Course: Calculus II
Topic: Integration Techniques
Subtopic: Partial Fractions


The process of decomposition of a rational function into a sum of partial fractions was covered in a pre-calculus class. For example the rational function `(2x-11)/(x^2+x-2)` can be factored `(2x-11)/[(x+2)(x-1)]` , expanded `A/(x+2)+B/(x-1)`, the A and B found, thus providing the final decomposition into the partial fractions, `(2x-11)/[(x+2)(x-1)] = 5/(x+2)-3/(x-1)`. The method of partial fractions is used in calculus to rewrite an integral of a rational function as a sum of integrals of simpler fractions. `int(2x-11)/(x^2+x-2)dx` becomes `int5/(x+2)dx +int(-3)/(x-1)dx` which are both easily integrable. Partial fractions ease the integration process when the function is rational.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: partial fraction expansion, partial fraction decomposition, linear factors, quadratic factors, repeated factors, "equating the coefficients" method, "nifty x" method of solving a system during PF decomposition

Mini-Lectures and Examples

STUDY: Integration Techniques - Partial Fractions

Supplemental Resources (recommended)

It is a good idea to review how to perform decomposition of partial fractions from a pre-calculus course before integrating by the partial fraction method. Here is a link to my lesson on partial fractions from a college algebra course to help you review if you need it: Prof. Keely's Review of Partial Fraction Decomposition from Pre-Calculus

If you need supplemental tutorial videos with examples reviewing partial fractions from pre-calculus go to James Sousa's MathIsPower4U >> Algebra and search for topic: "Performing Partial Fraction Decomposition". Or better yet go straight to his MathIsPoswer4U >> Calc II course and search for topic: "Integration Using Partial Fractions" which incorporates precalc decomposition steps with each integation.

Supplemental Resources (optional)

Video: Partial Fraction Expansions, Selwyn Hollis's Video Calculus

Lesson: Partial Fraction Decomposition, Dale Hoffman's Contemporary Calculus

rev. 2021-02-06