Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{1}{\left (d+e x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2},x\right ) \]
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Rubi [A] time = 0.0432489, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{\left (d+e x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{\left (d+e x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2} \, dx &=\int \frac{1}{\left (d+e x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 48.4118, size = 0, normalized size = 0. \[ \int \frac{1}{\left (d+e x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.185, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( a+b\arcsin \left ( cx \right ) \right ) ^{2}} \left ( e{x}^{2}+d \right ) ^{-{\frac{5}{2}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sqrt{e x^{2} + d}}{a^{2} e^{3} x^{6} + 3 \, a^{2} d e^{2} x^{4} + 3 \, a^{2} d^{2} e x^{2} + a^{2} d^{3} +{\left (b^{2} e^{3} x^{6} + 3 \, b^{2} d e^{2} x^{4} + 3 \, b^{2} d^{2} e x^{2} + b^{2} d^{3}\right )} \arcsin \left (c x\right )^{2} + 2 \,{\left (a b e^{3} x^{6} + 3 \, a b d e^{2} x^{4} + 3 \, a b d^{2} e x^{2} + a b d^{3}\right )} \arcsin \left (c x\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (e x^{2} + d\right )}^{\frac{5}{2}}{\left (b \arcsin \left (c x\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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