Integrand size = 12, antiderivative size = 12 \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\text {Int}\left (\frac {x^m}{\text {arcsinh}(a x)^{3/2}},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx \\ \end{align*}
Not integrable
Time = 0.34 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83
\[\int \frac {x^{m}}{\operatorname {arcsinh}\left (a x \right )^{\frac {3}{2}}}d x\]
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Exception generated. \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 4.08 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\int \frac {x^{m}}{\operatorname {asinh}^{\frac {3}{2}}{\left (a x \right )}}\, dx \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\int { \frac {x^{m}}{\operatorname {arsinh}\left (a x\right )^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\int { \frac {x^{m}}{\operatorname {arsinh}\left (a x\right )^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 2.46 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\text {arcsinh}(a x)^{3/2}} \, dx=\int \frac {x^m}{{\mathrm {asinh}\left (a\,x\right )}^{3/2}} \,d x \]
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