Partial Fraction Expansions
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.
- Partial Fraction Tutorial - A partial fraction tutorial with examples and explanations.
- Explanation of Partial Fractions - An explanation of how to break down a polynomial for partial fraction decomposition.
- How do you do partial fractions?
- What are partial fractions?
- How do you take integrals using partial fractions?
- How do you take the integral of 1/(x^3 - 2x^2)?
-
Staff Review
This is perhaps one of the most difficult things to remember and understand how to do in Calculus: partial fractions. This video steps you through the steps to learn how to do partial fraction decomposition of a rational expression. You are then able to integrate each of the individual fractions and usually obtain mostly natural log expressions. Some really great, complicated examples are shown step by step. Really a useful lesson.
