Inverse Laplace Transform

Sorry if this is in the wrong section.

Basically I am trying to find the inverse laplace transform of

$\displaystyle F(s)=\frac{s}{\left ( s+1 \right )^2+1}$

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

$\displaystyle \frac{1}{2\pi i}\int _\gamma \frac{e^{zt} z}{\left ( z+1 \right )^2+1} dz$

and I found the answer to be

$\displaystyle \left ( \frac{1}{2}+\frac{i}{2} \right )e^{\left ( -1+i \right )t}+\left ( \frac{1}{2}-\frac{i}{2} \right )e^{\left ( -1-i \right )t}$

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.