Find the inverse laplace transform :
If you mean Bromwich style, then look at this one first:
where is the contour below. It doesn't matter if this one doesn't have an inverse transform. Just first figure out how the integrand varies across the (finite) red-blue and yellow-green branch-cuts and also the remaining parts of the contour. Then try and extend that work to above. However, this may not be the best contour to use.