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Calculus Level 5

01ln(x)1x2dx\large \int_{0}^{1} \dfrac{\ln( x)}{1-x^2} \, dx

The above integral is equal to aπbc\dfrac{-a\pi^b}{c} for positive integers a,b,ca,b,c, for positive integers a,ba,b and cc with aa and cc coprime. Evaluate (a+b+c)2(a+b+c)^2.


You are given that ζ(2)=π26\zeta(2) = \dfrac{\pi^2}{6} .

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