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-(Sqrt[-1 + x]/(6 + 9*x)) + ArcTan[Sqrt[3/5]*Sqrt[-1 + x]]/(3*Sqrt[15])

Integrate[Sqrt[x - 1]/(2 + 3*x)^2, x] ==
-(Sqrt[-1 + x]/(6 + 9*x)) + ArcTan[Sqrt[3/5]*Sqrt[-1 + x]]/(3*Sqrt[15]) 

          Sqrt[x - 1]
Integrate[-----------, x] == 
                   2
          (2 + 3 x)

                              3
                  ArcTan[Sqrt[-] Sqrt[-1 + x]]
  Sqrt[-1 + x]                5
-(------------) + ----------------------------
    6 + 9 x                3 Sqrt[15]
Time to compute: 0.25 second
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