JEE Math Practice Question

If the value of the integral $$\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$$ is $${k \over 6}$$, then k is equal to :

1. A.$$2\sqrt 3 + \pi $$
2. B.$$3\sqrt 2 - \pi $$
3. C.$$3\sqrt 2 + \pi $$
4. D.$$2\sqrt 3 - \pi $$