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


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



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

                   x
         b + a Tan[-]
                   2
2 ArcTan[-------------]
               2    2
         Sqrt[a  - b ]
-----------------------
           2    2
     Sqrt[a  - b ]

Time to compute: 0.09 second

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