Integrand size = 24, antiderivative size = 24 \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\text {Int}\left (\frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}},x\right ) \]
[Out]
Not integrable
Time = 0.04 (sec) , antiderivative size = 24, 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 = {} \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx \\ \end{align*}
Not integrable
Time = 1.27 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx \]
[In]
[Out]
Not integrable
Time = 6.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92
\[\int \frac {x^{m}}{\left (a^{2} c \,x^{2}+c \right )^{2} \arctan \left (a x \right )^{\frac {5}{2}}}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.62 \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\int { \frac {x^{m}}{{\left (a^{2} c x^{2} + c\right )}^{2} \arctan \left (a x\right )^{\frac {5}{2}}} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\text {Timed out} \]
[In]
[Out]
Exception generated. \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\text {Exception raised: RuntimeError} \]
[In]
[Out]
Not integrable
Time = 221.16 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.12 \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\int { \frac {x^{m}}{{\left (a^{2} c x^{2} + c\right )}^{2} \arctan \left (a x\right )^{\frac {5}{2}}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.67 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {x^m}{\left (c+a^2 c x^2\right )^2 \arctan (a x)^{5/2}} \, dx=\int \frac {x^m}{{\mathrm {atan}\left (a\,x\right )}^{5/2}\,{\left (c\,a^2\,x^2+c\right )}^2} \,d x \]
[In]
[Out]