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Homework Statement
I am trying to integrate
\int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} cos(pu) dp.
Homework Equations
I know that
\int^\infty_0 \frac{e^{-tp^2}}{{p^2+b^2}} dp= \frac{\pi}{2b}e^{tb^2}erfc(\sqrt{a}x)
The Attempt at a Solution
I rewrote the problem in terms of the complex exponential and reduced the integrand to a form similar to
\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)
where s is complex but I was stuck here. Any suggestions would be much appreciated.