| Basic Conceptions |
Primitives and Indefinite Integrals
Properties of Integrals
| Properties: Explanatory Comments |
Transformation of a Table of Common Derivatives to a Table of Integrals
A Table of Common Integrals
| Integration |
Techniques of Integration
| Integration by Substitution | ||
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Integration by Parts |
| Integration of Rational Functions |
Basic Conceptions
Integration of Partial Fractions
Partial Fraction Decomposition
| Integration of Irrational Expressions |
Integrals Involving Rational Exponents
Integrals Involving Radicals
| Summary |
Extended List of Common Integrals
| Techniques of Integration |
| Key Topics Remaining: Integration of Rational Functions » Integrals Involving Rational Exponents &» Extended List of Common Integrals |
Evaluating integrals is much more difficult problem than evaluating derivatives. As for derivatives, there is a systematic procedure based on the chain rule that effectively allows any derivative to be worked out. However, there is not any similar procedure for integrals.
One of the main difficulties is to know what transformations of integrand will be needed for integration. Particularly, by the substitution method (see below) a problem of integration can be simplified in many cases. One can also try to manipulate the integrand algebraically, decompose the given integral into the sum of more simple integrals, apply integral properties, and so on.
The basic techniques of integration are
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