Integrand size = 22, antiderivative size = 22 \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\text {Int}\left (\frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2},x\right ) \]
[Out]
Not integrable
Time = 0.04 (sec) , antiderivative size = 22, 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 = {} \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx \\ \end{align*}
Timed out. \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\text {\$Aborted} \]
[In]
[Out]
Not integrable
Time = 1.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91
\[\int \frac {\left (a +b \arcsin \left (c x \right )\right )^{\frac {3}{2}}}{\left (e \,x^{2}+d \right )^{2}}d x\]
[In]
[Out]
Exception generated. \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Not integrable
Time = 106.55 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\int \frac {\left (a + b \operatorname {asin}{\left (c x \right )}\right )^{\frac {3}{2}}}{\left (d + e x^{2}\right )^{2}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.74 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\int { \frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{\frac {3}{2}}}{{\left (e x^{2} + d\right )}^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.35 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\int { \frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{\frac {3}{2}}}{{\left (e x^{2} + d\right )}^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b \arcsin (c x))^{3/2}}{\left (d+e x^2\right )^2} \, dx=\int \frac {{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^{3/2}}{{\left (e\,x^2+d\right )}^2} \,d x \]
[In]
[Out]