This material gives a straightforward introduction to techniques of integration, which is one of the most difficult areas of calculus. A lot of completely worked examples are used to introduce methods of integration and to demonstrate problem-solving techniques. The topics are written as self-guided tutorials. Each page contains necessary definitions and formulas, which are illustrated by typical problems with detailed solutions.
- Antiderivatives and Initial Value Problems
- The Indefinite Integral and Basic Rules of Integration. Table of Integrals
- Integration by Substitution
- Integration by Parts
- Integration by Completing the Square
- Partial Fraction Decomposition
- Integration of Rational Functions
- Integration of Irrational Functions
- Integration of Rational Expressions of Trigonometric Functions
- Integration of Some Classes of Trigonometric Functions
- Integration of Hyperbolic Functions
- Trigonometric and Hyperbolic Substitutions
- The Definite Integral and Fundamental Theorem of Calculus
- Improper Integrals