1. 5044 Integration by Parts AP Calculus

2. Integration by Parts Product Rules for Integration : A. Is it a function times its derivative; u-du B. Is it a function times the derivative of a second function; u-dv Integration by Parts

3. Proof with u-v : worked out

4. Proof with u-v

5. Proof / Formula Integration by parts In words: First * Second minus of Second * D (first )

6. Integration by parts : worked out In words: First * Second minus of Second * D (first )

7. Illustration: Choosing u and dv L I P E T L  Logarithmic I  Inverse Trig P  Polynomial E  Exponential T  Trig Let u be the first function from the mnemonic.

8. Illustration: u = dv = du = v =

9. Examples:

10. Examples: (hidden product)

11. Examples: ( hidden product - ln ) LEARN IT !, LOVE IT !, LIVE IT ! Write it on your Anti-derivative page.

12. Chart: Short Cut for Algebraic + _ + _

13. Examples: (shortcut for algebraic u)

15. Examples: (Solve like an equation )

17. S. O. B. Problem Creativity is ALWAYS the Main Ingredient!

18. Last Update: 03/08/12 Assignment: p. 346 # 1 – 29 odd