Ignited integrals 3

Calculus Level 3

01/2x2(1x2)3/2dx \int_{0}^{1/2}\dfrac{x^{2}}{(1-x^{2})^{3 / {2}}} \, dx

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

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