Integrand size = 12, antiderivative size = 12 \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\text {Int}\left (x^m \sqrt {\text {arcsinh}(a x)},x\right ) \]
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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 = {} \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\int x^m \sqrt {\text {arcsinh}(a x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int x^m \sqrt {\text {arcsinh}(a x)} \, dx \\ \end{align*}
Not integrable
Time = 0.37 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\int x^m \sqrt {\text {arcsinh}(a x)} \, dx \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83
\[\int x^{m} \sqrt {\operatorname {arcsinh}\left (a x \right )}d x\]
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Exception generated. \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 1.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\int x^{m} \sqrt {\operatorname {asinh}{\left (a x \right )}}\, dx \]
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Not integrable
Time = 0.36 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\int { x^{m} \sqrt {\operatorname {arsinh}\left (a x\right )} \,d x } \]
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Timed out. \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\text {Timed out} \]
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Not integrable
Time = 2.43 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \sqrt {\text {arcsinh}(a x)} \, dx=\int x^m\,\sqrt {\mathrm {asinh}\left (a\,x\right )} \,d x \]
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