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We know how to integrate polynomials and negative power of x-a. By the technique of "partial fractions" we can convert any rational function into a polynomial and fractions each with negative powers of only one factor (x-a); this allows us to integrate any rational function, once we know how to factor its denominator completely.
23.1 Idea of Method of Partial Fractions
23.2 Proof of the Partial Fraction Theorem
23.3 Finding the Coefficients in the Partial Fraction Expansion
23.3.1 Method 1: expansion
23.3.2 Method 2: cover up
23.3.3 Method 3: evaluate and solve equations
23.3.4 Method 4: common denominator
23.4 Examples