All Roads Lead To $\pi$

Calculus Level 3

$\displaystyle \large \int_{0} ^{1} \dfrac{(\ln x)^2}{(1-x)^{2}} \, dx$

If the value of the integral above equals $\dfrac{\pi ^{a!}}{a+1}$ , where $a$ is a positive integer, find $a$ .

All Roads Lead To π\piπ