Question Number 157742 by MathSh last updated on 27/Oct/21
$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{tan}^{-\mathrm{1}} \mathrm{x}\:\centerdot\:\mathrm{Li}_{\mathrm{2}} \left(\frac{\mathrm{1}-\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$