Integrand size = 29, antiderivative size = 29 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\text {Int}\left (\frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}},x\right ) \]
[Out]
Not integrable
Time = 0.10 (sec) , antiderivative size = 29, 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 = {} \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx \\ \end{align*}
Not integrable
Time = 4.56 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx \]
[In]
[Out]
Not integrable
Time = 0.37 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93
\[\int \frac {x^{m} \left (a +b \arcsin \left (c x \right )\right )^{2}}{\left (-c^{2} d \,x^{2}+d \right )^{\frac {5}{2}}}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.83 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\int { \frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2} x^{m}}{{\left (-c^{2} d x^{2} + d\right )}^{\frac {5}{2}}} \,d x } \]
[In]
[Out]
Not integrable
Time = 152.97 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\int \frac {x^{m} \left (a + b \operatorname {asin}{\left (c x \right )}\right )^{2}}{\left (- d \left (c x - 1\right ) \left (c x + 1\right )\right )^{\frac {5}{2}}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.66 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\int { \frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2} x^{m}}{{\left (-c^{2} d x^{2} + d\right )}^{\frac {5}{2}}} \,d x } \]
[In]
[Out]
Exception generated. \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {x^m (a+b \arcsin (c x))^2}{\left (d-c^2 d x^2\right )^{5/2}} \, dx=\int \frac {x^m\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2}{{\left (d-c^2\,d\,x^2\right )}^{5/2}} \,d x \]
[In]
[Out]