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proof-that-dx-x-2-ax-a-2-x-2-bx-b-2-equals-2pi-a-b-3ab-a-2-ab-b-2-




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

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