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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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