# Use Euler's ID for sin(x)

1. Feb 18, 2004

### meteor

Can somebody show me how to integrate this:?

$$\int ln (sin x) dx$$

thanks

2. Feb 18, 2004

### HallsofIvy

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

3. Feb 19, 2004

### 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)