Integrand size = 12, antiderivative size = 12 \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\text {Int}\left (\frac {\text {arcsinh}(a x)^{5/2}}{x},x\right ) \]
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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 = {} \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.14 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83
\[\int \frac {\operatorname {arcsinh}\left (a x \right )^{\frac {5}{2}}}{x}d x\]
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Exception generated. \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 19.29 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\int \frac {\operatorname {asinh}^{\frac {5}{2}}{\left (a x \right )}}{x}\, dx \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\int { \frac {\operatorname {arsinh}\left (a x\right )^{\frac {5}{2}}}{x} \,d x } \]
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Not integrable
Time = 0.60 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\int { \frac {\operatorname {arsinh}\left (a x\right )^{\frac {5}{2}}}{x} \,d x } \]
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Not integrable
Time = 2.37 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\text {arcsinh}(a x)^{5/2}}{x} \, dx=\int \frac {{\mathrm {asinh}\left (a\,x\right )}^{5/2}}{x} \,d x \]
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