Optimal. Leaf size=561 \[ \frac {31}{64} b^2 c^2 d^2 x \sqrt {d-c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2}-\frac {89 b^2 c d^2 \sqrt {d-c^2 d x^2} \text {ArcSin}(c x)}{64 \sqrt {1-c^2 x^2}}+\frac {15 b c^3 d^2 x^2 \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))}{8 \sqrt {1-c^2 x^2}}+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))-\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))^2-\frac {i c d^2 \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))^2}{\sqrt {1-c^2 x^2}}-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} (a+b \text {ArcSin}(c x))^2-\frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \text {ArcSin}(c x))^2}{x}-\frac {5 c d^2 \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))^3}{8 b \sqrt {1-c^2 x^2}}+\frac {2 b c d^2 \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x)) \log \left (1-e^{2 i \text {ArcSin}(c x)}\right )}{\sqrt {1-c^2 x^2}}-\frac {i b^2 c d^2 \sqrt {d-c^2 d x^2} \text {PolyLog}\left (2,e^{2 i \text {ArcSin}(c x)}\right )}{\sqrt {1-c^2 x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.42, antiderivative size = 561, normalized size of antiderivative = 1.00, number of steps
used = 23, number of rules used = 15, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.517, Rules used =
{4785, 4743, 4741, 4737, 4723, 327, 222, 4767, 201, 4773, 4721, 3798, 2221, 2317, 2438}
\begin {gather*} -\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))^2-\frac {5 c d^2 \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))^3}{8 b \sqrt {1-c^2 x^2}}-\frac {i c d^2 \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))^2}{\sqrt {1-c^2 x^2}}-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))+\frac {2 b c d^2 \sqrt {d-c^2 d x^2} \log \left (1-e^{2 i \text {ArcSin}(c x)}\right ) (a+b \text {ArcSin}(c x))}{\sqrt {1-c^2 x^2}}-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} (a+b \text {ArcSin}(c x))^2-\frac {\left (d-c^2 d x^2\right )^{5/2} (a+b \text {ArcSin}(c x))^2}{x}+\frac {15 b c^3 d^2 x^2 \sqrt {d-c^2 d x^2} (a+b \text {ArcSin}(c x))}{8 \sqrt {1-c^2 x^2}}-\frac {i b^2 c d^2 \sqrt {d-c^2 d x^2} \text {Li}_2\left (e^{2 i \text {ArcSin}(c x)}\right )}{\sqrt {1-c^2 x^2}}-\frac {89 b^2 c d^2 \text {ArcSin}(c x) \sqrt {d-c^2 d x^2}}{64 \sqrt {1-c^2 x^2}}+\frac {31}{64} b^2 c^2 d^2 x \sqrt {d-c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 201
Rule 222
Rule 327
Rule 2221
Rule 2317
Rule 2438
Rule 3798
Rule 4721
Rule 4723
Rule 4737
Rule 4741
Rule 4743
Rule 4767
Rule 4773
Rule 4785
Rubi steps
\begin {align*} \int \frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x^2} \, dx &=-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}-\left (5 c^2 d\right ) \int \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2 \, dx+\frac {\left (2 b c d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {\left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )}{x} \, dx}{\sqrt {1-c^2 x^2}}\\ &=\frac {1}{2} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}-\frac {1}{4} \left (15 c^2 d^2\right ) \int \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2 \, dx+\frac {\left (2 b c d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {\left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )}{x} \, dx}{\sqrt {1-c^2 x^2}}-\frac {\left (b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \left (1-c^2 x^2\right )^{3/2} \, dx}{2 \sqrt {1-c^2 x^2}}+\frac {\left (5 b c^3 d^2 \sqrt {d-c^2 d x^2}\right ) \int x \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right ) \, dx}{2 \sqrt {1-c^2 x^2}}\\ &=-\frac {1}{8} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2}+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}+\frac {\left (2 b c d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {a+b \sin ^{-1}(c x)}{x} \, dx}{\sqrt {1-c^2 x^2}}-\frac {\left (15 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{\sqrt {1-c^2 x^2}} \, dx}{8 \sqrt {1-c^2 x^2}}-\frac {\left (3 b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \sqrt {1-c^2 x^2} \, dx}{8 \sqrt {1-c^2 x^2}}+\frac {\left (5 b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \left (1-c^2 x^2\right )^{3/2} \, dx}{8 \sqrt {1-c^2 x^2}}-\frac {\left (b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \sqrt {1-c^2 x^2} \, dx}{\sqrt {1-c^2 x^2}}+\frac {\left (15 b c^3 d^2 \sqrt {d-c^2 d x^2}\right ) \int x \left (a+b \sin ^{-1}(c x)\right ) \, dx}{4 \sqrt {1-c^2 x^2}}\\ &=-\frac {11}{16} b^2 c^2 d^2 x \sqrt {d-c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2}+\frac {15 b c^3 d^2 x^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )}{8 \sqrt {1-c^2 x^2}}+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}-\frac {5 c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{8 b \sqrt {1-c^2 x^2}}+\frac {\left (2 b c d^2 \sqrt {d-c^2 d x^2}\right ) \text {Subst}\left (\int (a+b x) \cot (x) \, dx,x,\sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}}-\frac {\left (3 b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {1}{\sqrt {1-c^2 x^2}} \, dx}{16 \sqrt {1-c^2 x^2}}+\frac {\left (15 b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \sqrt {1-c^2 x^2} \, dx}{32 \sqrt {1-c^2 x^2}}-\frac {\left (b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {1}{\sqrt {1-c^2 x^2}} \, dx}{2 \sqrt {1-c^2 x^2}}-\frac {\left (15 b^2 c^4 d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {x^2}{\sqrt {1-c^2 x^2}} \, dx}{8 \sqrt {1-c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d-c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2}-\frac {11 b^2 c d^2 \sqrt {d-c^2 d x^2} \sin ^{-1}(c x)}{16 \sqrt {1-c^2 x^2}}+\frac {15 b c^3 d^2 x^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )}{8 \sqrt {1-c^2 x^2}}+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {i c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2}{\sqrt {1-c^2 x^2}}-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}-\frac {5 c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{8 b \sqrt {1-c^2 x^2}}-\frac {\left (4 i b c d^2 \sqrt {d-c^2 d x^2}\right ) \text {Subst}\left (\int \frac {e^{2 i x} (a+b x)}{1-e^{2 i x}} \, dx,x,\sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}}+\frac {\left (15 b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {1}{\sqrt {1-c^2 x^2}} \, dx}{64 \sqrt {1-c^2 x^2}}-\frac {\left (15 b^2 c^2 d^2 \sqrt {d-c^2 d x^2}\right ) \int \frac {1}{\sqrt {1-c^2 x^2}} \, dx}{16 \sqrt {1-c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d-c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2}-\frac {89 b^2 c d^2 \sqrt {d-c^2 d x^2} \sin ^{-1}(c x)}{64 \sqrt {1-c^2 x^2}}+\frac {15 b c^3 d^2 x^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )}{8 \sqrt {1-c^2 x^2}}+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {i c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2}{\sqrt {1-c^2 x^2}}-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}-\frac {5 c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{8 b \sqrt {1-c^2 x^2}}+\frac {2 b c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right ) \log \left (1-e^{2 i \sin ^{-1}(c x)}\right )}{\sqrt {1-c^2 x^2}}-\frac {\left (2 b^2 c d^2 \sqrt {d-c^2 d x^2}\right ) \text {Subst}\left (\int \log \left (1-e^{2 i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d-c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2}-\frac {89 b^2 c d^2 \sqrt {d-c^2 d x^2} \sin ^{-1}(c x)}{64 \sqrt {1-c^2 x^2}}+\frac {15 b c^3 d^2 x^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )}{8 \sqrt {1-c^2 x^2}}+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {i c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2}{\sqrt {1-c^2 x^2}}-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}-\frac {5 c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{8 b \sqrt {1-c^2 x^2}}+\frac {2 b c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right ) \log \left (1-e^{2 i \sin ^{-1}(c x)}\right )}{\sqrt {1-c^2 x^2}}+\frac {\left (i b^2 c d^2 \sqrt {d-c^2 d x^2}\right ) \text {Subst}\left (\int \frac {\log (1-x)}{x} \, dx,x,e^{2 i \sin ^{-1}(c x)}\right )}{\sqrt {1-c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d-c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1-c^2 x^2\right ) \sqrt {d-c^2 d x^2}-\frac {89 b^2 c d^2 \sqrt {d-c^2 d x^2} \sin ^{-1}(c x)}{64 \sqrt {1-c^2 x^2}}+\frac {15 b c^3 d^2 x^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )}{8 \sqrt {1-c^2 x^2}}+b c d^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1-c^2 x^2\right )^{3/2} \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {15}{8} c^2 d^2 x \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {i c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^2}{\sqrt {1-c^2 x^2}}-\frac {5}{4} c^2 d x \left (d-c^2 d x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (d-c^2 d x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2}{x}-\frac {5 c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{8 b \sqrt {1-c^2 x^2}}+\frac {2 b c d^2 \sqrt {d-c^2 d x^2} \left (a+b \sin ^{-1}(c x)\right ) \log \left (1-e^{2 i \sin ^{-1}(c x)}\right )}{\sqrt {1-c^2 x^2}}-\frac {i b^2 c d^2 \sqrt {d-c^2 d x^2} \text {Li}_2\left (e^{2 i \sin ^{-1}(c x)}\right )}{\sqrt {1-c^2 x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 1.40, size = 586, normalized size = 1.04 \begin {gather*} \frac {d^2 \left (-256 a^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2}-288 a^2 c^2 x^2 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2}+64 a^2 c^4 x^4 \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2}-160 b^2 c x \sqrt {d-c^2 d x^2} \text {ArcSin}(c x)^3+480 a^2 c \sqrt {d} x \sqrt {1-c^2 x^2} \text {ArcTan}\left (\frac {c x \sqrt {d-c^2 d x^2}}{\sqrt {d} \left (-1+c^2 x^2\right )}\right )-128 a b c x \sqrt {d-c^2 d x^2} \cos (2 \text {ArcSin}(c x))-4 a b c x \sqrt {d-c^2 d x^2} \cos (4 \text {ArcSin}(c x))+512 a b c x \sqrt {d-c^2 d x^2} \log (c x)-256 i b^2 c x \sqrt {d-c^2 d x^2} \text {PolyLog}\left (2,e^{2 i \text {ArcSin}(c x)}\right )+64 b^2 c x \sqrt {d-c^2 d x^2} \sin (2 \text {ArcSin}(c x))+b^2 c x \sqrt {d-c^2 d x^2} \sin (4 \text {ArcSin}(c x))-4 b \sqrt {d-c^2 d x^2} \text {ArcSin}(c x) \left (128 a \sqrt {1-c^2 x^2}+32 b c x \cos (2 \text {ArcSin}(c x))+b c x \cos (4 \text {ArcSin}(c x))-128 b c x \log \left (1-e^{2 i \text {ArcSin}(c x)}\right )+64 a c x \sin (2 \text {ArcSin}(c x))+4 a c x \sin (4 \text {ArcSin}(c x))\right )-8 b \sqrt {d-c^2 d x^2} \text {ArcSin}(c x)^2 \left (60 a c x+32 i b c x+32 b \sqrt {1-c^2 x^2}+16 b c x \sin (2 \text {ArcSin}(c x))+b c x \sin (4 \text {ArcSin}(c x))\right )\right )}{256 x \sqrt {1-c^2 x^2}} \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. 3584 vs. \(2 (521 ) = 1042\).
time = 0.42, size = 3585, normalized size = 6.39
method | result | size |
default | \(\text {Expression too large to display}\) | \(3585\) |
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]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (- d \left (c x - 1\right ) \left (c x + 1\right )\right )^{\frac {5}{2}} \left (a + b \operatorname {asin}{\left (c x \right )}\right )^{2}}{x^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \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 )}^{5/2}}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________