MTH 252 Integral Calculus Chapter 8 – Principles of Integral Evaluation Section 8.2 – Integration by Parts Copyright © 2005 by Ron Wallace, all rights reserved.

Review: The Product Rule Example:

Integration Equivalent

Integration by Parts NOTE: f(x) or g(x) can be equal to 1 (but not both).

Example

Choosing u & dv In general … u should be such that du is simpler dv should (must) be easy to integrate Previous Example: This made the problem MORE difficult!

Repeated Integration by Parts Sometimes the resulting integral is integrated by the same method! Example:

Circular Repeated Integration by Parts Example: