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

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

**Note**

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

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