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Question about Inverse Laplace transforms

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I have a transform F(s) of which I need the inverse transform for. The form of the transform is not of a common form and I am having trouble reducing it to a workable form.

I am looking at a problem that requires the inverse laplace transform of f(t) to be found using the following transform:

F(s) = (s*e^(-s/2))/(s^2 + pi^2)

I assume that I have to use partial fractions, but am unsure exactly how to tackle the problem. Further, should this reduce down into a single transform or a product set of Laplace transforms. I have taken a simpler inverse transform

F(s) = e^(-bs)/s^2

and separated it into two separate laplace transforms

F(s) = e^(-bs)/s x 1/s

the inverse transform of these individually are u_c(t) and 1 respectively which would make the inverse transform equal to u_c(t). If my understanding is wrong please address it in the first problem addressed above. Thanks.

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This solution demonstrates finding the answer regarding inverse Laplace Transforms and partial fractions.

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