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(2*ArcTan[(b + (-1 + a)*Tan[x/2])/Sqrt[-1 + a^2 - b^2]])/Sqrt[-1 + a^2 - b^2]

Integrate[1/(a + Cos[x] + b*Sin[x]), x] ==
(2*ArcTan[(b + (-1 + a)*Tan[x/2])/ Sqrt[-1 + a^2 - b^2]])/Sqrt[-1 + a^2 - b^2] 

                    1
Integrate[---------------------, x] == 
          a + Cos[x] + b Sin[x]

                          x
         b + (-1 + a) Tan[-]
                          2
2 ArcTan[-------------------]
                    2    2
         Sqrt[-1 + a  - b ]
-----------------------------
                2    2
     Sqrt[-1 + a  - b ]
Time to compute: 0.16 second
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