Integration training? I've been pretty frustrated lately with my poor integration skills. A lot of times I find that in my math or physics classes I understand the concepts behind a question, reduce it to an integral, and then find myself unable to solve it. Yet some people both on this board and at my university are deft hands at solving complicated integrals with a variety of tricks. I'd really like to get better at integrals and start approaching their level. I was hoping that there might be suggestions of workbooks or textbooks that are designed purely on increasing the reader's ability to solve difficult integrals, and also suggestions on a good general philosophy to take to get better at this as well. 
Also, I'm unsure if this is the wrong place to ask this question. If so, I apologize and I'll remove the question. 
 A: I'd have to agree with the other answer, I do not consider myself to be an integration master, nowhere near one, however your "basic" (avoiding things like residue and other crazy stuff) difficult integrals I can do fairly easily. I saw a certain beauty to an integral which motivated me from going to your basic reverse power rule to u subs, some interesting trig substitutions, and I would practice with those. Once you can handle those you can escalate, I liked looking for difficult integrals and then looking at how someone else solved them to add a new technique to my toolbox. So to sum all this up, start small and then master the little things, from there try and like google "really hard integrals" and see if you can see how those are done and then practice with more difficult stuff. (When you're ready for the big leagues MIT has an amazing integration bee whose problems and solutions are online)
A: I suggest doing the exercises in Spivak's Calculus, in the "techniques of integration" chapter. When you've done all of those, you'll be a pretty solid integrator. (BTW, almost none are easy). I guess the short form of this is "practice makes perfect, but only if you practice stuff you don't already know." 
