Finding inverse laplace of a rational polynomial function

Question

I've been looking at this problem for a few hours now and can't figure out a way to solve it. Does anyone have any suggestions? Thanks for any help.
$$\mathscr{L}^{-1}\{\frac{(2s^2+9s+11)}{(s^3+5s^2+9s+5)}\}$$

Answer 1

Hint: Do a partial fraction expansion, yielding:

$$\mathcal{L}^{-1}\left({\dfrac{2s^2+9s+11}{s^3+5s^2+9s+5}} \right) = \mathcal{L}^{-1} \left( \dfrac{2}{s+1} + \dfrac{1}{s^2 + 4 s + 5}\right)$$

This reduces to:

$$\mathcal{L}^{-1} \left(\dfrac{2}{s+1} + \dfrac{1}{(s-(-2))^2 + 1^2}\right)$$

Now, use a Table of Laplace Transforms or use the definitions to find the inverse.