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Q&A #4268 |
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I guess all integration is an art in some sense. Once you get beyond the easy ones, everything is a matter of substitution in some form or another. I guess I think of integration by parts as a substitution approach because it requires us to pick functions to represent u, and dv, etc. The best advice I can give you is to study lots of examples, and develop an arsenal of approaches, then, "if it looks like a duck" try what you would try for ducks. I'm sorry if that seems like not much help, but sometimes integration reminds me of geometry proofs, you stare at a proof and try lots of stuff and seem to get nowhere, then someone says "draw this line" and all is clear. Sometimes with integrals, its easy if you see what substitution to make, but seeing the right substitution is that "magic" part of genius that Marc Kac spoke of. good luck -Pat Ballew, for the Teacher2Teacher service Visit us again at http://mathforum.com/t2t/
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