Inverse Laplace transform of a function

[Punch]

I can't seem to find the ways to solve the inverse laplace transform of: $\displaystyle \, \dfrac{s^2\, +\, 2}{s^2\, +\, 2s\, +\, 5}$

I used completing square to make it become: $\displaystyle \, \dfrac{s^2\, +\, 2}{(s\, +\, 1)^2\, +\, 4}$

The inverse laplace transform of: $\displaystyle \, \dfrac{2}{(s\, +\, 1)^2\, +\, 4}$
is e^-t sin2t.

I am struck with: $\displaystyle \, \dfrac{s^2}{(s\, +\, 1)^2\, +\, 4}$

I do not know what to do next.

The final answer is ?(t) -(e^-t/2 )(4cos2t + sin2t). However, I don't understand what the Dirac delta function is for. Can you guys help me? Thanks in advance.