Question Number 100980 by bachamohamed last updated on 29/Jun/20
$$\:\:\:\:{prove}\:{that}\:\:\int_{−\infty} ^{+\infty} \left(\frac{\mathrm{1}}{\mathrm{1}+\left(\boldsymbol{{x}}+\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)\right)^{\mathrm{2}} }\boldsymbol{{dx}}\right)=\boldsymbol{\pi}\: \\ $$