Optimal. Leaf size=15 \[ \text {Int}\left (x^m \sinh ^{-1}(a x)^{3/2},x\right ) \]
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Rubi [A]
time = 0.01, 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 = {}
\begin {gather*} \int x^m \sinh ^{-1}(a x)^{3/2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int x^m \sinh ^{-1}(a x)^{3/2} \, dx &=\int x^m \sinh ^{-1}(a x)^{3/2} \, dx\\ \end {align*}
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Mathematica [A]
time = 2.47, size = 0, normalized size = 0.00 \begin {gather*} \int x^m \sinh ^{-1}(a x)^{3/2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.94, size = 0, normalized size = 0.00 \[\int x^{m} \arcsinh \left (a x \right )^{\frac {3}{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
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.
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Fricas [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.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{m} \operatorname {asinh}^{\frac {3}{2}}{\left (a x \right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int x^m\,{\mathrm {asinh}\left (a\,x\right )}^{3/2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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