Chapter 5.3, Problem 22P

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:

$2\frac{s^3+3s^2+4s+3}{\left(s^2+1\right)\left(s^2+4\right)}$

TABLE 5. 3. 1

Elementary Laplace transforms.

$\begin{array}{cc}f(t)=L^{-1}\{F(s)\}& F(s)=L\{f(t)\}\\ \sin at& \frac{a}{s^2+a^2},s>0\\ \cos at& \frac{s}{s^2+a^2},s>0\end{array}$