How to Integrate Almost Anything

A free textbook explaining the standard techniques for integration in great detail with a huge number of worked examples.

It is written to be useful as a learning resource as well as a reference book to help with difficult integration problems.  A full index of integrals evaluated allows the reader to locate an example in the text which may resemble any particularly challenging problem.

The book is free to download as a PDF.

Highlights

  • Integration by Substitution.  The book explains this common technique from easy examples to much more difficult ones.  Several different variants of the technique are included.
  • Integration by Parts.  This technique is also explained in great detail, including repeated integration by parts and the use of reduction formulae.
  • Algebraic and Trigonometric Techniques.  Methods including partial fractions, polynomial division and the use of trigonometric formulae are explained with the use of many worked examples.  The treatment of polynomial division includes the use of a particularly useful shorthand tabular approach.
  • All worked examples are given a careful, detailed explanation – no successive lines of algebra with no guidance on how you get from one to the next.
  • Several useful reference appendices are provided, with an additional appendix full of more advanced examples and investigations.
  • A full index of over one hundred worked examples is given to allow the easy location of material relevant to a particular problem.

Prerequisites

To make the most of this book, you will need to know how to differentiate, including use of the Chain Rule, the Product Rule and the Quotient Rule.  You should also know the rules for integrating simple powers of x, as well as the sine and cosine functions.

Any more advanced principles required by the text are explained at the point of use.

Download How to Integrate Almost Anything

You can download the book as a PDF (3.8Mb) free of charge by clicking on the following link:

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Licence

The book is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives International Licence 4.0 http://creativecommons.org/licenses/by-nc-nd/4.0/

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Can You Help?

If you would like to comment on the book in any way, or if find an error in the book, please do let the author know by emailing the address given on the second page of the PDF.