Inverse Laplace Transform of Discontinuous Function I'm currently studying transform of discontinuous and periodic functions (Differential Equations.) I was presented with the following question.
$$\dfrac{se^{-3s}}{s^2+4s+5}$$
(Sorry, I couldn't get the formatting to work properly. Feel free to fix it. ) 
I've identified $F(s)$ as:
$$\dfrac{s}{s^2+4s+5}$$
but I'm a little stuck on how to find the inverse Laplace transform of this. Do I complete the square? I'd appreciate some advice here. Thanks. 

Completing the square is a great way to go.  We could say
$$
\begin{align}
\frac{s}{s^2+4s+5} &=
\frac{s}{(s+2)^2+1} \\ &=
\frac{(s+2)-2}{(s+2)^2+1} \\ &=
\frac{(s+2)}{(s+2)^2+1} - \frac{2}{(s+2)^2+1}
\end{align}
$$
Where could you go from there?
