Can you explain this integral

So d/dx ln x = 1/x
But ∫1/x = ln |u| + c

What is the | | for? I mean, I know that it means absolute value, but why is it there?

Btw, the text I'm working from uses these, but WolframAlpha didn't.

d/dx ln x = 1/x is only true for x>0. To allow negative values for x, you need to use the absolute value.
So d/dx ln |x| = 1/x is true for both positive values of x as well as negative values.