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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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