Integrate $\int x^2(1-x^2)^{-\frac{3}{2}}dx$

I am tired of trying to evaluate 
$$\int x^2(1-x^2)^{-\frac{3}{2}}dx.$$
I am substituting $x=\sin \theta$, but get stuck in the remaining calculations. A detailed answer would be greatly appreciated. 


Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
The answer is accepted.