I have the next integral: $\int_{-\infty }^{\infty }\frac{e^{ik(x-x')}}{m^{2}+k^{2}}dk$.
I want to use Jordan's lemma to solve this integral so I started with proving that I can use it. I know that we can use Jordan's lemma if $\lim_{|x| \to \infty}f(x)=0$.
In my case: $\lim_{|x-x'| \to \infty}\frac{1}{m^{2}+k^{2}}=0$
But I don't see how can I prove it.