TITLE: Finding the inverse laplace transform of $s$
QUESTION [7 upvotes]: How do I find the inverse laplace transform of $s$, i.e. $$L^{-1}\{s\}=\ ?$$

REPLY [8 votes]: $\mathcal{L}^{-1}\{s\}=\delta'(t)$.
More generally:

$\forall n\in\mathbb{Z},~\mathcal{L}^{-1}\{s^n\}=\delta^{(n)}(t)$.