Is the information below correct?
Find the inverse Laplace transform of $ F(s) = \frac{s}{s^2 + 4s + 13}$
Soln: a) Complete the squares to simplify our denominator $ s^2 + 4s + 13 = (s+2)^2 + 9 = (s+2)^2 + 3^2$ $\mathscr{L}^{-1}\left\{F(s)\right\} = \frac{s}{(s+2)^2 + 3^2}. $ From the table we can deduce that this is $\mathscr{L}^{-1}\left\{F(s)\right\} = e^{-2t} \cos(3t).$