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Question Number 89240 by Ar Brandon last updated on 16/Apr/20

If I_n =∫_0 ^π e^x sin^n xdx, show that   (n^2 +1)I_n =n(n−1)I_(n−2)

$${If}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\pi} {e}^{{x}} {sin}^{{n}} {xdx},\:{show}\:{that}\: \\ $$$$\left({n}^{\mathrm{2}} +\mathrm{1}\right){I}_{{n}} ={n}\left({n}−\mathrm{1}\right){I}_{{n}−\mathrm{2}} \\ $$

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