Optimal. Leaf size=17 \[ \text {Int}\left (\frac {(b x)^m}{\sin ^{-1}(a x)^{3/2}},x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {(b x)^m}{\sin ^{-1}(a x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(b x)^m}{\sin ^{-1}(a x)^{3/2}} \, dx &=\int \frac {(b x)^m}{\sin ^{-1}(a x)^{3/2}} \, dx\\ \end {align*}
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Mathematica [A] time = 2.28, size = 0, normalized size = 0.00 \[ \int \frac {(b x)^m}{\sin ^{-1}(a x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x\right )^{m}}{\arcsin \left (a x\right )^{\frac {3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x \right )^{m}}{\arcsin \left (a x \right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {{\left (b\,x\right )}^m}{{\mathrm {asin}\left (a\,x\right )}^{3/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x\right )^{m}}{\operatorname {asin}^{\frac {3}{2}}{\left (a x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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