Optimal. Leaf size=455 \[ -\frac {1}{4 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \text {ArcSin}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {\text {ArcSin}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}-\frac {9 \text {ArcSin}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \text {ArcSin}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \text {ArcSin}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}-\frac {5 i \text {ArcSin}(a x) \text {ArcTan}\left (e^{i \text {ArcSin}(a x)}\right )}{a c^3}-\frac {3 i \text {ArcSin}(a x)^3 \text {ArcTan}\left (e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}+\frac {5 i \text {PolyLog}\left (2,-i e^{i \text {ArcSin}(a x)}\right )}{2 a c^3}+\frac {9 i \text {ArcSin}(a x)^2 \text {PolyLog}\left (2,-i e^{i \text {ArcSin}(a x)}\right )}{8 a c^3}-\frac {5 i \text {PolyLog}\left (2,i e^{i \text {ArcSin}(a x)}\right )}{2 a c^3}-\frac {9 i \text {ArcSin}(a x)^2 \text {PolyLog}\left (2,i e^{i \text {ArcSin}(a x)}\right )}{8 a c^3}-\frac {9 \text {ArcSin}(a x) \text {PolyLog}\left (3,-i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}+\frac {9 \text {ArcSin}(a x) \text {PolyLog}\left (3,i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}-\frac {9 i \text {PolyLog}\left (4,-i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}+\frac {9 i \text {PolyLog}\left (4,i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3} \]
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Rubi [A]
time = 0.36, antiderivative size = 455, normalized size of antiderivative = 1.00, number of steps
used = 28, number of rules used = 11, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.550, Rules used = {4747, 4749,
4266, 2611, 6744, 2320, 6724, 4767, 2317, 2438, 267} \begin {gather*} \frac {3 x \text {ArcSin}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}+\frac {x \text {ArcSin}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}-\frac {9 \text {ArcSin}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}-\frac {\text {ArcSin}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}+\frac {x \text {ArcSin}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {1}{4 a c^3 \sqrt {1-a^2 x^2}}-\frac {3 i \text {ArcSin}(a x)^3 \text {ArcTan}\left (e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}-\frac {5 i \text {ArcSin}(a x) \text {ArcTan}\left (e^{i \text {ArcSin}(a x)}\right )}{a c^3}+\frac {9 i \text {ArcSin}(a x)^2 \text {Li}_2\left (-i e^{i \text {ArcSin}(a x)}\right )}{8 a c^3}-\frac {9 i \text {ArcSin}(a x)^2 \text {Li}_2\left (i e^{i \text {ArcSin}(a x)}\right )}{8 a c^3}-\frac {9 \text {ArcSin}(a x) \text {Li}_3\left (-i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}+\frac {9 \text {ArcSin}(a x) \text {Li}_3\left (i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}+\frac {5 i \text {Li}_2\left (-i e^{i \text {ArcSin}(a x)}\right )}{2 a c^3}-\frac {5 i \text {Li}_2\left (i e^{i \text {ArcSin}(a x)}\right )}{2 a c^3}-\frac {9 i \text {Li}_4\left (-i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3}+\frac {9 i \text {Li}_4\left (i e^{i \text {ArcSin}(a x)}\right )}{4 a c^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rule 2317
Rule 2320
Rule 2438
Rule 2611
Rule 4266
Rule 4747
Rule 4749
Rule 4767
Rule 6724
Rule 6744
Rubi steps
\begin {align*} \int \frac {\sin ^{-1}(a x)^3}{\left (c-a^2 c x^2\right )^3} \, dx &=\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}-\frac {(3 a) \int \frac {x \sin ^{-1}(a x)^2}{\left (1-a^2 x^2\right )^{5/2}} \, dx}{4 c^3}+\frac {3 \int \frac {\sin ^{-1}(a x)^3}{\left (c-a^2 c x^2\right )^2} \, dx}{4 c}\\ &=-\frac {\sin ^{-1}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}+\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \sin ^{-1}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}+\frac {\int \frac {\sin ^{-1}(a x)}{\left (1-a^2 x^2\right )^2} \, dx}{2 c^3}-\frac {(9 a) \int \frac {x \sin ^{-1}(a x)^2}{\left (1-a^2 x^2\right )^{3/2}} \, dx}{8 c^3}+\frac {3 \int \frac {\sin ^{-1}(a x)^3}{c-a^2 c x^2} \, dx}{8 c^2}\\ &=\frac {x \sin ^{-1}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {\sin ^{-1}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}-\frac {9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \sin ^{-1}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}+\frac {\int \frac {\sin ^{-1}(a x)}{1-a^2 x^2} \, dx}{4 c^3}+\frac {9 \int \frac {\sin ^{-1}(a x)}{1-a^2 x^2} \, dx}{4 c^3}+\frac {3 \text {Subst}\left (\int x^3 \sec (x) \, dx,x,\sin ^{-1}(a x)\right )}{8 a c^3}-\frac {a \int \frac {x}{\left (1-a^2 x^2\right )^{3/2}} \, dx}{4 c^3}\\ &=-\frac {1}{4 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {\sin ^{-1}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}-\frac {9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \sin ^{-1}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}-\frac {3 i \sin ^{-1}(a x)^3 \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {\text {Subst}\left (\int x \sec (x) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}-\frac {9 \text {Subst}\left (\int x^2 \log \left (1-i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{8 a c^3}+\frac {9 \text {Subst}\left (\int x^2 \log \left (1+i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{8 a c^3}+\frac {9 \text {Subst}\left (\int x \sec (x) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}\\ &=-\frac {1}{4 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {\sin ^{-1}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}-\frac {9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \sin ^{-1}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}-\frac {5 i \sin ^{-1}(a x) \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{a c^3}-\frac {3 i \sin ^{-1}(a x)^3 \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (-i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {(9 i) \text {Subst}\left (\int x \text {Li}_2\left (-i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}+\frac {(9 i) \text {Subst}\left (\int x \text {Li}_2\left (i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}-\frac {\text {Subst}\left (\int \log \left (1-i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}+\frac {\text {Subst}\left (\int \log \left (1+i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}-\frac {9 \text {Subst}\left (\int \log \left (1-i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}+\frac {9 \text {Subst}\left (\int \log \left (1+i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}\\ &=-\frac {1}{4 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {\sin ^{-1}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}-\frac {9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \sin ^{-1}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}-\frac {5 i \sin ^{-1}(a x) \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{a c^3}-\frac {3 i \sin ^{-1}(a x)^3 \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (-i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {9 \sin ^{-1}(a x) \text {Li}_3\left (-i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {9 \sin ^{-1}(a x) \text {Li}_3\left (i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {i \text {Subst}\left (\int \frac {\log (1-i x)}{x} \, dx,x,e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}-\frac {i \text {Subst}\left (\int \frac {\log (1+i x)}{x} \, dx,x,e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {(9 i) \text {Subst}\left (\int \frac {\log (1-i x)}{x} \, dx,x,e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}-\frac {(9 i) \text {Subst}\left (\int \frac {\log (1+i x)}{x} \, dx,x,e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {9 \text {Subst}\left (\int \text {Li}_3\left (-i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}-\frac {9 \text {Subst}\left (\int \text {Li}_3\left (i e^{i x}\right ) \, dx,x,\sin ^{-1}(a x)\right )}{4 a c^3}\\ &=-\frac {1}{4 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {\sin ^{-1}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}-\frac {9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \sin ^{-1}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}-\frac {5 i \sin ^{-1}(a x) \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{a c^3}-\frac {3 i \sin ^{-1}(a x)^3 \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {5 i \text {Li}_2\left (-i e^{i \sin ^{-1}(a x)}\right )}{2 a c^3}+\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (-i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {5 i \text {Li}_2\left (i e^{i \sin ^{-1}(a x)}\right )}{2 a c^3}-\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {9 \sin ^{-1}(a x) \text {Li}_3\left (-i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {9 \sin ^{-1}(a x) \text {Li}_3\left (i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}-\frac {(9 i) \text {Subst}\left (\int \frac {\text {Li}_3(-i x)}{x} \, dx,x,e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {(9 i) \text {Subst}\left (\int \frac {\text {Li}_3(i x)}{x} \, dx,x,e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}\\ &=-\frac {1}{4 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)}{4 c^3 \left (1-a^2 x^2\right )}-\frac {\sin ^{-1}(a x)^2}{4 a c^3 \left (1-a^2 x^2\right )^{3/2}}-\frac {9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt {1-a^2 x^2}}+\frac {x \sin ^{-1}(a x)^3}{4 c^3 \left (1-a^2 x^2\right )^2}+\frac {3 x \sin ^{-1}(a x)^3}{8 c^3 \left (1-a^2 x^2\right )}-\frac {5 i \sin ^{-1}(a x) \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{a c^3}-\frac {3 i \sin ^{-1}(a x)^3 \tan ^{-1}\left (e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {5 i \text {Li}_2\left (-i e^{i \sin ^{-1}(a x)}\right )}{2 a c^3}+\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (-i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {5 i \text {Li}_2\left (i e^{i \sin ^{-1}(a x)}\right )}{2 a c^3}-\frac {9 i \sin ^{-1}(a x)^2 \text {Li}_2\left (i e^{i \sin ^{-1}(a x)}\right )}{8 a c^3}-\frac {9 \sin ^{-1}(a x) \text {Li}_3\left (-i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {9 \sin ^{-1}(a x) \text {Li}_3\left (i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}-\frac {9 i \text {Li}_4\left (-i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}+\frac {9 i \text {Li}_4\left (i e^{i \sin ^{-1}(a x)}\right )}{4 a c^3}\\ \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. \(1544\) vs. \(2(455)=910\).
time = 12.12, size = 1544, normalized size = 3.39 \begin {gather*} \text {Too large to display} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.31, size = 543, normalized size = 1.19
method | result | size |
derivativedivides | \(\frac {-\frac {3 a^{3} x^{3} \arcsin \left (a x \right )^{3}-9 \arcsin \left (a x \right )^{2} \sqrt {-a^{2} x^{2}+1}\, a^{2} x^{2}-5 a x \arcsin \left (a x \right )^{3}+2 a^{3} x^{3} \arcsin \left (a x \right )+11 \arcsin \left (a x \right )^{2} \sqrt {-a^{2} x^{2}+1}-2 a^{2} x^{2} \sqrt {-a^{2} x^{2}+1}-2 a x \arcsin \left (a x \right )+2 \sqrt {-a^{2} x^{2}+1}}{8 \left (a^{4} x^{4}-2 a^{2} x^{2}+1\right ) c^{3}}+\frac {3 \arcsin \left (a x \right )^{3} \ln \left (1-i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}-\frac {9 i \arcsin \left (a x \right )^{2} \polylog \left (2, i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}+\frac {9 \arcsin \left (a x \right ) \polylog \left (3, i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}+\frac {9 i \polylog \left (4, i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}-\frac {3 \arcsin \left (a x \right )^{3} \ln \left (1+i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}+\frac {9 i \arcsin \left (a x \right )^{2} \polylog \left (2, -i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}-\frac {9 \arcsin \left (a x \right ) \polylog \left (3, -i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}-\frac {9 i \polylog \left (4, -i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}-\frac {5 \arcsin \left (a x \right ) \ln \left (1+i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}+\frac {5 \arcsin \left (a x \right ) \ln \left (1-i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}+\frac {5 i \dilog \left (1+i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}-\frac {5 i \dilog \left (1-i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}}{a}\) | \(543\) |
default | \(\frac {-\frac {3 a^{3} x^{3} \arcsin \left (a x \right )^{3}-9 \arcsin \left (a x \right )^{2} \sqrt {-a^{2} x^{2}+1}\, a^{2} x^{2}-5 a x \arcsin \left (a x \right )^{3}+2 a^{3} x^{3} \arcsin \left (a x \right )+11 \arcsin \left (a x \right )^{2} \sqrt {-a^{2} x^{2}+1}-2 a^{2} x^{2} \sqrt {-a^{2} x^{2}+1}-2 a x \arcsin \left (a x \right )+2 \sqrt {-a^{2} x^{2}+1}}{8 \left (a^{4} x^{4}-2 a^{2} x^{2}+1\right ) c^{3}}+\frac {3 \arcsin \left (a x \right )^{3} \ln \left (1-i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}-\frac {9 i \arcsin \left (a x \right )^{2} \polylog \left (2, i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}+\frac {9 \arcsin \left (a x \right ) \polylog \left (3, i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}+\frac {9 i \polylog \left (4, i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}-\frac {3 \arcsin \left (a x \right )^{3} \ln \left (1+i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}+\frac {9 i \arcsin \left (a x \right )^{2} \polylog \left (2, -i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{8 c^{3}}-\frac {9 \arcsin \left (a x \right ) \polylog \left (3, -i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}-\frac {9 i \polylog \left (4, -i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{4 c^{3}}-\frac {5 \arcsin \left (a x \right ) \ln \left (1+i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}+\frac {5 \arcsin \left (a x \right ) \ln \left (1-i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}+\frac {5 i \dilog \left (1+i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}-\frac {5 i \dilog \left (1-i \left (i a x +\sqrt {-a^{2} x^{2}+1}\right )\right )}{2 c^{3}}}{a}\) | \(543\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.83, size = 78, normalized size = 0.17 \begin {gather*} -\frac {1}{16} \, {\left (\frac {2 \, {\left (3 \, a^{2} x^{3} - 5 \, x\right )}}{a^{4} c^{3} x^{4} - 2 \, a^{2} c^{3} x^{2} + c^{3}} - \frac {3 \, \log \left (a x + 1\right )}{a c^{3}} + \frac {3 \, \log \left (a x - 1\right )}{a c^{3}}\right )} \arcsin \left (a x\right )^{3} \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 {\operatorname {asin}^{3}{\left (a x \right )}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx}{c^{3}} \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 {{\mathrm {asin}\left (a\,x\right )}^3}{{\left (c-a^2\,c\,x^2\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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