1. 9.1 Integration by Parts &
Tabular Integration
Rita Korsunsky

2. Integration by Parts
Product Rule :

3. Rules for Choosing u & dv
∫ udv = uv - ∫ vdu
u u dv
Rules for choosing u and dv:
For dv:
Choose the most complicated integrand that can be readily integrated
For u:
Choose something that becomes simpler when differentiated

4. Example #1 possible choices for dv: dx, x dx, e2x dx, xe2x dx Plug In
Most complicated that can be readily integrated: e2x dx
Plug In

5. Example #2
Plug In

6. Example #3
Plug In

7. Use integration by parts again
Example #4
Use integration by parts again
Plug In
Plug In

8. Use integration by parts again
Example #5
Use integration by parts again

9. Example #5 cont'd.
Plug into original equation

10. Example #6
Use identity:
Plug In

11. Tabular Integration can be used only if f(x) is a polynomial.
Take the derivative of f(x) until you reach ZERO
Then take the integral of g(x) until the derivative of f(x) is ZERO

12. Example #1
Take the INTEGRAL
Take the DERIVATIVE

13. Example #2

14. Integration by parts: OR
Tabular
integration

15. OR

16. THE END