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

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

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

                              a x
  Log[Cos[a x]] - 2 Log[2 Sin[---]]
                               2
-(---------------------------------)
                  a
Time to compute: 0.04 second
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