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x - Tan[(a*x)/2]/a

Integrate[1/(1 + Sec[a*x]), x] ==
x - Tan[(a*x)/2]/a 

               1
Integrate[------------, x] == 
          1 + Sec[a x]

        a x
    Tan[---]
         2
x - --------
       a
Time to compute: 0.08 second
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