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ArcTan[(Cos[x]*Sin[x])/Sqrt[2]]/(4*Sqrt[2])

Integrate[Cos[2*x]/(8 + Sin[2*x]^2), x] ==
ArcTan[(Cos[x]*Sin[x])/Sqrt[2]]/(4*Sqrt[2]) 

            Cos[2 x]
Integrate[-------------, x] == 
                      2
          8 + Sin[2 x]

       Cos[x] Sin[x]
ArcTan[-------------]
          Sqrt[2]
---------------------
      4 Sqrt[2]
Time to compute: 0.03 second
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