I have to find the function of the Laplace transform:
s+1 / s^2+4
Can't seem to get to the right answer
You need to use termwise division to get
$\displaystyle \displaystyle \frac{s+1}{s^2+4}=\frac{s}{s^2+4}+\frac{1}{s^2+4}$
The first one should be in you Laplace transform table the 2nd one should not be far away but it will need to be "fixed up" by multiplying and dividing by the right number.
Good luck