Partial Fractions

AP Calculus · Axiom Academy

Integrating rational functions by decomposing them into simpler pieces The Partial Fractions Technique When you need to integrate a rational function where Q(x) factors into linear or quadratic terms, you can decompose it into simpler fractions that are easier to integrate. Setup for Distinct Linear Factors Multiply both sides by the denominator and solve for A and B . Factor the denominator completely first Each linear factor (x-a) gets a term Solve for constants using strategic substitution or comparing coefficients Each simple fraction integrates to a logarithm or power

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