let-tbe-fraction-F-x-1-x-n-1-with-n-from-n-and-n-2-1-find-the-poles-of-F-and-decompose-it-inside-C-x-2-decompose-F-x-inside-R-x-3-calculate-2-3-F-x-dx-

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Question Number 57234 by maxmathsup by imad last updated on 31/Mar/19

let tbe fraction F(x)=(1/(x^n −1)) with n from n and n≥2 1) find the poles of F and decompose it inside C(x) 2)decompose F(x)inside R(x) 3) calculate ∫_2 ^3 F(x)dx .

$${let}\:{tbe}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{{n}} −\mathrm{1}}\:\:{with}\:{n}\:{from}\:{n}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{poles}\:{of}\:{F}\:{and}\:{decompose}\:{it}\:{inside}\:{C}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){decompose}\:{F}\left({x}\right){inside}\:{R}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{2}} ^{\mathrm{3}} {F}\left({x}\right){dx}\:. \\ $$

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let-tbe-fraction-F-x-1-x-n-1-with-n-from-n-and-n-2-1-find-the-poles-of-F-and-decompose-it-inside-C-x-2-decompose-F-x-inside-R-x-3-calculate-2-3-F-x-dx-

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