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Integrate[(3*x + 7)^3/(x^3 - 1)^3, x] ==
-(1701 + 8394*x + 9261*x^2 - 5064*x^4 - 5292*x^5 + 1612*Sqrt[3]*(-1 + x^3)^2* ArcTan[(1 + 2*x)/Sqrt[3]] - 5140*(-1 + x^3)^2* Log[3*(-1 + x)] + 2570*Log[9*(1 + x + x^2)] - 5140*x^3*Log[9*(1 + x + x^2)] + 2570*x^6*Log[9*(1 + x + x^2)])/(54*(-1 + x^3)^2)



                   3
          (3 x + 7)
Integrate[----------, x] == 
            3     3
          (x  - 1)

                        2         4         5
-(1701 + 8394 x + 9261 x  - 5064 x  - 5292 x  + 
 
                         3 2        1 + 2 x
     1612 Sqrt[3] (-1 + x )  ArcTan[-------] - 
                                    Sqrt[3]
 
                 3 2
     5140 (-1 + x )  Log[3 (-1 + x)] + 
 
                          2
     2570 Log[9 (1 + x + x )] - 
 
           3                 2
     5140 x  Log[9 (1 + x + x )] + 
 
           6                 2                 3 2
     2570 x  Log[9 (1 + x + x )]) / (54 (-1 + x ) )

Time to compute: 0.32 second

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