An Integral Problem (reposted)

Calculus Level 5

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

The equation above is true for constants $$a,b$$ and $$n$$ with coprime positive integers $$a$$ and $$b$$.

Find $$\lfloor (ab)^n \rfloor$$.

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