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Integrate[1/(x^3 + 1)^4, x] ==
((27*x)/(1 + x^3)^3 + (36*x)/(1 + x^3)^2 + (60*x)/(1 + x^3) + 40*Sqrt[3]* ArcTan[(-1 + 2*x)/Sqrt[3]] + 40*Log[1 + x] - 20*Log[1 - x + x^2])/243



              1
Integrate[---------, x] == 
            3     4
          (x  + 1)

   27 x        36 x       60 x
(--------- + --------- + ------ + 
       3 3         3 2        3
 (1 + x )    (1 + x )    1 + x
 
                      -1 + 2 x
    40 Sqrt[3] ArcTan[--------] + 40 Log[1 + x] - 
                      Sqrt[3]
 
                    2
    20 Log[1 - x + x ]) / 243

Time to compute: 0.21 second

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