Integrand size = 20, antiderivative size = 20 \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\text {Int}\left (\frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2},x\right ) \]
[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 = {} \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx \\ \end{align*}
Not integrable
Time = 53.03 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx \]
[In]
[Out]
Not integrable
Time = 4.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (e \,x^{2}+d \right )^{2} \left (a +b \arcsin \left (c x \right )\right )^{2}}d x\]
[In]
[Out]
Not integrable
Time = 0.25 (sec) , antiderivative size = 98, normalized size of antiderivative = 4.90 \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\int { \frac {1}{{\left (e x^{2} + d\right )}^{2} {\left (b \arcsin \left (c x\right ) + a\right )}^{2}} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 2.63 (sec) , antiderivative size = 439, normalized size of antiderivative = 21.95 \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\int { \frac {1}{{\left (e x^{2} + d\right )}^{2} {\left (b \arcsin \left (c x\right ) + a\right )}^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 7.94 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\int { \frac {1}{{\left (e x^{2} + d\right )}^{2} {\left (b \arcsin \left (c x\right ) + a\right )}^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{\left (d+e x^2\right )^2 (a+b \arcsin (c x))^2} \, dx=\int \frac {1}{{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2\,{\left (e\,x^2+d\right )}^2} \,d x \]
[In]
[Out]