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Common Integrals
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
sech or
30.
csch or
31.
sech
32.
csch 2
u du =-coth u
33.
34.
coth 2
u du = u -coth u
35.
36.
37.
sech sech u
38.
csch ucoth u du = -csch u
39.
40.
coth
41.
42.
43.
or
44.
45.
46.
47.
48.
INTEGRALES CONTAINING Sin(ax)
1.
2.
3.
4.
5.
6.
7.
where the constants BB
n are the Bernoulli's numbers.
8.
9.
10.
11.
12.
13.
14.
provided .
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
INTEGRALS CONTAINING Cos(ax)
1.
2.
3.
4.
5.
6.
7.
8.
where the constants En are the Euler's numbers.
9.
10.
11.
12.
13.
14.
15.
provided .
16.
17.
18.
19.
20.
21.
22.
provided .
23.
provided .
24.
provided .
25.
provided and .
26.
27.
28.
29.
30.
INTEGRALS CONTAINING Tan(ax)
1.
2.
3.
4.
5.
6.
7.
where the constants BB
n are the Bernoulli's numbers.
8.
where the const...
10.
11.
INTEGRALS CONTAINING Csc(ax)
1.
2.
3.
4.
5.
6.
where the constants BB
n are the Bernoulli's numbers.
7.
where the constants BB
n are the Bernoulli's numbers.
8.
9.
10.
INTEGRALS CONTAINING Sec(ax)
1.
2.
3.
4.
5.
6.
where the constants En are the Euler's numbers.
7.
where the constants En are the Euler's numbers.
8.
9.
10.
INTEGRALS ...
4.
5.
6.
7.
where the constants BB
n are the Bernoulli's numbers.
8.
where the constants BB
n are the Bernoulli's numbers....
INTEGRALS CONTAINING Sinh(ax)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
INTEGRALS CONTAINING
1.
2.
3.
4.
5.
6.
where the constants BB
n are the Bernoulli's numbers.
7.
8.
where the constants BB
n are the Bernoulli's numbers.
9.
10...
4.
5.
6.
7.
where the constants En are the Euler's numbers.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
INTEGRALS CONTAINING
1.
2.
3.
4.
5.
6.
where the constants En are the Euler's numbers.
7.
8.
where the constants En are the Euler's numbers.
9.
10.
INTEGRALS CONTAINING Tanh(ax)
1.
2.
3.
4.
5.
6.
7.
where the constants BB
n are the Bernoulli's numbers.
8.
9.
where the constants BB
n are the Bernoulli's numbers.
10.
11.
INTEGRALS CONTAINING Coth(ax)
1.
2.
3.
4.
5.
6.
7.
where the constants BB
n are the Bernoulli's numbers.
8.
9.
where the constants BB
n are the Bernoulli's numbers.
10...
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
DEFINITE INTEGRALS CONTAINING
EXPONENTIAL FUNCTIONS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
where the constant is the Euler's constant.
18.
where the constant is the Euler's constant.
19.
where the ...
22.
DEFINITE INTEGRALS CONTAINING
LOGARITHMIC FUNCTIONS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
where the constant is the Euler's constant.
11.
where the constant is the Euler's constant.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
INTEGRALS CONTAINING ln(ax)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
INTEGRALS CONTAINING Sin(ax) And
Cos(ax)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
INTEGRALS CONTAINING Sinh(ax)
and Cosh(ax)(
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
DEFINITE INTEGRALS CONTAINING
HYPERBOLIC FUNCTIONS
1.
2.
3.
4.
5.
6.
Integrals with Inverse Trigonometric
Functions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
INTEGRALS CONTAINING
RECIPROCALS OF HYPERBOLIC
FUNCTIONS
1.
2.
3.
4.
where is |x| < a, is x>a, and is x<-a.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
Definite Integrals with Rational and
Irrational Expressions
1.
2.
,
for 0 < p <1
3.
,
for 0 < m+1 < n
4.
5.
6.
7.
8.
,
for 0 < m+1< n p
DEFINITE INTEGRALS THAT
CONTAIN TRIGONOMETRIC
FUNCTIONS
Note that all the constant are positiv...
4.
5.
,
m=1,2,...
6.
,
m=1,2,...
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
,
m=0,1,2,...
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
where the constant is the Euler's constant.
41.
where the constant is the Euler's constant.
42.
All Integral Formulas: A Self-Prepared guide book to your Integral Formulas A-Z | Mathematics | Calculus
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All Integral Formulas: A Self-Prepared guide book to your Integral Formulas A-Z | Mathematics | Calculus

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All Integral Formulas: A Self-Prepared guide book to your Integral Formulas A-Z | Mathematics | Calculus.
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse, differentiation, being the other. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral

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All Integral Formulas: A Self-Prepared guide book to your Integral Formulas A-Z | Mathematics | Calculus

  1. 1. Common Integrals 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
  2. 2. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
  3. 3. 23. 24. 25. 26. 27. 28. 29. sech or 30. csch or 31. sech 32. csch 2 u du =-coth u 33.
  4. 4. 34. coth 2 u du = u -coth u 35. 36. 37. sech sech u 38. csch ucoth u du = -csch u 39. 40. coth 41. 42. 43. or 44.
  5. 5. 45. 46. 47. 48. INTEGRALES CONTAINING Sin(ax) 1. 2. 3. 4.
  6. 6. 5. 6. 7. where the constants BB n are the Bernoulli's numbers. 8. 9. 10. 11. 12. 13.
  7. 7. 14. provided . 15. 16. 17. 18. 19. 20. 21.
  8. 8. 22. 23. 24. 25. 26. 27. 28.
  9. 9. 29. INTEGRALS CONTAINING Cos(ax) 1. 2. 3. 4. 5. 6. 7.
  10. 10. 8. where the constants En are the Euler's numbers. 9. 10. 11. 12. 13. 14. 15. provided . 16.
  11. 11. 17. 18. 19. 20. 21. 22. provided . 23. provided .
  12. 12. 24. provided . 25. provided and . 26. 27. 28. 29. 30.
  13. 13. INTEGRALS CONTAINING Tan(ax) 1. 2. 3. 4. 5. 6. 7. where the constants BB n are the Bernoulli's numbers. 8. where the constants BB n are the Bernoulli's numbers. 9.
  14. 14. 10. 11. INTEGRALS CONTAINING Csc(ax) 1. 2. 3. 4. 5. 6. where the constants BB n are the Bernoulli's numbers.
  15. 15. 7. where the constants BB n are the Bernoulli's numbers. 8. 9. 10. INTEGRALS CONTAINING Sec(ax) 1. 2. 3. 4. 5.
  16. 16. 6. where the constants En are the Euler's numbers. 7. where the constants En are the Euler's numbers. 8. 9. 10. INTEGRALS CONTAINING Cot(ax) 1. 2. 3.
  17. 17. 4. 5. 6. 7. where the constants BB n are the Bernoulli's numbers. 8. where the constants BB n are the Bernoulli's numbers. 9. 10. 11. 12.
  18. 18. INTEGRALS CONTAINING Sinh(ax) 1. 2. 3. 4. 5. 6. 7. 8. 9.
  19. 19. 10. 11. 12. 13. 14. 15. 16. 17. 18.
  20. 20. 19. 20. 21. 22. INTEGRALS CONTAINING 1. 2. 3. 4. 5.
  21. 21. 6. where the constants BB n are the Bernoulli's numbers. 7. 8. where the constants BB n are the Bernoulli's numbers. 9. 10. INTEGRALS CONTAINING Cosh(ax) 1. 2. 3.
  22. 22. 4. 5. 6. 7. where the constants En are the Euler's numbers. 8. 9. 10. 11. 12.
  23. 23. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
  24. 24. 23. 24. 25. 26. 27. 28. INTEGRALS CONTAINING
  25. 25. 1. 2. 3. 4. 5. 6. where the constants En are the Euler's numbers. 7. 8. where the constants En are the Euler's numbers. 9.
  26. 26. 10. INTEGRALS CONTAINING Tanh(ax) 1. 2. 3. 4. 5. 6. 7. where the constants BB n are the Bernoulli's numbers. 8.
  27. 27. 9. where the constants BB n are the Bernoulli's numbers. 10. 11. INTEGRALS CONTAINING Coth(ax) 1. 2. 3. 4. 5.
  28. 28. 6. 7. where the constants BB n are the Bernoulli's numbers. 8. 9. where the constants BB n are the Bernoulli's numbers. 10. 11. INTEGRALS CONTAINING eax 1.
  29. 29. 2. 3. 4. 5. 6. 7. 8. 9. 10.
  30. 30. 11. 12. 13. 14. 15. 16. DEFINITE INTEGRALS CONTAINING EXPONENTIAL FUNCTIONS 1. 2. 3.
  31. 31. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
  32. 32. 14. 15. 16. 17. where the constant is the Euler's constant. 18. where the constant is the Euler's constant. 19. where the constant is the Euler's constant. 20. 21.
  33. 33. 22. DEFINITE INTEGRALS CONTAINING LOGARITHMIC FUNCTIONS 1. 2. 3. 4. 5. 6. 7.
  34. 34. 8. 9. 10. where the constant is the Euler's constant. 11. where the constant is the Euler's constant. 12. 13. 14. 15. 16.
  35. 35. 17. 18. 19. 20. 21. 22. 23. INTEGRALS CONTAINING ln(ax) 1. 2.
  36. 36. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
  37. 37. 13. 14. 15. INTEGRALS CONTAINING Sin(ax) And Cos(ax) 1. 2. 3. 4. 5.
  38. 38. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
  39. 39. 17. 18. 19. 20. 21. 22. 23. 24. 25.
  40. 40. 26. 27. 28. 29. 30.
  41. 41. INTEGRALS CONTAINING Sinh(ax) and Cosh(ax)( 1. 2. 3. 4. 5. 6. 7.
  42. 42. 8. 9. 10. 11. 12. 13. 14. DEFINITE INTEGRALS CONTAINING HYPERBOLIC FUNCTIONS 1. 2.
  43. 43. 3. 4. 5. 6. Integrals with Inverse Trigonometric Functions 1. 2. 3. 4. 5.
  44. 44. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
  45. 45. 16. 17. 18. 19. 20. 21. 22. 23. 24.
  46. 46. 25. 26. 27. 28. 29. 30.
  47. 47. 31. 32. 33. 34. 35. 36. 37. 38.
  48. 48. INTEGRALS CONTAINING RECIPROCALS OF HYPERBOLIC FUNCTIONS 1. 2. 3. 4. where is |x| < a, is x>a, and is x<-a. 5.
  49. 49. 6. 7. 8. 9. 10. 11. 12. 13.
  50. 50. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
  51. 51. 24. 25. 26. 27. 28. 29. 30.
  52. 52. 31. 32. Definite Integrals with Rational and Irrational Expressions 1. 2. , for 0 < p <1 3. , for 0 < m+1 < n 4. 5.
  53. 53. 6. 7. 8. , for 0 < m+1< n p DEFINITE INTEGRALS THAT CONTAIN TRIGONOMETRIC FUNCTIONS Note that all the constant are positive. 1. 2. 3.
  54. 54. 4. 5. , m=1,2,... 6. , m=1,2,... 7. 8. 9. 10. 11. 12. 13.
  55. 55. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
  56. 56. , m=0,1,2,... 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.
  57. 57. 35. 36. 37. 38. 39. 40. where the constant is the Euler's constant. 41. where the constant is the Euler's constant. 42.

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