This is the formulafor integrationby parts.With the properchoiceof and the secondintegralmay
be easierto integrate.The followingexampleswill showyou how to properlychoose and
Example1:
Evaluate.
Solution:
We use the formula.
Choose
and
To completethe formula,we take the differentialof and the simplestantiderivativeof
The formulabecomes
A Guideto Integrationby Parts
Whichchoicesof and lead to a successfulevaluationof the originalintegral?In general,choose
to be somethingthat simplifieswhendifferentiated,and to be somethingthat remainsmanageablewhen
integrated.Lookingat the examplethat we havejust done,we chose and That led
to a successfulevaluationof our integral.However, let’s assumethat we madethe followingchoice,