1. Miss Battaglia AP Calculus
8-2 Integration by Parts 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. Logs Inverse Trig Algebraic Trig Exponential
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 dv 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. Repeated Use of Integration by Parts
Find

11. Integration by Parts
Find

12. Summary of Common Integrals Using Integration by Parts
1. For integrals of the form
let u = xn and let dv = eaxdx, sin ax dx, or cos ax dx
2. For integrals of the form
let u = lnx, arcsin ax, or arctan ax and let dv = xnd
3. For the integrals of the form
let u = sin bx or cos bx and let dv = eaxdx

13. Classwork/ Homework
Read 8.2 Page 533 #11, 13, 15, 19, 27, 29, 32, 83, 99