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Absolute values in standard integrals

  1. Feb 7, 2010 #1
    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

    [tex]\int dx \cot{x}[/tex].

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

    My first guess is that the [tex]| |[/tex] 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?
  2. jcsd
  3. Feb 7, 2010 #2
    log(-x) isn't defined.
  4. Feb 7, 2010 #3
    You are right, of course. And the cotangent is not a bounded function, so the solution not being smooth is not so strange.
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