What does π\pi have to do with ln\ln integrals ?

Calculus Level 5

01lnx(ln(1x))2xdx=aπbc,\int_0^1 \frac{\ln x \left(\ln(1-x)\right)^2}{x} dx = \frac{-a \pi^b}{c},

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

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