Integrand size = 18, antiderivative size = 18 \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\text {Int}\left (\frac {1}{(d x)^{3/2} (a+b \arcsin (c x))},x\right ) \]
[Out]
Not integrable
Time = 0.02 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx \\ \end{align*}
Not integrable
Time = 0.79 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx \]
[In]
[Out]
Not integrable
Time = 0.08 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89
\[\int \frac {1}{\left (d x \right )^{\frac {3}{2}} \left (a +b \arcsin \left (c x \right )\right )}d x\]
[In]
[Out]
Not integrable
Time = 0.23 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.72 \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\int { \frac {1}{\left (d x\right )^{\frac {3}{2}} {\left (b \arcsin \left (c x\right ) + a\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 3.48 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{\left (d x\right )^{\frac {3}{2}} \left (a + b \operatorname {asin}{\left (c x \right )}\right )}\, dx \]
[In]
[Out]
Not integrable
Time = 0.51 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\int { \frac {1}{\left (d x\right )^{\frac {3}{2}} {\left (b \arcsin \left (c x\right ) + a\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\int { \frac {1}{\left (d x\right )^{\frac {3}{2}} {\left (b \arcsin \left (c x\right ) + a\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.09 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(d x)^{3/2} (a+b \arcsin (c x))} \, dx=\int \frac {1}{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )\,{\left (d\,x\right )}^{3/2}} \,d x \]
[In]
[Out]