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


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

Time to compute: 0.03 second

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