The Partial Fractions Technique: Denominator Contains Repeated Linear or Quadratic Factors

By Mark Ryan

This article on the partial fractions technique assumes you’re familiar with the basics of the partial fractions technique for integration. If you’ve done some partial fractions problems, they likely involved integrals where the denominators contained linear and/or irreducible quadratic factors with only one of each factor.

The article concerns the somewhat gnarly problems where the denominators contain repeated linear or quadratic factors — that is, factors raised to a power more than 1. Other than beginning the solution process with a longer type of decomposition, solving these problems is basically the same as solving more basic problems without repeated factors. The algebra involved in solving for the capital-letter unknowns is a bit messier, but the approach is the same.

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