Find the Laplace inverse of the following. $$
\frac{2s+5}{s^2+6s+34}
$$
I am stuck on this part:
Wolfram has the step by step showing that you simply split up the original fraction into 
$$
\frac{2s}{s^2+6s+34} + \frac{5}{s^2+6s+34}
$$
and then it solves it. But that doesn't help. Could someone please help me understand how to do this problem?

Consider the following.
\begin{align}
\frac{2s+5}{s^2+6s+34} = \frac{2 s + 5}{ (s+3)^{2} + 5^{2}} = 2 \, \frac{(s+3)}{(s+3)^{2} + 5^{2}} - \frac{1}{5} \, \frac{5}{(s+3)^{2} + 5^{2}}
\end{align}
Now, for
\begin{align}
f(s) \doteqdot \int_{0}^{\infty} e^{-st } \, f(t) \, dt,
\end{align}
then
\begin{align}
\frac{2s+5}{s^2+6s+34} \doteqdot 2 e^{-3t} \, \cos(5 t) - \frac{1}{5} \, e^{-3t} \, \sin(5t).
\end{align}
