$3^{-t}$ is that a mistake? Should it instead be $3e^{-t}$?

Here's what I get;

$\mathcal{L}^{-1} \{ \frac{3s+2}{(s+1)^2 +3^2} \}$

add $+1$, $-1$ to the numerator

$\mathcal{L}^{-1} \{ \frac{3s+2+1-1}{(s+1)^2 +3^2} \}$

Group and carry out the division

$\mathcal{L}^{-1} \{ \frac{3s+3}{(s+1)^2 +3^2} \} - \mathcal{L}^{-1} \{ \frac{1}{(s+1)^2 +3^2} \}$

$ 3 \mathcal{L}^{-1} \{ \frac{s+1}{(s+1)^2 +3^2} \} - \frac{1}{3} \mathcal{L}^{-1} \{ \frac{3}{(s+1)^2 +3^2} \}$

$ 3 e^{-t}\mathcal{L}^{-1} \{ \frac{s}{(s)^2 +3^2} \} - \frac{1}{3}e^{-t} \mathcal{L}^{-1} \{ \frac{3}{(s)^2 +3^2} \}$

Since $\mathcal{L} \{ cos(\omega t) \}= \frac{s}{(s)^ +\omega^2}$ and $\mathcal{L} \{ sin(\omega t) \}= \frac{\omega}{(s)^2 +\omega^2} $ we have,

$3e^{-t} cos(3t) -\frac{1}{3}e^{-t}sin(3t)$