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(1 - 2*(Log[Cos[(a*x)/2]] - Log[Sin[(a*x)/2]])*Sin[(a*x)/2]^2)/(2*a*(-1 + Cos[a*x]))

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

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

               a x             a x        a x 2
1 - 2 (Log[Cos[---]] - Log[Sin[---]]) Sin[---]
                2               2          2
-----------------------------------------------
              2 a (-1 + Cos[a x])
Time to compute: 0.07 second
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