# 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 $$a$$.

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