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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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    Thanks everyone for helpful suggestions! And J.M., thanks for the pointer to the DLMF!2011-09-27

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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.2019-04-20