Question Number 108305 by Sayantan chakraborty last updated on 16/Aug/20
$${proof}\:{that}\underset{−\infty} {\overset{\infty} {\int}}\frac{{dx}}{\left({x}^{\mathrm{2}} +{ax}+{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} +{bx}+{b}^{\mathrm{2}} \right)}\:{equals}\:\:\frac{\mathrm{2}\pi\left(\mathrm{a}+\mathrm{b}\right)}{\:\sqrt{}\mathrm{3ab}\left(\mathrm{a}^{\mathrm{2}} +\mathrm{ab}+\mathrm{b}^{\mathrm{2}} \right)}. \\ $$