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


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



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

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

Time to compute: 0.05 second

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