# Inverse Laplace Transform of Polynomial

I'm trying to find the inverse laplace transform of the following function:

The resulting inverse laplace is in the form:

Not sure where the derivatives came from, or what the inverse laplace of a polynomial is, as I couldn't find it on LT table.

Multiplication by $s$ in the Laplace domain corresponds to differentiation in time. Thus, $f^{(n)}(t) \iff s^n F(s)$.
Similarly, division by $s$ in the Laplace domain corresponds to integration in time.