Page 53 - Standard Handbook Of Petroleum & Natural Gas Engineering

42 Mathematics

Table 1-7
Table of Integrals'

1. 1 df(x) = f(x) + C
2. d f(x)dx = f(x)dx
3. jO*dx=C
4. af(x)dx = a f(x)dx
5. (u f v)dx = udx f vdx
6. udv = uv - vdu
udv du
7. dx dx=uv-jv dx
8. f(y)dx = 1 f(y)dy
3-
dx
U"+l
9. u"du = n+l + C, n f -1
10. j $ = log$ + c

11. eUdu = e" + C

12. b"du = b" +c
13. ./sin u du = -cos u + c
14. jcos u du = sin u + c
15. tan u du = log, sec u + C = -log, cos u + c
16. 1 cot u du = log, sin u + C = -log, csc u + c

+
17. sec u du = log,(sec u + tan u) + C = log, tan [ + t) C
U
2
18. csc u du = log,(csc u - cot u) + C = log, tan - + C
1
1
19. sinz u du = - u - 5 sin u cos u + c
2
1
1
20. cos2 u du = - u + 5 sin u cos u + c
2
21. sec2 u du = tan u + c
22. cscz u du = -cot u + C
23. tanz u du = tan u - u + C
24. j ctn2 u du = -cot u - u + c
1
U
25. j du = 2 tan-' - + c
u +a a