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(x + (2*a*ArcTanh[((a - b)*Tan[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2])/b

Integrate[Cos[x]/(a + b*Cos[x]), x] ==
(x + (2*a*ArcTanh[((a - b)*Tan[x/2])/ Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2])/b 

             Cos[x]
Integrate[------------, x] == 
          a + b Cos[x]

                            x
                (a - b) Tan[-]
                            2
    2 a ArcTanh[--------------]
                       2    2
                Sqrt[-a  + b ]
x + ---------------------------
                 2    2
          Sqrt[-a  + b ]
-------------------------------
               b
Time to compute: 0.11 second
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