Find the inverse Laplace Transform of $F(s) = \frac{(3s^2+9s+14)*e^{-5s}}{(s^3+4s^2+7s)}$
I have found the Simplified $F(s) = (\frac2s+\frac{s+1}{(s+2)^2+3})*e^{-5s}$
I am having trouble figuring out the inverse transform from this point on (I think you have to use $(F(s)*e^{-at})$
How would you go about solving the rest of the transform, knowing which formulas to use.
$e^{-2t}\cos(\sqrt{3}t) - e^{-2t}\sin(\sqrt{3}t) + 2U(t-5)$