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Log[Sin[x/2]] - Log[Cos[x/2] + Sin[x/2]]

Integrate[1/(1 - Cos[x] + Sin[x]), x] ==
Log[Sin[x/2]] - Log[Cos[x/2] + Sin[x/2]] 

                   1
Integrate[-------------------, x] == 
          1 - Cos[x] + Sin[x]

        x             x        x
Log[Sin[-]] - Log[Cos[-] + Sin[-]]
        2             2        2
Time to compute: 0.03 second
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