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

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

Integrate[Sec[a x], x] == 

         a x        a x             a x        a x
-Log[Cos[---] - Sin[---]] + Log[Cos[---] + Sin[---]]
          2          2               2          2
----------------------------------------------------
                         a
Time to compute: < 0.01 second
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