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# Integral of ln (sin x) Watch

1. 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
2. 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!!!
3. Isn't that the definite integral which is possible?

http://www.wolframalpha.com/input/?i...+ln%28sin+x%29
4. Yay for complex numbers.
5. ...umm damn I've completely forgotton all of C4...
6. (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
7. Let's not torture him:

http://math.ucsd.edu/~ebender/20B/7_DefInt.pdf
8. Similarly, try ...
9. 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.
10. Thanks for every one for the help. My problem is resolved.

Updated: September 27, 2009
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