Inverse Laplace transform of a rational function

Question

Could you please help me the following Inverse Laplace problem

$$\frac{2s^2+4s+3}{s(s^2+s+0.5)}$$

$F(t)$ is required.

Answer 1

Hint: First use partial fraction to get

$$ \frac{6}{s} - \frac{2}{\left( s+1/2+i/2 \right)}-\frac{2}{\left( s+1/2-i/2 \right)}\quad i=\sqrt{-1}$$

then you can use the tables.