1. 4.5 Integration by Substitution
Outside Function
Derivative of
Inside Function
Inside Function

2. Official Description
Problem

3. 4.5 Integration by Substitution
Composite Function?
Derivative of Inside Function?
Substitution

4. 4.5 Integration by Substitution

5. 4.5 Integration by Substitution

6. 4.5 Integration by Substitution

7. 4.5 Integration by Substitution

8. 4.5 Integration by Substitution

9. 4.5 Integration by Substitution
We do not need change of variables!

10. 4.5 Integration by Substitution

11. 4.5 Integration by Substitution
GOTO (f)

12. 4.5 Integration by Substitution

13. 4.5 Integration by Substitution

14. 4.5 Integration by Substitution

15. 4.5 Integration by Substitution

16. 4.5 Integration by Substitution

17. 4.5 Integration by Substitution

18. 4.5 Integration by Substitution
You can change the bounds and keep everything in terms of u!
Change of Variables

19. 4.5 Integration by Substitution
Change of Variables
Differential of x?

20. 4.5 Integration by Substitution
Odd FCTN
Even FCTN

21. 4.5 Integration by Substitution
Even or Odd??

22. 4.5 Integration by Substitution

23. 4.5 Integration by Substitution
WAY