You may find the following notes and other materials helpful.
“Notes on Diffy Qs: Differential Equations for Engineers”
These notes, by Prof. Ji?r´? Lebl for his course at the University of Illinois, include additional examples. You may download it at no cost from his web site.
Table of Laplace transforms
This table is the same table used in class.
The final exam booklet will include this table or an abbreviated version of it sufficient to do the problems. So will quizzes where the table is relevant.
Of course you should still learn how to compute Laplace transforms from the definition as in improper integral.)