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

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

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

                           x
           b + (a - c) Tan[-]
                           2
-2 ArcTanh[-------------------]
                  2    2    2
           Sqrt[-a  + b  + c ]
-------------------------------
             2    2    2
      Sqrt[-a  + b  + c ]
Time to compute: 0.23 second
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