Chapter 5.3, Problem 23P

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:

$\frac{s^3-2s^2-6s-6}{\left(s^2+2s+2\right)s^2}$

TABLE 5. 3. 1

Elementary Laplace transforms.

$\begin{array}{cc}f(t)=L^{-1}\{F(s)\}& F(s)=L\{f(t)\}\\ e^{at}\cos bt& \frac{s-a}{{(s-a)}^2+b^2},s>a\\ t^n,n=\text{positive}\text{integer}& \frac{n!}{s^{n+1}},s>0\end{array}$