Optimal. Leaf size=64 \[ \frac{\sin ^{-1}(a x)^4 (b x)^{m+1}}{b (m+1)}-\frac{4 a \text{Unintegrable}\left (\frac{\sin ^{-1}(a x)^3 (b x)^{m+1}}{\sqrt{1-a^2 x^2}},x\right )}{b (m+1)} \]
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Rubi [A] time = 0.121914, 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 = {} \[ \int (b x)^m \sin ^{-1}(a x)^4 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (b x)^m \sin ^{-1}(a x)^4 \, dx &=\frac{(b x)^{1+m} \sin ^{-1}(a x)^4}{b (1+m)}-\frac{(4 a) \int \frac{(b x)^{1+m} \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx}{b (1+m)}\\ \end{align*}
Mathematica [A] time = 1.06375, size = 0, normalized size = 0. \[ \int (b x)^m \sin ^{-1}(a x)^4 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.828, size = 0, normalized size = 0. \begin{align*} \int \left ( bx \right ) ^{m} \left ( \arcsin \left ( ax \right ) \right ) ^{4}\, 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: ValueError} \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 (\left (b x\right )^{m} \arcsin \left (a x\right )^{4}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (b x\right )^{m} \operatorname{asin}^{4}{\left (a x \right )}\, dx \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 )^{m} \arcsin \left (a x\right )^{4}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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