Inverse Laplace Transform

Sorry if this is in the wrong section.

Basically I am trying to find the inverse laplace transform of

using the bromiwich integral and the standard bromwich contour. I therefore used the residue theorem to evaluate

and I found the answer to be

Which I believe is right, however when I try to show that the curved part of the contour goes to zero as R tends to infinity I find that it does not, and so my answer if not what I want.

Now I have been looking at ways around this and jordans lemma keeps appearing, although I really have no idea how to apply it (or even if this is the right approach), could someone please explain it or point me in the right direction?

Thanks,

Lewis.