The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. Which one of the following is the unilateral Laplace transform of $g(t) = t \cdot f(t)$?
- $\frac{-s}{(s^2+s+1)^2}$
- $\frac{-(2s+1)}{(s^2+s+1)^2}$
- $\frac{s}{(s^2+s+1)^2}$
- $\frac{2s+1}{(s^2+s+1)^2}$