Find the Inverse Laplace Transforms Find the inverse Laplace transform of:
$$\frac{3s+5}{s(s^2+9)}$$
Workings:
$\frac{3s+5}{s(s^2+9)}$
$= \frac{3s}{s(s^2+9} + \frac{5}{s(s^2+9)}$
$ = \frac{3}{s^2+9} + \frac{5}{s}\frac{1}{s^2+9}$
$ = \sin(3t) + \frac{5}{s}\frac{1}{s^2+9}$
Now I'm not to sure on what to do.
Any help will be appreciated.

$\frac{3s+5}{s(s^2+9)} = -\frac{5}{9} \frac{s}{s^2+9} + \frac{2}{3}\frac{3}{s^2+9}+\frac{5}{9}\frac{1}{s}$ with ILT $-\frac{5}{9}\cos(3t)+\frac{2}{3}\sin(3t)+\frac{5}{9}step(t)$
