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Use Euler's ID for sin(x)

  1. Feb 18, 2004 #1
    Can somebody show me how to integrate this:?

    \int ln (sin x) dx

  2. jcsd
  3. Feb 18, 2004 #2


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    Science Advisor

    Do you have any reason to believe that its anti-dervivative is an elementary function?
  4. Feb 19, 2004 #3


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    I tried a sloppy method that got me close:
    1) use Euler's ID for sin(x)
    2) factor out an exponential
    3) write the ln as a sum of simpler ln's
    4) do a substitution for one of the ln's

    This got me to an integral I didn't know how to solve, but that is probably simpler in principle. The integrand is:
    ln(u)/(1 - u)
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