What are partial fractions used for in real life? ... ?

If you are going into electrical or mechanical engineering, you will soon find that the method of partial fractions is used not only for finding integrals, but also for analyzing linear differential systems like resonant circuits and feedback-control systems. If you have an interest in these fields, consider taking some extra time now to learn the method of partial fractions well, so you won't have to waste time relearning it when you get to your circuits or linear systems courses.