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 .

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 totellhim 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 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.