Integrand size = 20, antiderivative size = 20 \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=\text {Int}\left (x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3,x\right ) \]
[Out]
Not integrable
Time = 0.02 (sec) , antiderivative size = 20, 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 = {} \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=\int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx \\ \end{align*}
Not integrable
Time = 0.74 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=\int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx \]
[In]
[Out]
Not integrable
Time = 3.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int x^{m} \left (a^{2} c \,x^{2}+c \right ) \arctan \left (a x \right )^{3}d x\]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=\int { {\left (a^{2} c x^{2} + c\right )} x^{m} \arctan \left (a x\right )^{3} \,d x } \]
[In]
[Out]
Not integrable
Time = 12.47 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.55 \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=c \left (\int x^{m} \operatorname {atan}^{3}{\left (a x \right )}\, dx + \int a^{2} x^{2} x^{m} \operatorname {atan}^{3}{\left (a x \right )}\, dx\right ) \]
[In]
[Out]
Not integrable
Time = 6.27 (sec) , antiderivative size = 435, normalized size of antiderivative = 21.75 \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=\int { {\left (a^{2} c x^{2} + c\right )} x^{m} \arctan \left (a x\right )^{3} \,d x } \]
[In]
[Out]
Not integrable
Time = 145.87 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.15 \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=\int { {\left (a^{2} c x^{2} + c\right )} x^{m} \arctan \left (a x\right )^{3} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.46 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int x^m \left (c+a^2 c x^2\right ) \arctan (a x)^3 \, dx=\int x^m\,{\mathrm {atan}\left (a\,x\right )}^3\,\left (c\,a^2\,x^2+c\right ) \,d x \]
[In]
[Out]