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Integral Table

For the following, the letters a, b, n, and C represent constants.

Note: Most of the following integral entries are written for indefinite integrals, but they also apply to definite integrals.

Basic Forms

1. , where n ≠ –1

2.

3.

4. , where a > 0 and a ≠ 1

5.

6.

7.

8.

9.

10.

11. , where F(u) is an antiderivative of f(u)

Other Basic Trig and Inverse Trig Forms

12.

13.

14.

15.

16.

17. for a > 0

18.

19. for a > 0

20. for u > 1

21. for u > a > 0


Basic Rational Forms

22. for a > 0

23. for a > 0


Trig Forms

24.

25.

26.


Inverse Trig Forms

27.

28.

29.

30.

31. for u > 1

32. for u > 1


Forms Involving

33. for a > 0


Forms Involving

34.

Forms Involving

35. for u > a > 0


Forms Involving  au + b

36.

37.


Exponential Forms

38.

39.

40.

41.

42.


Logarithmic Forms

43.


Definite Integrals

44.

 

See also

Integration methods, integral rules

 


  this page updated 27-aug-12
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes