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I am searching for two kinds of books.

(1) Comprehensive books that collect, explain, and provide many examples (that is, fully worked problems) of advanced integration techniques (that is, something at the level of difficulty of the tables written by Gradshteyn and Ryzhik, but obviously with explanations, examples and proofs).

(2) Comprehensive books that collect, explain, and provide many examples (that is, fully worked problems) of really unusual and slick integration techniques (which may however not be so advanced or use special functions).

Can you point out some good references?

Related question: "Really advanced techniques of integration (definite or indefinite)".

Remark: Clearly, an answer should add some references that have not been mentioned yet (either in the comments or in the related thread),.

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Dal
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    http://www.amazon.com/gp/aw/d/0521791863?pc_redir=1410176046&robot_redir=1 – ClassicStyle Oct 05 '14 at 14:13
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    Some suggestions:

    [1] G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004.

    [2] I. S. Gradshteyn, I. M. Ryzhik, and D. Zwillinger (editor), Table of Integrals, Series, and Products, 8th edition, Academic Press, New York, 2008.

    [3] P. J. Nahin, Inside Interesting Integrals, Springer, New York, 2014.

    [4] D. Zwillinger, The Handbook of Integration, A K Peters/CRC Press, Boston, 1992.

     –  Oct 09 '14 at 13:47
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    Also, you can have a look at the references listed here. –  Oct 09 '14 at 13:48
  • Thank you very much for these valuable references. – Dal Oct 09 '14 at 14:51
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    I know you don't have the background yet, but this book, though expensive, is quite a treasure chest: http://www.amazon.com/The-Cauchy-Method-Residues-Applications/dp/9027716234 – Ron Gordon Oct 10 '14 at 13:23
  • @RonGordon I'll keep it in mind for when the time comes :) – Dal Oct 10 '14 at 13:28
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    Also, check this answer out as well. http://math.stackexchange.com/questions/765198/some-users-are-mind-bogglingly-skilled-at-integration-how-did-they-get-there/769444#769444 – Ron Gordon Oct 10 '14 at 13:36
  • @RonGordon Wow. I'm simply amazed: that is a great answer. Again, thank you very much for being here. – Dal Oct 10 '14 at 13:45
  • Some of my notes http://folk.ntnu.no/oistes/Diverse/Integral%20Kokeboken.pdf =) – N3buchadnezzar Oct 11 '14 at 09:46

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I think the collected works of Ron Gordon on math.stackexchange is definitely worth mentioning!!

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JP McCarthy
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