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

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

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

                                 a x
                         1 + Tan[---]
             1/4                  2
(-1 + I) (-1)    ArcTanh[------------]
                           Sqrt[2]
--------------------------------------
                  a
Time to compute: 0.07 second
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