Page 23 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II Richa Nandra, Lovely Professional University

Notes Unit 2: Integration by Partial Fraction

CONTENTS
Objectives
Introduction
2.1 Integration by Partial Fractions

2.1.1 Idea of Method of Partial Fractions
2.1.2 The Partial Fraction Theorem
2.2 Finding the Coefficients in the Partial Fraction Expansion
2.2.1 Method 1: Expansion
2.2.2 Method 2: Cover Up
2.2.3 Method 3: Evaluate and Solve Equations
2.2.4 Method 4: Common Denominator

2.3 Partial Fractions
2.3.1 Distinct Linear Factors
2.3.2 Repeated Linear Factors
2.3.3 Distinct Quadratic Factors
2.3.4 Repeated Quadratic Factors
2.4 Summary
2.5 Keywords
2.6 Review Questions
2.7 Further Readings

Objectives

After studying this unit, you will be able to:
 Understand the concept of integration by partial fraction

 Discuss the partial fraction theorem
 Identify how to find the coefficients in the partial fraction expansion
Introduction

We recognize the process to integrate polynomials and negative power of x–a. By the method of
“partial fractions” we can translate any rational function into a polynomial and fractions each
one with negative powers of just one factor (x–a); this permits us to integrate any rational
function, when we identify the process to factor its denominator entirely.

2.1 Integration by Partial Fractions

A rational function is defined as the proportion of two polynomials in the form of P(x)/Q(x) , where
P (x) and Q(x) are polynomials in x and Q( x)  0. If the degree of P( x) is less than the degree of Q( x),

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