# Trying to impress my girlfriends father - working needed

• Oct 19th 2011, 12:32 PM
HappyMonkeys
Trying to impress my girlfriends father - working needed
Hello

I am trying to answer a question for my girlfriends father but am failing. Could someone please show the working for this. I will obviously give credit to the forum rather than taking for it myself.

Integral (between infinity and -infinity) cos(x)/1+x(2) dx = pie/e

Sorry I am working on Latex as I speak.

Without the spaces in [ tex ] and [ \tex ] it would be $\int_{-\infty}^\infty \frac{cos(x)}{x^2+ 1}dx$.
I might feel it was wrong to get other people to help you with a problem to impress your girlfriend's father (are you planning to tell him what help you got?) except for a feeling that he is putting you on. I don't believe that can be integrated in terms of "elementary function". Writing $cos(x)= \frac{e^{ix}+e^{-x}}{2}$ and doing it in terms of a path integral, say on a path that goes from -R to R on the real line, then along the semi-circle, in the positive imaginary half plane, of radius R from R to -R, might give something, finally taking the limit as R goes to infinity.