Absolute values in standard integrals

[NanakiXIII]

In a lot of compilations of standard integrals (my Calculus book does this, Wikipedia does this), a lot of the integrals of trigonometric functions have an absolute value in their solution which seems out of place to me. For example, take the integral

$$\int dx \cot{x}$$.

My Calculus book says this equals $$\log |\sin{x}|$$. Now, I could be mistaken, but it seems to me that $$\log (\sin{x})$$ would do just fine and in fact, since $$|\sin{x}|$$ isn't a smooth function, I wouldn't expect to find it as a solution.

My first guess is that the $$| |$$ are for some reason used without their meaning as absolute value. Is this the case? If so, what's the point of using them instead of regular brackets?

 

[Gavins]

log(-x) isn't defined.

 

[NanakiXIII]

You are right, of course. And the cotangent is not a bounded function, so the solution not being smooth is not so strange.