9.
10.
11.
Integrationby PartialFractions
LearningObjectives
A studentwill be able to:
- Computeby handthe integralsof a wide varietyof functionsby usingtechniqueof Integrationby Partial
Fractions. - Combinethe techniqueof partialfractionswith -substitutionto solvevariousintegrals.
This is the third techniquethat we will study. This techniqueinvolvesdecomposinga rationalfunctioninto
a sum of two or moresimplerationalfunctions.For example,the rationalfunction
can be decomposedinto
The two partialsumson the right are calledpartialfactions.Supposethat we wish to integratethe rational
functionabove.By decomposingit into two partialfractions,the integralbecomesmanageable:
To use this method,we mustbe able to factorthe denominatorof the originalfunctionand then decompose
the rationalfunctioninto two or morepartialfractions.The examplesbelowillustratethe method.
Example1:
Find the partialfractiondecompositionof