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

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

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

                                  x
                         -1 + Tan[-]
             3/4                  2
(-1 - I) (-1)    ArcTanh[-----------]
                           Sqrt[2]
Time to compute: 0.05 second
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