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-ArcTan[(3*Cos[x])/2]/6

Integrate[(Sec[x]*Tan[x])/(9 + 4*Sec[x]^2), x] ==
-ArcTan[(3*Cos[x])/2]/6 

          Sec[x] Tan[x]
Integrate[-------------, x] == 
                      2
          9 + 4 Sec[x]

        3 Cos[x]
-ArcTan[--------]
           2
-----------------
        6
Time to compute: 0.04 second
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