Chapter 5.3, Problem 20P

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:

$2\frac{s^3-2s^2+8}{s^2\left(s-2\right)\left(s+2\right)}$

TABLE 5. 3. 1

Elementary Laplace transforms.

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