# Who could have done it? 2

Calculus Level 4

$\displaystyle\int_0^1 \frac{x^3}{2(2-x^2)(1+x^2) + 3\sqrt{(2-x^2)(1+x^2)}}\,\mathrm dx=\dfrac{a-b\sqrt{b}}{c}$

Where $$a,b$$ are coprime and $$c$$ is multiple of both $$b,a$$.Find $$a+b+c$$.

Clarification: $$a,b,c$$ are all integers.

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