(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the integral [tex] I(k)= \int_{-\infty}^{\infty} \frac{dx}{(x^{2}+1)^{k}} [/tex] with 'k' being a real number

2. Relevant equationsthe integral equation above

3. The attempt at a solution

from the residue theorem , there is a pole of order one at [tex] 2+ix=0 [/tex] , my problem is the pole of order 'k' at s=i and s=-i , in order to handel with this pole i have thought that using residue theorem

[tex] \frac{1}{\Gamma(s)}D^{k-1}((s-i)^{k}\frac{1}{(x^{2}+1)^{k}} [/tex]

evaluated at both s=i and s=-i

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# Homework Help: Residue theorem appliation

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