integral_04

Calculus Level 5

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

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

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