Note: Updated on February 13, 2019, by Su Jianlin of Scientific Space (https://kexue.fm), correcting formula 76 and simplifying the LaTeX code.
As research in physics and astronomy deepens, the application of calculus naturally increases (in fact, many fields utilize calculus). When a geometric or mechanical problem arises, one can easily write down an integral or a differential equation; at that point, solving it becomes the most important task. For me, finding derivatives is a straightforward process that can be handled with ease; integration, however, is more difficult. This is partly due to personal skill, but more importantly, it is due to the fact that derivatives have almost universal formulas, while integrals often have to be "manipulated and matched."
Therefore, for many integrals, I simply rely on existing formulas and do not bother to derive them myself. However, a copy of Mathematical Analysis is not always at hand, and I am not particularly proficient with computer mathematics software. In such cases, I can only turn to this "Integral Table." As long as one is not intentionally delving into competition-level mathematical puzzles, this is sufficient to handle applications in physics and other fields.
With this, there is no longer any need to worry about searching everywhere for the result of \int \sqrt{a^2-x^2} \, dx.
Quoting the author:
Once, I needed to look up an integral formula but found nothing on the web. Later, I came across LaTeX and, as a practice exercise, I converted an entire integral table from a book into LaTeX format. In the spirit of "I help others, others help me," I am dedicating this complete collection of integral formulas to everyone.
A few notes:
All formulas in this attachment are taken from Higher Mathematics (Third Edition).
Book Information: Edited by the Department of Mathematics, Tongji University, published by Higher Education Press, April 1988, Third Edition, ISBN 7-04-000894-7/O.344.Although the creator of the .tex file has carefully proofread all formulas, the creator does not guarantee the correctness of all formulas and assumes no responsibility for any losses caused by the use of these formulas.
Creator of the .tex file: liangbch. Last updated: 2008-04-02. This document was first published on April 3, 2008, at the Mathematics R&D Forum. Please credit the source when reprinting.
Source: http://bbs.emath.ac.cn/viewthread.php?tid=293
When reprinting, please include the original address of this article: https://kexue.fm/archives/354
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