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((-2 + Cos[a*x])*Sin[a*x])/(3*a*(-1 + Cos[a*x])^2)

Integrate[(1 - Cos[a*x])^(-2), x] ==
((-2 + Cos[a*x])*Sin[a*x])/(3*a*(-1 + Cos[a*x])^2) 

                        -2
Integrate[(1 - Cos[a x])  , x] == 

(-2 + Cos[a x]) Sin[a x]
------------------------
                     2
  3 a (-1 + Cos[a x])
Time to compute: 0.03 second
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