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find-A-n-0-dx-1-x-2-n-with-n-from-N-




Question Number 29447 by prof Abdo imad last updated on 08/Feb/18
find   A_n =    ∫_0 ^∞    (dx/((1+x^2 )^n ))  with n from N^★ .
$${find}\:\:\:{A}_{{n}} =\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$

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