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Lecture

# 7.4 Integration of Rational Functions by Partial Fractions: Overview

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
7.4 Integration Techniques Partial Fractions for Rational Functions: Overview Rational functions are functions with a polynomial in the numerator and the denominator, so that: ( ) ( ) ( ) If the degree of ( ) is less than ( ), it is called proper rational function. If the degree of ( ) is greater than ( ), it is called improper rational function. Then before proceeding to applying partial fractions, it must be written in the form of ) ( ) ( ) ( ), ( ) ( ) where ( ) is the remainder obtained from long division. 4 Cases of Rational Functions Case 1: When the function in the denominator can be factored into linear functions. Then split the function in the numerator and integrate separately. Case 2: Similar to Case 1, but some of the factored terms in the denominator have order greater than 1. Then write out each power occurrence, and decompose the numerator accordingly, and then integrate separately. Case 3: When the factored ter
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