Chapter 5.1, Problem 19P

In each of Problems $18$ through $21$, find the Laplace transform of the given function; $a$ and $b$ are real constants. Recall that $\cosh bt=\left(e^{bt}+e^{-bt}\right)/2$ and $\sinh bt=\left(e^{bt}-e^{-bt}\right)/2$.

$\sinh bt$