Solving an indefinite integral

[GAGS]

Homework Statement

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.

Homework Equations

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.

 

[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>