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I've started dealing with a lot of (many times nasty) integrals in my research. When there an integral that I can't readily solve using usual methods (like substitution and integration by parts), I try the following sources, in this order:

  1. Gradshtein & Ryzhik 7th ed.

  2. Wofram Functions page

  3. Handbook of Mathematical Functions

  4. Google (which is how I found this website)

I am wondering what sources of help do others employ when faced with difficult integration problems that require analytical solution (other than posting here.)

Thank you!

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DLMF would be the updated Abramowitz and Stegun... – J. M. Sep 12 '11 at 4:57
The Integrals and Series books by Prudnikov, Brychkov, and Marichev would also be a nice compendium. – J. M. Sep 12 '11 at 5:00
In the good old days before the internet, I used to use the Handbook of Mathematics by Bronshtein (whose name is spelled "Bronstein" in the German version). It contains quite a number of integrals, but I don't know whether any of them go beyond the other resources listed; I haven't used it for a while now. – joriki Sep 12 '11 at 5:46
@joriki: I haven't checked my copy in a while to see if it has stuff that the others don't, but it's good to add that to Bullmoose's list anyway. :) Well, that and Jahnke-Emde... – J. M. Sep 12 '11 at 6:01
Thanks everyone for helpful suggestions! And J.M., thanks for the pointer to the DLMF! – M.B.M. Sep 27 '11 at 4:28

Computer algebra systems could be of great help here. For example, Mathematica boasts to be able to solve most of indefinite and definite integrals from books like Gradshtein & Ryzhik.

There is also Wolfram alpha, which uses the Mathematica kernel. But the time spent on a problem is strictly limited, so it doesn't work for more or less complicated expressions.

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But note that a. it remains useful to be skeptical of the results a computing environment spits out, and b. computing environments won't necessarily return the most convenient closed form for a given integral. – J. M. Sep 12 '11 at 8:56

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