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Question Number 44178 by abdo.msup.com last updated on 22/Sep/18

find  f(x)=∫_0 ^π   ((sin^2 t)/((x^2 −2x cost +1)^2 ))dt  2)find the value of ∫_0 ^π   ((sin^2 t)/((x^2 −cost +1)^2 ))dt

$${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$

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