integral

[meteor]

Can somebody show me how to integrate this:?


\int ln (sin x) dx


thanks

[HallsofIvy]

Do you have any reason to believe that its anti-dervivative is an elementary function?

[turin]

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)