integration of dx/x and absolute value sign?

Question

when we integrate dx/x then we write "int dx/x = ln |x| + C".But why
we give "absolute value sign ( | x |)"?

Answer 1

the argument of ln must always be positive. (in other words, there is no power to which raising e to would result in a negative.)

Answer 2

They are sort of correct. When you start using complex numbers, the log function is defined for negative values as well--it turns into a multi-valued thing, depending on something called the "winding number". The absolute value bars are to tell you which part of the function you're using. So just treat it like a positive number, but be careful if, in an actual problem, your integration range covers zero--then you'll have a divergence.

Answer 3

Because the function ln is only defined on the inteterval (0, +infinite) and x can take any values in R

Answer 4

Because ln x is undefined for negative values of x. Actually it is kind of silly putting it in because it only confirms that ln x is true for x > 0. However it says nothing about x = 0 and ln 0 is also undefined. Again, another one of those idiosyncrasies of anal-retentive academics.