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(Log[Cos[(a*x)/2]] - Log[Cos[(a*x)/2] - Sin[(a*x)/2]])/a

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

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

        a x             a x        a x
Log[Cos[---]] - Log[Cos[---] - Sin[---]]
         2               2          2
----------------------------------------
                   a
Time to compute: 0.02 second
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