← MATH 01131 · Calculus II
MATH 01131 · Advanced integration
Partial fractions
Definition
Rewrite a proper rational P/Q as a sum of simpler fractions by factoring Q into linears/irreducible quadratics, then solve for undetermined coefficients.
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If improper, polynomial-divide first. Linear factors → A/(x−r); repeated → A/(x−r)+B/(x−r)²+…; irreducible quadratic → (Ax+B)/(x²+…).
Clear denominators and equate coefficients or plug convenient x-values.
After decomposing, integrate termwise (logs and arctans appear often).
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Attempt each problem first, then open the worked solution.
1.Decompose (2x+3)/((x−1)(x+2)) and integrate.