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Integral of ln (sin x)

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    Hi,
    Could some one tell me how to do the following indefinite integral


    integral { ln (sin x) dx }

    I thought I can do this by integration by parts. But it doesn't seem to work.

    Thanks
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    I remembered seeing this before somewhere and Google was my friend.

    http://community.boredofstudies.org/...ml#post3316947

    and here:

    http://mathforum.org/library/drmath/view/72243.html

    You may struggle with an indefinite integral!!!
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    Isn't that the definite integral which is possible?

    http://www.wolframalpha.com/input/?i...+ln%28sin+x%29
  4. Offline

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    Yay for complex numbers.
  5. Offline

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    ...umm damn I've completely forgotton all of C4...
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    (Original post by SimonM)
    Isn't that the definite integral which is possible?

    http://www.wolframalpha.com/input/?i...+ln%28sin+x%29
    the 'polylogarithm function'?

    I get dibs on the loganomial function
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    Let's not torture him:

    http://math.ucsd.edu/~ebender/20B/7_DefInt.pdf
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    Similarly, try \int \ln(1+\tan x)\,dx...
  9. Offline

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    Hi,
    Thanks for every one who responded. I made a mistake. It was the improper integral, that I needed to find.

    Actually the definite integral I needed to find is integral {ln (t*cos t) dt.}

    I think I should be able to do it now with the above help.

    Thanks for the help again.
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    Thanks for every one for the help. My problem is resolved.

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