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

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

Integrate[Sin[a x] Tan[a x], x] == 

          a x        a x
  Log[Cos[---] - Sin[---]]
           2          2
-(------------------------) + 
             a
 
          a x        a x
  Log[Cos[---] + Sin[---]]
           2          2      Sin[a x]
  ------------------------ - --------
             a                  a
Time to compute: 0.02 second
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