 1\right )}^{5}}}{120 \, d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 7.88, size = 2500, normalized size = 8.62 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________