1. Monday 8 th November, 2010 Introduction

2. Objective: Derive the formula for integration by parts using the product rule

3. Deriving the Formula Start with the product rule: This is the Integration by Parts formula.

4. u differentiates to zero (usually). dv is easy to integrate. Choose u in this order: LIPET Logs, Inverse trig, Polynomial, Exponential, Trig Choosing u and dv

5. Formula for Integration by parts The idea is to use the above formula to simplify an integration task. One wants to find a representation for the function to be integrated in the form udv so that the function vdu is easier to integrate than the original function.

6. Objective: Use the integration by parts formula for combinations of functions

7. Example 1: polynomial factor LIPET

8. Example 2: logarithmic factor LIPET

9. This is still a product, so we need to use integration by parts again. Example 3: LIPET

10. Example 4: LIPET This is the expression we started with!

11. Example 4(cont.): LIPET This is called “solving for the unknown integral.” It works when both factors integrate and differentiate forever.

12. Exercise