Mystery Zeta

Calculus Level 5

\[ \large \int_0^1 \dfrac{ \ln(1-x) \ln(1+x) } x \, dx \]

If the value of the integral above is equal to \( -\dfrac ab \zeta (c) \), where \(a,b\) and \(c\) are positive integers with \(a,b\) coprime, find \(a+b+c\).

Notation: \(\zeta(\cdot) \) denotes the Riemann zeta function.

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