L7 Integration by Partial Fractions - Part 1
Completion requirements
Unit 7A
Integrals Part 1
Lesson 7: Integration by Partial Fractions
Integration by Partial Fractions
Consider the functions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#8722;«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/mrow»«/mfrac»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»3«/mn»«/mrow»«/mfrac»«mo»§#8722;«/mo»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»2«/mn»«/mrow»«/mfrac»«/math». The result of the subtraction (the difference) in «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» is the same as the function «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#8722;«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/mrow»«/mfrac»«/math». Try to determine the integral of each function. Which of the two is easier to integrate?