CK12 Calculus - Single Variable

Integrationby Substitution

LearningObjectives

• Integratecompositefunctions


• Use changeof variablesto evaluatedefiniteintegrals


• Use substitutionto computedefiniteintegrals

Introduction
In this lessonwe will expandour methodsfor evaluatingdefiniteintegrals.We first look at a coupleof situations
wherefindingantiderivativesrequiresspecialmethods.Theseinvolvefindingantiderivativesof composite
functionsand findingantiderivativesof productsof functions.
Antiderivativesof Composites
Supposewe neededto computethe followingintegral:

Our rulesof integrationare of no help here.We note that the integrandis of the form where
and

Sincewe are lookingfor an antiderivative of and we knowthat we can re-writeour integral
as

In practice,we use the followingsubstitutionschemeto verifythat we can integratein this way:

1. Let