This document discusses rules for integrating exponential, trigonometric, and other functions. It provides examples of using u-substitution to find integrals of functions involving exponentials, trigonometric functions, and other substitutions. The document also reviews rules of differentiation and discusses how indefinite integrals result from trigonometric identities and u-substitution techniques.

1. Rules of
Integration
Exponential and
Trigonometric Function

2. • ... finding an Integral is the reverse of finding a
Derivative.
• (So you should really know about Derivatives )
• Like here:
• Example: What is an integral of 2x?
• We know that the derivative of x2 is 2x ...
• ... so an integral of 2x is x2

3. Rules of Integration in Exponential
Function
1.
2.
3.

4. Remember the three General rules for
Integration
1.
2.
3.

5. Examples:
1. Integrate
2. Integrate .

6. 3. Integrate
u-substitution
u = -x
du = -1 dx
-1 du = dx

7. Example:
Integrate

8. Example:
Integrate

9. Examples:
Integrate

10. Examples:
Integrate
u-substitution
u = 2x+3
du = 2 dx
(1/2) du = dx

11. Rules of Integration in
Trigonometric Function

12. Trigonometric Functions
A.
B.
C.
D.
C.
D.
E.
F.
G.
H.
I.

13. Rules of Differentiation

14. Indefinite Integrals

15. Indefinite integrals result from trigonometric
identities and u-substitution

16. Examples
A. Integrate
u-substitution
u = 3x
du = 3dx
(1/3) du = dx
Recall

17. B. Integrate
Examples
u-substitution
u = 5x
du = 5dx
(1/5) du = dx
Recall

18. C. Integrate
Examples u-substitution
u = 4x
du = 4dx
(1/4) du = dx
Recall

19. D. Integrate
Examples

20. Trigonometric Functions
A.
B.
C.
D.
C.
D.
E.
F.
G.
H.
I.

21. D. Integrate
Examples

22. Indefinite Integrals

23. D. Integrate
Examples u-substitution
u = sin x
du = cos x dx

24. Rules of Differentiation

25. D. Integrate
Examples u-substitution
u = sin x
du = cos x dx

26. E. Integrate
Examples

27. Trigonometric Functions
A.
B.
C.
D.
C.
D.
E.
F.
G.
H.
I.

28. E. Integrate
Examples u-substitution
u = 10x
du = 10dx
(1/10)du = dx

29. F. Integrate
Example
u-substitution
u = sin x
du = cos dx
Recall

30. INTEGRATE THE FOLLOWING
1.
u-substitution u-substitution

31. Thank You
and
God Bless