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Hi, I am having some difficulties integrating the following expression..

[tex]\int\int\left(\frac{k}{\pi}\right)^2 \frac{1}{k^2+\omega'^2}\frac{1}{k^2+\omega^2}e^{-i\omega'\tau}e^{i\omega\tau}d\omega d\omega'[/tex]

I've tried by part but it doesn't look like it's going to give me the right answer which is

[tex]e^{-2k|\tau|}[/tex]

Omega and Omega primed can be integrated from -infinity to infinity ... if that helps

Any ideas?

[tex]\int\int\left(\frac{k}{\pi}\right)^2 \frac{1}{k^2+\omega'^2}\frac{1}{k^2+\omega^2}e^{-i\omega'\tau}e^{i\omega\tau}d\omega d\omega'[/tex]

I've tried by part but it doesn't look like it's going to give me the right answer which is

[tex]e^{-2k|\tau|}[/tex]

Omega and Omega primed can be integrated from -infinity to infinity ... if that helps

Any ideas?

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