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

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

                     1
Integrate[------------------------, x] == 
           2    2
          a  + b  - 2 a b Cos[c x]

                     c x
         (a + b) Tan[---]
                      2
2 ArcTan[----------------]
              a - b
--------------------------
         2    2
       (a  - b ) c
Time to compute: 0.10 second
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