How does one approach a integral such as this $\int _0^{\infty }\frac{\left(\ln x\right)^2}{\sqrt{x}\left(1-x\right)^2}\text{dx}$?
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$