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What the best book to learn about the Feynman technique or Leibnitz's rule about differentiation under Integral sign.

Sometimes you have to pre-decide whether you can solve for the C that comes with Indefinite Integral

Rifat
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    Any real analysis textbook covers that. As for "best", I have no idea what it means.. – AlvinL Jan 28 '20 at 08:15
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    Do you want a book with lots of examples or a book that gives rigorous proofs of various versions of the technique? Off-hand, the best reference I know is Article 118: Integrals containing a parameter (pp. 281-288) in Advanced Calculus by Edwin Bidwell Wilson (1912). I first discovered this method in Wilson's book in 1997, while looking for interesting supplementary ideas for a strong high school honors calculus class I was teaching, and I immediately recognized that this must be what Feynman (continued) – Dave L. Renfro Jan 28 '20 at 08:41
  • @DaveL.Renfro yes kind of like that. Thank you so much ^_^ – Rifat Jan 28 '20 at 08:48
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    was talking about in his book. I'd gotten a copy of Feynman's book in 1985 when it first appeared, and had read it several times by then. I posted a detailed example of this method in sci.math on 8 April 2000, which is probably one of the first times this was explicitly explained on the internet (the only earlier explanation I know are these 1990 posts). – Dave L. Renfro Jan 28 '20 at 08:57
  • @DaveL.Renfro hopefully I'll go through all of them ^_^ – Rifat Jan 28 '20 at 09:11
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    If I get a chance sometime (don't have time now; in fact, leaving home to go somewhere right now), I'll see if I can dig up some more references (for an actual answer), although probably just googling things like "under the integral" and "parameter" with "integration" in google-books or archive.org will give lots of books having sections devoted to this topic. FYI, I have a .pdf scan of a 46 page 1927 MS thesis by Herman Edwin Ellingson, Integrals Containing a Parameter (University of Iowa, under Edward Wilson Chittenden) that contains a lot of examples. See my profile for my email. – Dave L. Renfro Jan 28 '20 at 09:41
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    @DaveL.Renfro this is beyond my expectation, have seen tons of people online, nobody was as helpful as you are, truly grateful – Rifat Jan 28 '20 at 09:44

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