8-2 Integration by Parts (Day 2) Objective: Find an antiderivative using integration by parts.

1. 8-2 Integration by Parts(Day 2)Objective: Find an antiderivative using integration by parts. Miss Battaglia AP Calculus

2. Integration by Parts If u and v are functions of x and have continuous derivatives, then

4. LIATE Logs Inverse Trig Algebraic Trig Exponential

5. Derived from…

6. Guidelines for Integration by Parts • Try letting dv be the most complicated portion of the integrand that fits a basic integration rule. Then u will be the remaining factor(s) of the integrand. • Try letting u be the portion of the integrand whose derivative is a function simpler than u. Then dbv will be the remaining factor(s) of the integrand. Note that dv always includes the dx of the original integrand.

7. Integration by Parts Find

8. Integration by Parts Find

9. An Integrand with a Single Term Find

10. Integration by Parts Find

11. Summary of Common Integrals Using Integration by Parts 1. For integrals of the form let u = xnand let dv = eaxdx, sin ax dx, or cosax dx 2. For integrals of the form let u = lnx, arcsinax, or arctanax and let dv = xnd 3. For the integrals of the form let u = sin bx or cosbx and let dv = eaxdx

12. Classwork/ Homework • Page 533 #33, 35, 37, 42, 55, 61, 63, 67, 119