Question Number 37345 by math khazana by abdo last updated on 12/Jun/18
$${calculate}\:{I}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{\mathrm{1}+{acost}}{\mathrm{1}+\mathrm{2}{acost}\:+{a}^{\mathrm{2}} }{dt}\:\: \\ $$ $$\left.\mathrm{1}\right)\:{if}\:\:\mid{a}\mid<\mathrm{1} \\ $$ $$\left.\mathrm{2}\right)\:{if}\:\mid{a}\mid>\mathrm{1} \\ $$