integral_04

Calculus Level 5

0ln(x)1x2dx\int _{ 0 }^{ \infty }{ \frac { \ln { ( } x) }{ 1-x^{ 2 } } dx }

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

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

inspired by Vishwak Srinivasan

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