Question

I need more work on antiderivatives. Any suggestions on where to find more exercises?

Answer 1

One way to round out your understanding is to take a derivative first and fully simplify before you try to take its antiderivative and work your way back to the initial function. Start with a basic function (you can use the table for basic derivatives at the front of a calculus text for inspiration) and jam some random numbers in various places (I use dice sometimes). Get creative: multiply two functions together, divide two functions, put a function inside another, use a trig identity to change what you start with, etc... I just did 5xtanx. I wound up having to use a hard to remember antiderivative and by parts to get back... endless fun!

Answer 2

I use similar ideas to Euler Groupie as well, however in the beginning and or if you are new to integrals then I would suggest doing all of Pauls online math notes for integrals, start from the beginning and work right through to all the substitutions, after you finish ALL the exercises you will have developed a fairly solid ability to compute antiderivatives. Here is the link to the first page.
http://tutorial.math.lamar.edu/Classes/CalcI/ComputingIndefiniteIntegrals.aspx