Integrand size = 21, antiderivative size = 21 \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\text {Int}\left (\frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2},x\right ) \]
[Out]
Not integrable
Time = 0.03 (sec) , antiderivative size = 21, 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 = {} \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx \\ \end{align*}
Not integrable
Time = 0.80 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx \]
[In]
[Out]
Not integrable
Time = 37.74 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90
\[\int \frac {\left (a^{2} c \,x^{2}+c \right )^{\frac {5}{2}}}{\arctan \left (a x \right )^{2}}d x\]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.19 \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\int { \frac {{\left (a^{2} c x^{2} + c\right )}^{\frac {5}{2}}}{\arctan \left (a x\right )^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 14.73 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\int \frac {\left (c \left (a^{2} x^{2} + 1\right )\right )^{\frac {5}{2}}}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.41 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\int { \frac {{\left (a^{2} c x^{2} + c\right )}^{\frac {5}{2}}}{\arctan \left (a x\right )^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 85.36 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.14 \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\int { \frac {{\left (a^{2} c x^{2} + c\right )}^{\frac {5}{2}}}{\arctan \left (a x\right )^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.41 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {\left (c+a^2 c x^2\right )^{5/2}}{\arctan (a x)^2} \, dx=\int \frac {{\left (c\,a^2\,x^2+c\right )}^{5/2}}{{\mathrm {atan}\left (a\,x\right )}^2} \,d x \]
[In]
[Out]