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Question Number 103080 by abdomsup last updated on 12/Jul/20

calculate A_n =∫_0 ^∞  ((cos(nx))/((1+x^2 )^n ))dx  with n integr natural

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }{dx} \\ $$$${with}\:{n}\:{integr}\:{natural} \\ $$

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