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Integrating 1/sin*|sin|

  1. Feb 7, 2010 #1
    1. The problem statement, all variables and given/known data

    I need to solve the integral

    [tex]\int \frac{dx}{\sin{x} |\sin{x}|}.[/tex]

    2. Relevant equations


    3. The attempt at a solution

    I know it's possible, the solution is [tex]-\frac{\cos{x} |\sin{x}|}{\sin^2{x}}[/tex], and I probably need to write the absolute as the square root of a square. I also probably need a substitution to simplify. I'm not having any luck finding such a substitution, however.
  2. jcsd
  3. Feb 7, 2010 #2


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    Homework Helper

    Integrate it for sinx>0, then for sinx<0. Compare.
  4. Feb 8, 2010 #3
    That worked perfectly. Thanks. I suppose that's the usual way to tackle an integral over an absolute value?
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