preface to fifteenth edition

GENERAL INFORMATION, CONVERSION TABLES, AND MATHEMATICS 2.105
TABLE 2.24 Integrals
From Baumeister and Marks, Standard Handbook for Mechanical Engineers, 7th ed., McGraw-Hill Book
Company, New York (1967); by permission.
An integral of f(x) dx is any function whose differential is f(x) dx, and is denoted by f(x) dx. All the integrals
of f(x) dx are included in the expression f(x) dx C, where f(x) dx is any particular integral, and C is an
arbitrary constant. The process of finding (when possible) an integral of a given function consists in recognizing
by inspection a function which, when differentiated, will produce the given function; or in transforming the
given function into a form in whichsuchrecognition is easy. The most common integrable forms are collected
in the following brief table; for a more extended list, see Peirce, Table of Integrals, Ginn, or Dwight, Table of
Integrals and other Mathematical Data, Macmillan.
1. adu a du au C
General formulas
2. (u v) dx udx
vdx
4. f(x) dx
f[F(y)]F(y) dy, x F(y)
3. udv uv vdu
5. dy f(x, y) dx dx f(x, y) dy
Fundamental integrals
x n1
n
n 1
6. x dx C, when n 1
dx
7. ln x C ln cx
8. ex dx ex
C
x
9. sin xdxcos x C
10. cos xdx sin x C
dx
dx
11. cot x C
12.
sin2
tan x C
x
cos2
x
dx
13. sin1
x C cos1
x c
1 x2
p
dx
1 1
14. tan x C cot x c
1 x2
Rational functions
(a bx) n1
15. (a bx)
n
dx C
(n 1)b
dx 1 1
16. ln(a bx) C ln c(a bx)
a bx b b
1 1
dx 1
17. dx C
18.
x2
C
x
(a bx)
2
b(a bx)
dx 1 x
1
1
19. ⁄2 ln C tanh x C, when x 1
1 x2
1 x
dx x 1
20.
1⁄2 ln C coth1
x C, when x 1
x2
1 x 1
dx 1 b
21. tan1
x
C
a bx2
pab qa
dx 1 pab bx
22. ln C [a 0, b 0]
a bx2
2pab pab bx
1 b
1
tanh x
C
pab qa