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∫01/2x2(1−x2)3/2 dx \int_{0}^{1/2}\dfrac{x^{2}}{(1-x^{2})^{3 / {2}}} \, dx∫01/2(1−x2)3/2x2dx
Given that the integral above is of the form : AB−πC,\dfrac{A\sqrt{B}-\pi }{C},CAB−π, where A A A and CC C are positive integers, B B B is a square-free integer, find A+B+C A + B + C A+B+C.
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