Question Number 44178 by abdo.msup.com last updated on 22/Sep/18
$${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$