1. Section 7.2 Integration by Parts

2. Consider the function We can’t use substitution We can use the fact that we have a product

3. While integration by substitution is based on the chain rule, integration by parts is based on the product rule We know So integrate both sides and get After switching things around we get

4. Integration by parts General formula Let’s go back and apply this to

5. How to choose u and v’ Whatever you let v’ be, you have to be able to find v It helps if u’ is simpler than u (or at least no more complicated than u) It helps if v is simpler than v’ (or at least no more complicated than v’)

6. Let’s try a few