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

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

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

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