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


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



            Tan[a x]
Integrate[------------, x] == 
          1 - Cos[a x]

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

Time to compute: 0.05 second

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