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∫01(lnx)2(1−x)2 dx \displaystyle \large \int_{0} ^{1} \dfrac{(\ln x)^2}{(1-x)^{2}} \, dx ∫01(1−x)2(lnx)2dx
If the value of the integral above equals πa!a+1\dfrac{\pi ^{a!}}{a+1}a+1πa!, where aaa is a positive integer, find aaa.
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