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

I am trying to integrate

[tex]\int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} cos(pu) dp[/tex].

2. Relevant equations

I know that

[tex]\int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} dp= \frac{\pi}{2b}e^{tb^2}erfc(\sqrt{a}x)[/tex]

3. The attempt at a solution

I rewrote the problem in terms of the complex exponential and reduced the integrand to a form similar to

[tex]\int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} cos(pu) dp= Re(\int^\infty_0 \frac{e^{-t(p-s)^2}}{{p^2+b^2}} dp)[/tex]

where s is complex but I was stuck here. Any suggestions would be much appreciated.

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# Tricky semi-infinite integral

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