Four Approaches to Integration 1. Recognition Review list on pages 511-512 2. Computer Algebra Systems (CAS) Examples: Mathematica, Maple, Derive Problems: Can’t solve some and others give unnecessary complicated answers. 3. Tables See inside front & back covers Problem: Not exhaustive 4. Transformation Methods Change to something recognizable. Examples: Substitution & Algebraic Equivalence The topic of this chapter! Also, for definite integrals, numerical approximation methods.
Transformation Methods Substitution Integration by Parts Trigonometric Integrals Powers of Trigonometric Functions Trigonometric Substitutions Partial Fractions All of these attempt to change the integral into something that can be integrated by recognition. Many problems will require the use of two or more of these methods!