Integrand size = 10, antiderivative size = 10 \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\text {Int}\left (\frac {\text {arcsinh}(a x)^n}{x},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\int \frac {\text {arcsinh}(a x)^n}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {arcsinh}(a x)^n}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\int \frac {\text {arcsinh}(a x)^n}{x} \, dx \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {arcsinh}\left (a x \right )^{n}}{x}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\int { \frac {\operatorname {arsinh}\left (a x\right )^{n}}{x} \,d x } \]
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Not integrable
Time = 0.48 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\int \frac {\operatorname {asinh}^{n}{\left (a x \right )}}{x}\, dx \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\int { \frac {\operatorname {arsinh}\left (a x\right )^{n}}{x} \,d x } \]
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Not integrable
Time = 0.43 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\int { \frac {\operatorname {arsinh}\left (a x\right )^{n}}{x} \,d x } \]
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Not integrable
Time = 2.58 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\text {arcsinh}(a x)^n}{x} \, dx=\int \frac {{\mathrm {asinh}\left (a\,x\right )}^n}{x} \,d x \]
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