Page 54 - Standard Handbook Of Petroleum & Natural Gas Engineering

Differential and Integral Calculus 43

du u-a
a

27. A
sin-'
=
@=iF
28. du lo&(u+dm)'+C
7T=i-F
29. j = cos-'(~]+C
VGiTF
du
1
30. = -sec-'(:]+~ = -cos-'a+~
1
u~FT a U
a
31. du = -;IO&( U
u a' f uz
a I
(
+
+ C
32. d G du = 1 u~G
sin-'
a'
2
33. dG*du = 1[udG*a210g,(u+dm)]'+C
2
34. sinh u du = cosh u + C
35. jcosh u du = sinh u + C
36. tanh u du = log,(cosh u) + C
37. I coth u du = loge(sinh u) + C
38. sech u du = sin-l(tanh u) + C

40. sech u tanh u du = -sech u + C
41. csch u coth u du = -csch u + C
' Note: u and v represent functions of x.