Optimal. Leaf size=439 \[ -\frac {2 b^2 (a+b \text {ArcSin}(c+d x))^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3}{3 d e^4 (c+d x)^2}-\frac {(a+b \text {ArcSin}(c+d x))^4}{3 d e^4 (c+d x)^3}-\frac {8 b^3 (a+b \text {ArcSin}(c+d x)) \tanh ^{-1}\left (e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}-\frac {4 b (a+b \text {ArcSin}(c+d x))^3 \tanh ^{-1}\left (e^{i \text {ArcSin}(c+d x)}\right )}{3 d e^4}+\frac {4 i b^4 \text {PolyLog}\left (2,-e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}+\frac {2 i b^2 (a+b \text {ArcSin}(c+d x))^2 \text {PolyLog}\left (2,-e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}-\frac {4 i b^4 \text {PolyLog}\left (2,e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}-\frac {2 i b^2 (a+b \text {ArcSin}(c+d x))^2 \text {PolyLog}\left (2,e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}-\frac {4 b^3 (a+b \text {ArcSin}(c+d x)) \text {PolyLog}\left (3,-e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}+\frac {4 b^3 (a+b \text {ArcSin}(c+d x)) \text {PolyLog}\left (3,e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}-\frac {4 i b^4 \text {PolyLog}\left (4,-e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}+\frac {4 i b^4 \text {PolyLog}\left (4,e^{i \text {ArcSin}(c+d x)}\right )}{d e^4} \]
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Rubi [A]
time = 0.40, antiderivative size = 439, normalized size of antiderivative = 1.00, number of steps
used = 21, number of rules used = 12, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.522, Rules used = {4889, 12,
4723, 4789, 4803, 4268, 2611, 6744, 2320, 6724, 2317, 2438} \begin {gather*} -\frac {4 b^3 \text {Li}_3\left (-e^{i \text {ArcSin}(c+d x)}\right ) (a+b \text {ArcSin}(c+d x))}{d e^4}+\frac {4 b^3 \text {Li}_3\left (e^{i \text {ArcSin}(c+d x)}\right ) (a+b \text {ArcSin}(c+d x))}{d e^4}-\frac {8 b^3 \tanh ^{-1}\left (e^{i \text {ArcSin}(c+d x)}\right ) (a+b \text {ArcSin}(c+d x))}{d e^4}+\frac {2 i b^2 \text {Li}_2\left (-e^{i \text {ArcSin}(c+d x)}\right ) (a+b \text {ArcSin}(c+d x))^2}{d e^4}-\frac {2 i b^2 \text {Li}_2\left (e^{i \text {ArcSin}(c+d x)}\right ) (a+b \text {ArcSin}(c+d x))^2}{d e^4}-\frac {2 b^2 (a+b \text {ArcSin}(c+d x))^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3}{3 d e^4 (c+d x)^2}-\frac {(a+b \text {ArcSin}(c+d x))^4}{3 d e^4 (c+d x)^3}-\frac {4 b \tanh ^{-1}\left (e^{i \text {ArcSin}(c+d x)}\right ) (a+b \text {ArcSin}(c+d x))^3}{3 d e^4}+\frac {4 i b^4 \text {Li}_2\left (-e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}-\frac {4 i b^4 \text {Li}_2\left (e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}-\frac {4 i b^4 \text {Li}_4\left (-e^{i \text {ArcSin}(c+d x)}\right )}{d e^4}+\frac {4 i b^4 \text {Li}_4\left (e^{i \text {ArcSin}(c+d x)}\right )}{d e^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2317
Rule 2320
Rule 2438
Rule 2611
Rule 4268
Rule 4723
Rule 4789
Rule 4803
Rule 4889
Rule 6724
Rule 6744
Rubi steps
\begin {align*} \int \frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{(c e+d e x)^4} \, dx &=\frac {\text {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^4}{e^4 x^4} \, dx,x,c+d x\right )}{d}\\ &=\frac {\text {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^4}{x^4} \, dx,x,c+d x\right )}{d e^4}\\ &=-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}+\frac {(4 b) \text {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^3}{x^3 \sqrt {1-x^2}} \, dx,x,c+d x\right )}{3 d e^4}\\ &=-\frac {2 b \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{3 d e^4 (c+d x)^2}-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}+\frac {(2 b) \text {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^3}{x \sqrt {1-x^2}} \, dx,x,c+d x\right )}{3 d e^4}+\frac {\left (2 b^2\right ) \text {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^2}{x^2} \, dx,x,c+d x\right )}{d e^4}\\ &=-\frac {2 b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{3 d e^4 (c+d x)^2}-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}+\frac {(2 b) \text {Subst}\left (\int (a+b x)^3 \csc (x) \, dx,x,\sin ^{-1}(c+d x)\right )}{3 d e^4}+\frac {\left (4 b^3\right ) \text {Subst}\left (\int \frac {a+b \sin ^{-1}(x)}{x \sqrt {1-x^2}} \, dx,x,c+d x\right )}{d e^4}\\ &=-\frac {2 b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{3 d e^4 (c+d x)^2}-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}-\frac {4 b \left (a+b \sin ^{-1}(c+d x)\right )^3 \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{3 d e^4}-\frac {\left (2 b^2\right ) \text {Subst}\left (\int (a+b x)^2 \log \left (1-e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}+\frac {\left (2 b^2\right ) \text {Subst}\left (\int (a+b x)^2 \log \left (1+e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}+\frac {\left (4 b^3\right ) \text {Subst}\left (\int (a+b x) \csc (x) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}\\ &=-\frac {2 b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{3 d e^4 (c+d x)^2}-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}-\frac {8 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 b \left (a+b \sin ^{-1}(c+d x)\right )^3 \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{3 d e^4}+\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {\left (4 i b^3\right ) \text {Subst}\left (\int (a+b x) \text {Li}_2\left (-e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}+\frac {\left (4 i b^3\right ) \text {Subst}\left (\int (a+b x) \text {Li}_2\left (e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}-\frac {\left (4 b^4\right ) \text {Subst}\left (\int \log \left (1-e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}+\frac {\left (4 b^4\right ) \text {Subst}\left (\int \log \left (1+e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}\\ &=-\frac {2 b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{3 d e^4 (c+d x)^2}-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}-\frac {8 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 b \left (a+b \sin ^{-1}(c+d x)\right )^3 \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{3 d e^4}+\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \text {Li}_3\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {4 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \text {Li}_3\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {\left (4 i b^4\right ) \text {Subst}\left (\int \frac {\log (1-x)}{x} \, dx,x,e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {\left (4 i b^4\right ) \text {Subst}\left (\int \frac {\log (1+x)}{x} \, dx,x,e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {\left (4 b^4\right ) \text {Subst}\left (\int \text {Li}_3\left (-e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}-\frac {\left (4 b^4\right ) \text {Subst}\left (\int \text {Li}_3\left (e^{i x}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{d e^4}\\ &=-\frac {2 b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{3 d e^4 (c+d x)^2}-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}-\frac {8 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 b \left (a+b \sin ^{-1}(c+d x)\right )^3 \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{3 d e^4}+\frac {4 i b^4 \text {Li}_2\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 i b^4 \text {Li}_2\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \text {Li}_3\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {4 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \text {Li}_3\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {\left (4 i b^4\right ) \text {Subst}\left (\int \frac {\text {Li}_3(-x)}{x} \, dx,x,e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {\left (4 i b^4\right ) \text {Subst}\left (\int \frac {\text {Li}_3(x)}{x} \, dx,x,e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}\\ &=-\frac {2 b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{d e^4 (c+d x)}-\frac {2 b \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{3 d e^4 (c+d x)^2}-\frac {\left (a+b \sin ^{-1}(c+d x)\right )^4}{3 d e^4 (c+d x)^3}-\frac {8 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 b \left (a+b \sin ^{-1}(c+d x)\right )^3 \tanh ^{-1}\left (e^{i \sin ^{-1}(c+d x)}\right )}{3 d e^4}+\frac {4 i b^4 \text {Li}_2\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 i b^4 \text {Li}_2\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {2 i b^2 \left (a+b \sin ^{-1}(c+d x)\right )^2 \text {Li}_2\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \text {Li}_3\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {4 b^3 \left (a+b \sin ^{-1}(c+d x)\right ) \text {Li}_3\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}-\frac {4 i b^4 \text {Li}_4\left (-e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}+\frac {4 i b^4 \text {Li}_4\left (e^{i \sin ^{-1}(c+d x)}\right )}{d e^4}\\ \end {align*}
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Mathematica [B] Both result and optimal contain complex but leaf count is larger than twice
the leaf count of optimal. \(1274\) vs. \(2(439)=878\).
time = 9.14, size = 1274, normalized size = 2.90 \begin {gather*} -\frac {a^4}{3 d e^4 (c+d x)^3}+\frac {a^2 b^2 \left (8 i \text {PolyLog}\left (2,-e^{i \text {ArcSin}(c+d x)}\right )-\frac {2 \left (2+4 \text {ArcSin}(c+d x)^2-2 \cos (2 \text {ArcSin}(c+d x))-3 (c+d x) \text {ArcSin}(c+d x) \log \left (1-e^{i \text {ArcSin}(c+d x)}\right )+3 (c+d x) \text {ArcSin}(c+d x) \log \left (1+e^{i \text {ArcSin}(c+d x)}\right )+4 i (c+d x)^3 \text {PolyLog}\left (2,e^{i \text {ArcSin}(c+d x)}\right )+2 \text {ArcSin}(c+d x) \sin (2 \text {ArcSin}(c+d x))+\text {ArcSin}(c+d x) \log \left (1-e^{i \text {ArcSin}(c+d x)}\right ) \sin (3 \text {ArcSin}(c+d x))-\text {ArcSin}(c+d x) \log \left (1+e^{i \text {ArcSin}(c+d x)}\right ) \sin (3 \text {ArcSin}(c+d x))\right )}{(c+d x)^3}\right )}{4 d e^4}+\frac {a b^3 \left (-24 \text {ArcSin}(c+d x) \cot \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-4 \text {ArcSin}(c+d x)^3 \cot \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-6 \text {ArcSin}(c+d x)^2 \csc ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-(c+d x) \text {ArcSin}(c+d x)^3 \csc ^4\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )+24 \text {ArcSin}(c+d x)^2 \log \left (1-e^{i \text {ArcSin}(c+d x)}\right )-24 \text {ArcSin}(c+d x)^2 \log \left (1+e^{i \text {ArcSin}(c+d x)}\right )+48 \log \left (\tan \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )\right )+48 i \text {ArcSin}(c+d x) \text {PolyLog}\left (2,-e^{i \text {ArcSin}(c+d x)}\right )-48 i \text {ArcSin}(c+d x) \text {PolyLog}\left (2,e^{i \text {ArcSin}(c+d x)}\right )-48 \text {PolyLog}\left (3,-e^{i \text {ArcSin}(c+d x)}\right )+48 \text {PolyLog}\left (3,e^{i \text {ArcSin}(c+d x)}\right )+6 \text {ArcSin}(c+d x)^2 \sec ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {16 \text {ArcSin}(c+d x)^3 \sin ^4\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )}{(c+d x)^3}-24 \text {ArcSin}(c+d x) \tan \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-4 \text {ArcSin}(c+d x)^3 \tan \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )\right )}{12 d e^4}+\frac {b^4 \left (-2 i \pi ^4+4 i \text {ArcSin}(c+d x)^4-24 \text {ArcSin}(c+d x)^2 \cot \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-2 \text {ArcSin}(c+d x)^4 \cot \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-4 \text {ArcSin}(c+d x)^3 \csc ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {1}{2} (c+d x) \text {ArcSin}(c+d x)^4 \csc ^4\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )+16 \text {ArcSin}(c+d x)^3 \log \left (1-e^{-i \text {ArcSin}(c+d x)}\right )+96 \text {ArcSin}(c+d x) \log \left (1-e^{i \text {ArcSin}(c+d x)}\right )-96 \text {ArcSin}(c+d x) \log \left (1+e^{i \text {ArcSin}(c+d x)}\right )-16 \text {ArcSin}(c+d x)^3 \log \left (1+e^{i \text {ArcSin}(c+d x)}\right )+48 i \text {ArcSin}(c+d x)^2 \text {PolyLog}\left (2,e^{-i \text {ArcSin}(c+d x)}\right )+48 i \left (2+\text {ArcSin}(c+d x)^2\right ) \text {PolyLog}\left (2,-e^{i \text {ArcSin}(c+d x)}\right )-96 i \text {PolyLog}\left (2,e^{i \text {ArcSin}(c+d x)}\right )+96 \text {ArcSin}(c+d x) \text {PolyLog}\left (3,e^{-i \text {ArcSin}(c+d x)}\right )-96 \text {ArcSin}(c+d x) \text {PolyLog}\left (3,-e^{i \text {ArcSin}(c+d x)}\right )-96 i \text {PolyLog}\left (4,e^{-i \text {ArcSin}(c+d x)}\right )-96 i \text {PolyLog}\left (4,-e^{i \text {ArcSin}(c+d x)}\right )+4 \text {ArcSin}(c+d x)^3 \sec ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {8 \text {ArcSin}(c+d x)^4 \sin ^4\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )}{(c+d x)^3}-24 \text {ArcSin}(c+d x)^2 \tan \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-2 \text {ArcSin}(c+d x)^4 \tan \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )\right )}{24 d e^4}+\frac {4 a^3 b \left (-\frac {1}{12} \text {ArcSin}(c+d x) \cot \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {1}{24} \csc ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {1}{24} \text {ArcSin}(c+d x) \cot \left (\frac {1}{2} \text {ArcSin}(c+d x)\right ) \csc ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {1}{6} \log \left (\cos \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )\right )+\frac {1}{6} \log \left (\sin \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )\right )+\frac {1}{24} \sec ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {1}{12} \text {ArcSin}(c+d x) \tan \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )-\frac {1}{24} \text {ArcSin}(c+d x) \sec ^2\left (\frac {1}{2} \text {ArcSin}(c+d x)\right ) \tan \left (\frac {1}{2} \text {ArcSin}(c+d x)\right )\right )}{d e^4} \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [B] Both result and optimal contain complex but leaf count of result is larger than twice
the leaf count of optimal. 1211 vs. \(2 (525 ) = 1050\).
time = 0.58, size = 1212, normalized size = 2.76
method | result | size |
derivativedivides | \(\text {Expression too large to display}\) | \(1212\) |
default | \(\text {Expression too large to display}\) | \(1212\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {\int \frac {a^{4}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac {b^{4} \operatorname {asin}^{4}{\left (c + d x \right )}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac {4 a b^{3} \operatorname {asin}^{3}{\left (c + d x \right )}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac {6 a^{2} b^{2} \operatorname {asin}^{2}{\left (c + d x \right )}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac {4 a^{3} b \operatorname {asin}{\left (c + d x \right )}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\left (a+b\,\mathrm {asin}\left (c+d\,x\right )\right )}^4}{{\left (c\,e+d\,e\,x\right )}^4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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