Page 165 - Calculus Demystified

CHAPTER 6
152

Fig. 6.2 Transcendental Functions

discuss the function ln |x| when x = 0 (Fig. 6.3):

Fig. 6.3
If x = 0 then

d 1
(ln |x|) = .
dx x
In other words,

1
dx = ln |x|+ C.
x
More generally, we have

d 1 du
ln |u|=
dx u dx
and

1 du
dx = ln |u|+ C.
u dx
EXAMPLE 6.4
Calculate

4 1
dx, dx.
x + 1 −2 + 3x