Chapter 5.3, Problem 10P

In each of Problems 9 through 24, using the linearity of $L^{-1}$, partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function:

$\frac{4}{{\left(s-3\right)}^3}$

TABLE 5. 3. 1

Elementary Laplace transforms.

$\begin{array}{cc}f(t)=L^{-1}\{F(s)\}& F(s)=L\{f(t)\}\\ t^n{e}^{at},n=\text{positive}\text{integer}& \frac{n!}{{(s-a)}^{n+1}},s>0\end{array}$