Ignited integrals 3

Calculus Level 3

\[ \int_{0}^{1/2}\dfrac{x^{2}}{(1-x^{2})^{3 / {2}}} \, dx\]

Given that the integral above is of the form : \[\dfrac{A\sqrt{B}-\pi }{C},\] where \( A \) and \(C \) are positive integers, \( B \) is a square-free integer, find \( A + B + C \).