Optimal. Leaf size=16 \[ \text{Unintegrable}\left ((b x)^{3/2} \sin ^{-1}(a x)^n,x\right ) \]
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Rubi [A] time = 0.0214075, 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 = {} \[ \int (b x)^{3/2} \sin ^{-1}(a x)^n \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (b x)^{3/2} \sin ^{-1}(a x)^n \, dx &=\int (b x)^{3/2} \sin ^{-1}(a x)^n \, dx\\ \end{align*}
Mathematica [A] time = 3.57054, size = 0, normalized size = 0. \[ \int (b x)^{3/2} \sin ^{-1}(a x)^n \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.089, size = 0, normalized size = 0. \begin{align*} \int \left ( bx \right ) ^{{\frac{3}{2}}} \left ( \arcsin \left ( ax \right ) \right ) ^{n}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \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 (\sqrt{b x} b x \arcsin \left (a x\right )^{n}, 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 \left (b x\right )^{\frac{3}{2}} \arcsin \left (a x\right )^{n}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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