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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.

Thanks in advance

Matthew

Re: Trying to impress my girlfriends father - working needed

The LaTeX for that would be [ tex ]\int_{-\infty}\infty \frac{cos(x)}{x^2+ 1}dx[ /tex ]

Without the spaces in [ tex ] and [ \tex ] it would be $\displaystyle \int_{-\infty}^\infty \frac{cos(x)}{x^2+ 1}dx$.

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 $\displaystyle cos(x)= \frac{e^{ix}+e^{-x}}{2}$ 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.

Re: Trying to impress my girlfriends father - working needed

Thank you for the LaTeX, I did say in my question that I would give all credit to the forum. The post title was being playful that's all.