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

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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