# Substitution! (8)

Calculus Level 3

$\large \displaystyle \int_0^{1/2} \frac{x^2}{(1-x^2)^{{3} / {2}}} \, dx$

If the value of the integral above can be expressed as $$\dfrac{a \sqrt{b} - \pi}{c}$$, where $$a,b$$ and $$c$$ are integers with $$b$$ square-free, find $$a\times b\times c$$.

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