# Solving an indefinite integral

1. Dec 14, 2008

### GAGS

1. The problem statement, all variables and given/known data

1. The calculation of the probability of excitation of an atom originally in the
ground state to an excited state, involves the contour integral
INTEGRAL(-INF TO +INF) [S exp(iwt)/(t2 + s2)2dt
Evaluate the above integral.

2. Relevant equations

3. The attempt at a solution
Attempt: what i know that LAPLACE TRANSFORM OF (COS at) = s/(s2+ a2)
Moreover this integral is looking inverse FOURIER TRANSFORM, But how to solve it. I am not getting it.

2. Dec 14, 2008

### CompuChip

Well, you mentioned the term "contour integral" and then wrote an integral over the real axis. So I guess the point is that you make it into a contour integral (close the integration by an infinitely large semi-arc in the complex plane) and use calculus of residues to evaluate it. Have you seen / done this before?

<nitpick>By the way, it is an improper integral, but not an indefinite one.</nitpick>