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((-1 - I)*(-1)^(3/4)*ArcTanh[(-1 + Tan[(a*x)/2])/Sqrt[2]])/a

Integrate[1/(Cos[a*x] + Sin[a*x]), x] ==
((-1 - I)*(-1)^(3/4)*ArcTanh[(-1 + Tan[(a*x)/2])/ Sqrt[2]])/a 

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

                                  a x
                         -1 + Tan[---]
             3/4                   2
(-1 - I) (-1)    ArcTanh[-------------]
                            Sqrt[2]
---------------------------------------
                   a
Time to compute: 0.13 second
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