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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: 0.04 second

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