Where can I find the derivation of all integral formulae?

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Discussion Overview

The discussion revolves around the search for a comprehensive source that provides the derivation of integral formulae commonly found in calculus textbooks and online resources. Participants express interest in understanding the derivation process rather than just the formulae themselves.

Discussion Character

  • Exploratory, Debate/contested

Main Points Raised

  • One participant notes that integral formulae are typically listed in textbooks or websites, such as Wikipedia, but expresses a desire to see the derivations of these formulae.
  • Another participant shares a link to a website that aims to compile proofs of integrals from the Gradshteyn and Ryzhik integral tables, although they mention that there are still many gaps in the content.
  • A different participant comments that the website only provides an outline rather than complete derivations.
  • One participant raises a concern about the lack of consensus on what constitutes "all the integral formulae," pointing out that different integral tables vary in what they consider fundamental and what can be derived from existing integrals.

Areas of Agreement / Disagreement

Participants express differing views on the availability and completeness of integral derivations, with no consensus on what "all the integral formulae" entails.

Contextual Notes

The discussion highlights the variability in integral tables and the subjective nature of what is considered fundamental, indicating that assumptions about the completeness of integral formulae may differ among participants.

swampwiz
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There is usually a set of integral formulae that is listed in a calculus textbook or website (such as Wikipedia.) I'd like to see the derivation of all those formulae. Yes, I know that they use various combinations of integration by substitution and integration by parts, but I'd like to see exactly how they are derived.

Does anyone know a website where all (or at least a number of) these integral formulae are so presented?
 
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This website is an attempt to compile proofs of all integrals listed in the Gradshteyn and Ryzhik integral tables:

http://129.81.170.14/~vhm/Table.html"

There are still lots of gaps to be filled in though!
 
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I went through that website, and the only thing up seems to be the outline!
 


I doubt that there is such any consensus as to what "all the integral formulae" would be! Different tables of integrals differ as to what is "fundamental", and are given, and what can be derived fairly easily from the given integrals.
 

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