Chapter 5.3, Problem 21P

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:

$12\frac{s^2-7s+28}{\left(s^2-8s+25\right)\left(s+3\right)}$

TABLE 5. 3. 1

Elementary Laplace transforms.

$\begin{array}{cc}f(t)=L^{-1}\{F(s)\}& F(s)=L\{f(t)\}\\ e^{at}& \frac{1}{s-a},s>a\\ e^{at}\sin bt& \frac{b}{{(s-a)}^2+b^2},s>a\end{array}$