How do you integrate log(z - e^(ix))?

I x
Integrate[Log[z - E   ], x] =

-I  2           I x
-- x  + x Log[-E    + z] - 
2
 
                          I x
                         E
         2   I x Log[1 - ----]
       -x                 z
  I z (--- - ----------------- - 
       2 z           z
 
                 I x
                E
     PolyLog[2, ----]
                 z
     ----------------)
            z

Answer provided by:  http://integrals.wolfram.com/
Go there, enter "Log[z-E^(I*x)]" and click "Compute" to see the result
in a better (non-ASCII) format.

Regards,
df

using the taylor series you get e^ix = cosx +isinx, this may make is
easier to integrate.

Also trying using intergrator.com. I swear by it.
Hope this helps.

Preston

Would you please clarify this question? You could mean log(z - exp( i
Re(z))), but then you would have to describe the contour. Or you could
simply have made a mistake using z and x and want the indefinite
integral of log( x - exp (ix)). Or ... ?