1. Integration By Substitution And By Parts
Brought to you by
Tutorial Services – The Math Center

2. Substitution By Parts Tool used to simplify integral Use:
Integral with two multiplying functions

3. I-Substitution: Recognize Pattern Identify “inside” function
Use substitution to simplify the integrand

4. Change of variables Identify the derivative of the “inside” function
Example:
If the derivative is not in the integrand, then solve for x and dx.

5. II- By Parts:
Recognize Pattern
Choose a u and a dv
Use:

6. Find your components
Choosing u and dv
Example choosing dv and u :

7. Integrating
Plug into formula:
Solve

8. Integration By Substitution And By Parts Links
Integration by Substitution and by Parts Handout
Integrals and Derivatives Handout
Integration by Parts Handout
Integration by Parts Quiz