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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 $g(t) = t \cdot f(t)$?

1. $\frac{-s}{(s^2+s+1)^2}$
2. $\frac{-(2s+1)}{(s^2+s+1)^2}$
3. $\frac{s}{(s^2+s+1)^2}$
4. $\frac{2s+1}{(s^2+s+1)^2}$