| 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
| Integrals Involving Radicals |
| Key Topics Remaining: Extended List of Common Integrals |
Problem. Eliminate the radical sing in a rational expression involving
.
Solution. The trigonometric identity
1 – sin 2 u = cos 2 u
suggests the substitution x = a sin u.Indeed,
Another solution. The same idea works for the cosine-substitution:
.
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