preface to fifteenth edition

GENERAL INFORMATION, CONVERSION TABLES, AND MATHEMATICS 2.109
TABLE 2.24
Integrals (Continued)
Transcendental functions (continued)
sin xdx 1
76. ln (a b cos x) C
a b cos x b
A B cos x C sin x
dy
77.
dx A
a b cos x c sin x
a p cos y
cos ydy
sin ydy
(B cos u C sin u)
(B sin u C cos u)
,
a p cos y
a p cos y
where b p cos u, c p sin u, and x u y
a sin bx b cos bx
ax
ax
78. e sin bx dx e C
2 2
a b
a cos bx b sin bx
ax
ax
79. e cos bx dx e C
2 2
a b
1 1 2
80. sin xdx x sin x 1 x C
81. cos1 xdx x cos1 x 1 x2
C
1 1 1
2
82. tan xdx x tan x ⁄2 ln(1 x ) C
p
p
83. cot1 xdx x cot1 x
1⁄2 ln(1 x
2) C
84. sinh xdx cosh x C
85. tanh xdx ln cosh x C
86. cosh xdx sinh x C
87. coth xdx ln sinh x C
x
88. sech xdx 2 tan
1
(e
x
) C
89. csch xdx ln tanh
C 2
90. sinh2 xdx
1⁄2 sinh x cosh x
1⁄2x C
2
91. cosh xdx
1⁄2 sinh x cosh
1⁄2x C
2
92. sech2
xdx tanh x C
93. csch xdxcoth x C
2.2.2 Surface Areas and Volumes*
Let a, b, c, d, and s denote lengths, A denote areas, and V denote volumes.
Triangle. A bh/2, where b denotes the base and h the altitude.
Rectangle. A ab, where a and b denote the lengths of the sides.
Parallelogram (opposite sides parallel). A ah ab sin , where a and b denote the sides, h
the altitude, and the angle between the sides.
Trapezoid (four sides, two parallel). A 1⁄2h(a b), where a and b are the sides and h the
altitude.
* Adapted by permission from Burington, Handbook of Mathematical Tables and Formulas, 3d. ed., McGraw-Hill Book
Company, New York (1959).