Question Number 142613 by Rankut last updated on 02/Jun/21
$$\boldsymbol{\mathrm{Evaluate}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{log}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}}\right)}{\:\sqrt{\frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}}}}\boldsymbol{\mathrm{dx}} \\ $$$$ \\ $$