# What does $$\pi$$ have to do with $$\ln$$ integrals ?

Calculus Level 5

$\int_0^1 \frac{\ln x \left(\ln(1-x)\right)^2}{x} dx = \frac{-a \pi^b}{c},$

where $$a,b,c$$ are positive integers and $$\gcd(a,c)=1.$$ Find $$a+b+c.$$

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