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((-2*x*Cot[(a*x)/2])/a + (4*Log[Sin[(a*x)/2]])/a^2)/2

Integrate[x/(1 - Cos[a*x]), x] ==
((-2*x*Cot[(a*x)/2])/a + (4*Log[Sin[(a*x)/2]])/a^2)/2 

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

         a x              a x
-2 x Cot[---]   4 Log[Sin[---]]
          2                2
------------- + ---------------
      a                2
                      a
-------------------------------
               2
Time to compute: 0.02 second
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