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(2*Sqrt[2]*ArcTan[Sqrt[x]/Sqrt[2]] + Log[-1 + Sqrt[x]] - Log[1 + Sqrt[x]])/3

Integrate[Sqrt[x]/((-1 + x)*(2 + x)), x] ==
(2*Sqrt[2]*ArcTan[Sqrt[x]/Sqrt[2]] + Log[-1 + Sqrt[x]] - Log[1 + Sqrt[x]])/3 

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

                  Sqrt[x]
(2 Sqrt[2] ArcTan[-------] + Log[-1 + Sqrt[x]] - 
                  Sqrt[2]
 
    Log[1 + Sqrt[x]]) / 3
Time to compute: 0.03 second
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