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I am trying to determine two Melnikov Integrals (after some manipulation) of the form:

[tex]\int^{\infty}_{-\infty}cos(at)sech(bt) dt[/tex]

and

[tex]\int^{\infty}_{-\infty}cos(at)sech^{3}(bt) dt[/tex]

The textbook I've been reading (Litchenberg & Libermann), says that the way to integrate similar problems is to use the method of residues. I have a superficial understanding of how that works, but every other time I've used the method of residue I've dealt with rationale functions so that I could find poles and then just apply apply the Cauchy integral formula at the isolated poles.

Can anyone give me a kick-start on how to begin solving these 2 integrals by the method of residues ?