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Integrate[1/(1 + x^5), x] ==
(-2*Sqrt[10 - 2*Sqrt[5]]*ArcTan[(1 + Sqrt[5] - 4*x)/ Sqrt[10 - 2*Sqrt[5]]] + 2*Sqrt[2*(5 + Sqrt[5])]* ArcTan[(-1 + Sqrt[5] + 4*x)/ Sqrt[2*(5 + Sqrt[5])]] + 4*Log[1 + x] + (-1 + Sqrt[5])*Log[1 + ((-1 + Sqrt[5])*x)/2 + x^2] - (1 + Sqrt[5])* Log[1 - ((1 + Sqrt[5])*x)/2 + x^2])/20



            1
Integrate[------, x] == 
               5
          1 + x

(-2 Sqrt[10 - 2 Sqrt[5]] 
 
             1 + Sqrt[5] - 4 x
     ArcTan[--------------------] + 
            Sqrt[10 - 2 Sqrt[5]]
 
    2 Sqrt[2 (5 + Sqrt[5])] 
 
             -1 + Sqrt[5] + 4 x
     ArcTan[---------------------] + 4 Log[1 + x] + 
            Sqrt[2 (5 + Sqrt[5])]
 
                           (-1 + Sqrt[5]) x    2
    (-1 + Sqrt[5]) Log[1 + ---------------- + x ] - 
                                  2
 
                          (1 + Sqrt[5]) x    2
    (1 + Sqrt[5]) Log[1 - --------------- + x ]) / 20
                                 2

Time to compute: 0.29 second

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