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Integrate[Sqrt[x]/(-1 + x^4), x] ==
(2*Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[x]] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[x]] + 4*ArcTan[Sqrt[x]] + 2*Log[-1 + Sqrt[x]] - 2*Log[1 + Sqrt[x]] - Sqrt[2]*Log[1 - Sqrt[2]*Sqrt[x] + x] + Sqrt[2]*Log[1 + Sqrt[2]*Sqrt[x] + x])/8



          Sqrt[x]
Integrate[-------, x] == 
                4
          -1 + x

(2 Sqrt[2] ArcTan[1 - Sqrt[2] Sqrt[x]] - 
 
    2 Sqrt[2] ArcTan[1 + Sqrt[2] Sqrt[x]] + 
 
    4 ArcTan[Sqrt[x]] + 2 Log[-1 + Sqrt[x]] - 
 
    2 Log[1 + Sqrt[x]] - 
 
    Sqrt[2] Log[1 - Sqrt[2] Sqrt[x] + x] + 
 
    Sqrt[2] Log[1 + Sqrt[2] Sqrt[x] + x]) / 8

Time to compute: 0.07 second

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