January 17, 2014
Chapter 5.5 - Substitution Rule
The Substitution Rule If u=g(x) is a differentiable function whose range is an Interval I
and f is continuous on I , then…
• If u=g(x), then du=g’(x)dx, so a way to remember the Substitution Rule is to think
of dx and du as differentials.
• Thus the Substitution Rule says: It is permissible (allowed) to operate with dx
and du after integral signs as if they were differentials.
Example 1: Find
1 let u= (being the most ugly looking one in the question)
2 : let du= dx and plug these to the question to make it look simpler.