Sunday, 6 April 2014

Standard tricks for integration

To access the document version of the notes please go to the "Notes Corner" or my personal site directly.

Why do I make the list

For most of the textbook the tricks are usually classified into (1) standard result (the most obvious stuff) (2) substitution and (3) by part. For normal students a systematic way is required to learn which trick (in detail) to be used and how against different integral. I tried to list all the standard tricks via a standard form so that readers may realize the pairing up between tricks and integrals.

Abstract

This document aims to provide standard tricks to do proper integration. Most of them are making good use of various identities, which should have been well known to readers. The following list is a selection of integrals, that provides the most common tricks to tackle inegral. It is expected that readers should try to learn and apply the tricks, rather than to recite the integration formulae. Here we only cover indefinite integral, that maximizes the extend to find a closed form of a given integral, but there are many more tricks also applicable for definte integral and readers may want to master them as well.

About the content

There are 9 sections in the list, namely (1) Basic theory (2) differential results (3) ordinary substitution (4) By part (5) Trigonometric substitution (6) Fractions (7) Recursion (8) Complex method (9) tan x/2 substitution.

The first 7 parts are somewhat expected for an AL student or first year undergraduates, and the last two are still standard tricks but less common. I found one related questions from AL Pure 2003 about the tan x/2 substitution, but the substitution is instructed in the paper so that it's not very fun, though.

If there are any typos, or any tricks that you think I should/should not include here, just tell me here.

Chris
Apr., 2014

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