In this lesson on partial fraction expansions, students learn how to decompose a general rational function into simpler, partial fractions, making integration easier. The instructor walks through several examples, demonstrating how to factor the denominator and then write each term as a constant divided by a linear factor or quadratic factor raised to a power. The lesson emphasizes the importance of careful expansion to ensure the end result is equal to the original function. The instructor also highlights how to handle rational functions that are not proper and provides examples of how to integrate the resulting partial fractions.
Partial fraction expansions. Integration of general rational functions.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.