Integrand size = 12, antiderivative size = 12 \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\text {Int}\left (\frac {x^m}{\sqrt {\text {arccosh}(a x)}},x\right ) \]
[Out]
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 = {} \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx \\ \end{align*}
Not integrable
Time = 1.69 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx \]
[In]
[Out]
Not integrable
Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83
\[\int \frac {x^{m}}{\sqrt {\operatorname {arccosh}\left (a x \right )}}d x\]
[In]
[Out]
Exception generated. \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Not integrable
Time = 0.92 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {x^{m}}{\sqrt {\operatorname {acosh}{\left (a x \right )}}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.51 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\int { \frac {x^{m}}{\sqrt {\operatorname {arcosh}\left (a x\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.34 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\int { \frac {x^{m}}{\sqrt {\operatorname {arcosh}\left (a x\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.61 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\sqrt {\text {arccosh}(a x)}} \, dx=\int \frac {x^m}{\sqrt {\mathrm {acosh}\left (a\,x\right )}} \,d x \]
[In]
[Out]