Optimal. Leaf size=332 \[ \frac {b^2 x}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b (a+b \text {ArcSin}(c x))}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {3 b (a+b \text {ArcSin}(c x))}{4 c d^3 \sqrt {1-c^2 x^2}}+\frac {x (a+b \text {ArcSin}(c x))^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 x (a+b \text {ArcSin}(c x))^2}{8 d^3 \left (1-c^2 x^2\right )}-\frac {3 i (a+b \text {ArcSin}(c x))^2 \text {ArcTan}\left (e^{i \text {ArcSin}(c x)}\right )}{4 c d^3}+\frac {5 b^2 \tanh ^{-1}(c x)}{6 c d^3}+\frac {3 i b (a+b \text {ArcSin}(c x)) \text {PolyLog}\left (2,-i e^{i \text {ArcSin}(c x)}\right )}{4 c d^3}-\frac {3 i b (a+b \text {ArcSin}(c x)) \text {PolyLog}\left (2,i e^{i \text {ArcSin}(c x)}\right )}{4 c d^3}-\frac {3 b^2 \text {PolyLog}\left (3,-i e^{i \text {ArcSin}(c x)}\right )}{4 c d^3}+\frac {3 b^2 \text {PolyLog}\left (3,i e^{i \text {ArcSin}(c x)}\right )}{4 c d^3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.25, antiderivative size = 332, normalized size of antiderivative = 1.00, number of steps
used = 15, number of rules used = 9, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.375, Rules used = {4747, 4749,
4266, 2611, 2320, 6724, 4767, 212, 205} \begin {gather*} -\frac {3 i \text {ArcTan}\left (e^{i \text {ArcSin}(c x)}\right ) (a+b \text {ArcSin}(c x))^2}{4 c d^3}-\frac {3 b (a+b \text {ArcSin}(c x))}{4 c d^3 \sqrt {1-c^2 x^2}}-\frac {b (a+b \text {ArcSin}(c x))}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}+\frac {3 x (a+b \text {ArcSin}(c x))^2}{8 d^3 \left (1-c^2 x^2\right )}+\frac {x (a+b \text {ArcSin}(c x))^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 i b \text {Li}_2\left (-i e^{i \text {ArcSin}(c x)}\right ) (a+b \text {ArcSin}(c x))}{4 c d^3}-\frac {3 i b \text {Li}_2\left (i e^{i \text {ArcSin}(c x)}\right ) (a+b \text {ArcSin}(c x))}{4 c d^3}-\frac {3 b^2 \text {Li}_3\left (-i e^{i \text {ArcSin}(c x)}\right )}{4 c d^3}+\frac {3 b^2 \text {Li}_3\left (i e^{i \text {ArcSin}(c x)}\right )}{4 c d^3}+\frac {b^2 x}{12 d^3 \left (1-c^2 x^2\right )}+\frac {5 b^2 \tanh ^{-1}(c x)}{6 c d^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 205
Rule 212
Rule 2320
Rule 2611
Rule 4266
Rule 4747
Rule 4749
Rule 4767
Rule 6724
Rubi steps
\begin {align*} \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{\left (d-c^2 d x^2\right )^3} \, dx &=\frac {x \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {(b c) \int \frac {x \left (a+b \sin ^{-1}(c x)\right )}{\left (1-c^2 x^2\right )^{5/2}} \, dx}{2 d^3}+\frac {3 \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{\left (d-c^2 d x^2\right )^2} \, dx}{4 d}\\ &=-\frac {b \left (a+b \sin ^{-1}(c x)\right )}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}+\frac {x \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 x \left (a+b \sin ^{-1}(c x)\right )^2}{8 d^3 \left (1-c^2 x^2\right )}+\frac {b^2 \int \frac {1}{\left (1-c^2 x^2\right )^2} \, dx}{6 d^3}-\frac {(3 b c) \int \frac {x \left (a+b \sin ^{-1}(c x)\right )}{\left (1-c^2 x^2\right )^{3/2}} \, dx}{4 d^3}+\frac {3 \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{d-c^2 d x^2} \, dx}{8 d^2}\\ &=\frac {b^2 x}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b \left (a+b \sin ^{-1}(c x)\right )}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {3 b \left (a+b \sin ^{-1}(c x)\right )}{4 c d^3 \sqrt {1-c^2 x^2}}+\frac {x \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 x \left (a+b \sin ^{-1}(c x)\right )^2}{8 d^3 \left (1-c^2 x^2\right )}+\frac {b^2 \int \frac {1}{1-c^2 x^2} \, dx}{12 d^3}+\frac {\left (3 b^2\right ) \int \frac {1}{1-c^2 x^2} \, dx}{4 d^3}+\frac {3 \text {Subst}\left (\int (a+b x)^2 \sec (x) \, dx,x,\sin ^{-1}(c x)\right )}{8 c d^3}\\ &=\frac {b^2 x}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b \left (a+b \sin ^{-1}(c x)\right )}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {3 b \left (a+b \sin ^{-1}(c x)\right )}{4 c d^3 \sqrt {1-c^2 x^2}}+\frac {x \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 x \left (a+b \sin ^{-1}(c x)\right )^2}{8 d^3 \left (1-c^2 x^2\right )}-\frac {3 i \left (a+b \sin ^{-1}(c x)\right )^2 \tan ^{-1}\left (e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}+\frac {5 b^2 \tanh ^{-1}(c x)}{6 c d^3}-\frac {(3 b) \text {Subst}\left (\int (a+b x) \log \left (1-i e^{i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{4 c d^3}+\frac {(3 b) \text {Subst}\left (\int (a+b x) \log \left (1+i e^{i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{4 c d^3}\\ &=\frac {b^2 x}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b \left (a+b \sin ^{-1}(c x)\right )}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {3 b \left (a+b \sin ^{-1}(c x)\right )}{4 c d^3 \sqrt {1-c^2 x^2}}+\frac {x \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 x \left (a+b \sin ^{-1}(c x)\right )^2}{8 d^3 \left (1-c^2 x^2\right )}-\frac {3 i \left (a+b \sin ^{-1}(c x)\right )^2 \tan ^{-1}\left (e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}+\frac {5 b^2 \tanh ^{-1}(c x)}{6 c d^3}+\frac {3 i b \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (-i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}-\frac {3 i b \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}-\frac {\left (3 i b^2\right ) \text {Subst}\left (\int \text {Li}_2\left (-i e^{i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{4 c d^3}+\frac {\left (3 i b^2\right ) \text {Subst}\left (\int \text {Li}_2\left (i e^{i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{4 c d^3}\\ &=\frac {b^2 x}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b \left (a+b \sin ^{-1}(c x)\right )}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {3 b \left (a+b \sin ^{-1}(c x)\right )}{4 c d^3 \sqrt {1-c^2 x^2}}+\frac {x \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 x \left (a+b \sin ^{-1}(c x)\right )^2}{8 d^3 \left (1-c^2 x^2\right )}-\frac {3 i \left (a+b \sin ^{-1}(c x)\right )^2 \tan ^{-1}\left (e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}+\frac {5 b^2 \tanh ^{-1}(c x)}{6 c d^3}+\frac {3 i b \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (-i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}-\frac {3 i b \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}-\frac {\left (3 b^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2(-i x)}{x} \, dx,x,e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}+\frac {\left (3 b^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2(i x)}{x} \, dx,x,e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}\\ &=\frac {b^2 x}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b \left (a+b \sin ^{-1}(c x)\right )}{6 c d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {3 b \left (a+b \sin ^{-1}(c x)\right )}{4 c d^3 \sqrt {1-c^2 x^2}}+\frac {x \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}+\frac {3 x \left (a+b \sin ^{-1}(c x)\right )^2}{8 d^3 \left (1-c^2 x^2\right )}-\frac {3 i \left (a+b \sin ^{-1}(c x)\right )^2 \tan ^{-1}\left (e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}+\frac {5 b^2 \tanh ^{-1}(c x)}{6 c d^3}+\frac {3 i b \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (-i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}-\frac {3 i b \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}-\frac {3 b^2 \text {Li}_3\left (-i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}+\frac {3 b^2 \text {Li}_3\left (i e^{i \sin ^{-1}(c x)}\right )}{4 c d^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 3.28, size = 556, normalized size = 1.67 \begin {gather*} \frac {\frac {24 a^2 x}{\left (-1+c^2 x^2\right )^2}-\frac {36 a^2 x}{-1+c^2 x^2}-\frac {18 a^2 \log (1-c x)}{c}+\frac {18 a^2 \log (1+c x)}{c}+\frac {72 i a b \text {PolyLog}\left (2,-i e^{i \text {ArcSin}(c x)}\right )}{c}-\frac {4 b^2 \left (\frac {2 c x}{-1+c^2 x^2}+\frac {4 \text {ArcSin}(c x)}{\left (1-c^2 x^2\right )^{3/2}}+\frac {18 \text {ArcSin}(c x)}{\sqrt {1-c^2 x^2}}-\frac {6 c x \text {ArcSin}(c x)^2}{\left (-1+c^2 x^2\right )^2}+\frac {9 c x \text {ArcSin}(c x)^2}{-1+c^2 x^2}+18 i \text {ArcSin}(c x)^2 \text {ArcTan}\left (e^{i \text {ArcSin}(c x)}\right )-20 \tanh ^{-1}(c x)-18 i \text {ArcSin}(c x) \text {PolyLog}\left (2,-i e^{i \text {ArcSin}(c x)}\right )+18 i \text {ArcSin}(c x) \text {PolyLog}\left (2,i e^{i \text {ArcSin}(c x)}\right )+18 \text {PolyLog}\left (3,-i e^{i \text {ArcSin}(c x)}\right )-18 \text {PolyLog}\left (3,i e^{i \text {ArcSin}(c x)}\right )\right )}{c}+\frac {a b \left (30-70 \sqrt {1-c^2 x^2}+40 \cos (2 \text {ArcSin}(c x))-18 \cos (3 \text {ArcSin}(c x))+10 \cos (4 \text {ArcSin}(c x))-72 i \left (-1+c^2 x^2\right )^2 \text {PolyLog}\left (2,i e^{i \text {ArcSin}(c x)}\right )+3 \text {ArcSin}(c x) \left (22 c x+9 \log \left (1-i e^{i \text {ArcSin}(c x)}\right )+12 \cos (2 \text {ArcSin}(c x)) \left (\log \left (1-i e^{i \text {ArcSin}(c x)}\right )-\log \left (1+i e^{i \text {ArcSin}(c x)}\right )\right )+3 \cos (4 \text {ArcSin}(c x)) \left (\log \left (1-i e^{i \text {ArcSin}(c x)}\right )-\log \left (1+i e^{i \text {ArcSin}(c x)}\right )\right )-9 \log \left (1+i e^{i \text {ArcSin}(c x)}\right )+6 \sin (3 \text {ArcSin}(c x))\right )\right )}{c \left (-1+c^2 x^2\right )^2}}{96 d^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Both result and optimal contain complex but leaf count of result is larger than twice
the leaf count of optimal. 843 vs. \(2 (339 ) = 678\).
time = 0.22, size = 844, normalized size = 2.54
method | result | size |
derivativedivides | \(\frac {-\frac {3 b^{2} \arcsin \left (c x \right )^{2} c^{3} x^{3}}{8 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {3 b^{2} \polylog \left (3, i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}-\frac {3 b^{2} \polylog \left (3, -i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 a^{2} \ln \left (c x +1\right )}{16 d^{3}}-\frac {3 i b^{2} \arcsin \left (c x \right ) \polylog \left (2, i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 i b^{2} \arcsin \left (c x \right ) \polylog \left (2, -i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 i a b \dilog \left (1+i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}-\frac {3 i a b \dilog \left (1-i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}-\frac {3 a b \arcsin \left (c x \right ) \ln \left (1+i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 a b \arcsin \left (c x \right ) \ln \left (1-i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {5 b^{2} \arcsin \left (c x \right )^{2} c x}{8 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {3 b^{2} \arcsin \left (c x \right )^{2} \ln \left (1-i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{8 d^{3}}-\frac {3 b^{2} \arcsin \left (c x \right )^{2} \ln \left (1+i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{8 d^{3}}-\frac {5 i b^{2} \arctan \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )}{3 d^{3}}+\frac {3 b^{2} \arcsin \left (c x \right ) \sqrt {-c^{2} x^{2}+1}\, c^{2} x^{2}}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {3 a b \arcsin \left (c x \right ) c^{3} x^{3}}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {3 a b \,c^{2} x^{2} \sqrt {-c^{2} x^{2}+1}}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {5 a b \arcsin \left (c x \right ) c x}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {11 b^{2} \arcsin \left (c x \right ) \sqrt {-c^{2} x^{2}+1}}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {11 a b \sqrt {-c^{2} x^{2}+1}}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {b^{2} c^{3} x^{3}}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {b^{2} c x}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {3 a^{2} \ln \left (c x -1\right )}{16 d^{3}}-\frac {a^{2}}{16 d^{3} \left (c x +1\right )^{2}}-\frac {3 a^{2}}{16 d^{3} \left (c x +1\right )}+\frac {a^{2}}{16 d^{3} \left (c x -1\right )^{2}}-\frac {3 a^{2}}{16 d^{3} \left (c x -1\right )}}{c}\) | \(844\) |
default | \(\frac {-\frac {3 b^{2} \arcsin \left (c x \right )^{2} c^{3} x^{3}}{8 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {3 b^{2} \polylog \left (3, i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}-\frac {3 b^{2} \polylog \left (3, -i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 a^{2} \ln \left (c x +1\right )}{16 d^{3}}-\frac {3 i b^{2} \arcsin \left (c x \right ) \polylog \left (2, i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 i b^{2} \arcsin \left (c x \right ) \polylog \left (2, -i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 i a b \dilog \left (1+i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}-\frac {3 i a b \dilog \left (1-i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}-\frac {3 a b \arcsin \left (c x \right ) \ln \left (1+i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {3 a b \arcsin \left (c x \right ) \ln \left (1-i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{4 d^{3}}+\frac {5 b^{2} \arcsin \left (c x \right )^{2} c x}{8 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {3 b^{2} \arcsin \left (c x \right )^{2} \ln \left (1-i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{8 d^{3}}-\frac {3 b^{2} \arcsin \left (c x \right )^{2} \ln \left (1+i \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )\right )}{8 d^{3}}-\frac {5 i b^{2} \arctan \left (i c x +\sqrt {-c^{2} x^{2}+1}\right )}{3 d^{3}}+\frac {3 b^{2} \arcsin \left (c x \right ) \sqrt {-c^{2} x^{2}+1}\, c^{2} x^{2}}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {3 a b \arcsin \left (c x \right ) c^{3} x^{3}}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {3 a b \,c^{2} x^{2} \sqrt {-c^{2} x^{2}+1}}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {5 a b \arcsin \left (c x \right ) c x}{4 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {11 b^{2} \arcsin \left (c x \right ) \sqrt {-c^{2} x^{2}+1}}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {11 a b \sqrt {-c^{2} x^{2}+1}}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {b^{2} c^{3} x^{3}}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}+\frac {b^{2} c x}{12 d^{3} \left (c^{4} x^{4}-2 c^{2} x^{2}+1\right )}-\frac {3 a^{2} \ln \left (c x -1\right )}{16 d^{3}}-\frac {a^{2}}{16 d^{3} \left (c x +1\right )^{2}}-\frac {3 a^{2}}{16 d^{3} \left (c x +1\right )}+\frac {a^{2}}{16 d^{3} \left (c x -1\right )^{2}}-\frac {3 a^{2}}{16 d^{3} \left (c x -1\right )}}{c}\) | \(844\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2}{{\left (d-c^2\,d\,x^2\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________