These problems are basically plug-and-chug once you get the hang of them. This first video covers most of the problems you'll see, where a power of x is multiplied by an exponential or trig function. Beware: teachers love to mess with your head by putting straightforward U-sub problems on quizzes and tests about Integration By Parts, so keep your eye out for that!
Integration By Parts: Natural Logs
This video is just for problems that have an ln in the integral, because it's such a common type of trick problem. Why are they tricky? Because often they're just U-sub problems in disguise, and the rest of the time they're the opposite of a normal Integration By Parts scenario. This video explains the difference, and how to defeat your teacher's trickery.
Advanced Integration By Parts Problems
This video covers integration of arctan, and what to do when you have an exponential multiplied by a trig function. Both are tricky, but the second is more likely to show up on your quiz or test!
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)