Appears as an exercise on page 505 of this (excellent and freely downloadable, at least for now) book: https://link.springer.com/book/10.1007%2F978-3-319-01195-0.

From my time at the uni, I wish we'd had a proper course that covered Laplace (and the important special cases, e.g. Fourier and z) transforms properly. Instead, the coverage was interspersed to general math courses and to the courses that needed to apply them.