Integrand size = 12, antiderivative size = 12 \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\text {Int}\left (x^m \text {arcsinh}(a x)^{5/2},x\right ) \]
[Out]
Not integrable
Time = 0.02 (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 = {} \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\int x^m \text {arcsinh}(a x)^{5/2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int x^m \text {arcsinh}(a x)^{5/2} \, dx \\ \end{align*}
Not integrable
Time = 0.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\int x^m \text {arcsinh}(a x)^{5/2} \, dx \]
[In]
[Out]
Not integrable
Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83
\[\int x^{m} \operatorname {arcsinh}\left (a x \right )^{\frac {5}{2}}d x\]
[In]
[Out]
Exception generated. \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Timed out. \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 0.35 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\int { x^{m} \operatorname {arsinh}\left (a x\right )^{\frac {5}{2}} \,d x } \]
[In]
[Out]
Timed out. \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 2.45 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \text {arcsinh}(a x)^{5/2} \, dx=\int x^m\,{\mathrm {asinh}\left (a\,x\right )}^{5/2} \,d x \]
[In]
[Out]