I did the laplace transform of a function to end up with $\displaystyle \frac{s-se^{-s-1}}{(s+1)(s^2+2s+1)}$, but now I'm stuck. How would I go about finding the inverse laplace transform of that function?
First step in doing the inverse, I think, would be to separate things out:
$\displaystyle \frac{s-se^{-s-1}}{(s+1)(s^2+2s+1)}=\frac{s}{(s+1)(s^2+2s+1)}-\frac{se^{-(s+1)}}{(s+1)(s^2+2s+1)}.$
The denominators all simplify considerably, don't they? Where does that lead?