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(-4*Sqrt[-1 + x] + 2*Sqrt[2]*Sqrt[-1 + x]*Sqrt[x] - 2*Sqrt[2]*ArcTan[(Sqrt[2] + Sqrt[x])/Sqrt[-1 + x]] - I*Sqrt[2]*Log[16])/4

Integrate[Sqrt[x - 1]/(1 + Sqrt[2*x]), x] ==
(-4*Sqrt[-1 + x] + 2*Sqrt[2]*Sqrt[-1 + x]*Sqrt[x] - 2*Sqrt[2]*ArcTan[(Sqrt[2] + Sqrt[x])/ Sqrt[-1 + x]] - I*Sqrt[2]*Log[16])/4 

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

(-4 Sqrt[-1 + x] + 2 Sqrt[2] Sqrt[-1 + x] Sqrt[x] - 
 
                     Sqrt[2] + Sqrt[x]
    2 Sqrt[2] ArcTan[-----------------] - 
                       Sqrt[-1 + x]
 
    I Sqrt[2] Log[16]) / 4
Time to compute: 0.16 second
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