# 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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