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Integrate[x^7/(1 + x^12), x] ==
(2*Sqrt[3]*ArcTan[(1 + Sqrt[3] - 2*Sqrt[2]*x)/ (1 - Sqrt[3])] - 2*Sqrt[3]* ArcTan[(1 - Sqrt[3] + 2*Sqrt[2]*x)/ (1 + Sqrt[3])] + 2*Sqrt[3]* ArcTan[(-1 + Sqrt[3] + 2*Sqrt[2]*x)/ (1 + Sqrt[3])] - 2*Sqrt[3]* ArcTan[(1 + Sqrt[3] + 2*Sqrt[2]*x)/ (-1 + Sqrt[3])] - 2*Log[1 - Sqrt[2]*x + x^2] - 2*Log[1 + Sqrt[2]*x + x^2] + Log[2 + Sqrt[2]*x - Sqrt[6]*x + 2*x^2] + Log[2 + Sqrt[2]*(-1 + Sqrt[3])*x + 2*x^2] + Log[2 - (Sqrt[2] + Sqrt[6])*x + 2*x^2] + Log[2 + (Sqrt[2] + Sqrt[6])*x + 2*x^2])/24



             7
            x
Integrate[-------, x] == 
               12
          1 + x

                  1 + Sqrt[3] - 2 Sqrt[2] x
(2 Sqrt[3] ArcTan[-------------------------] - 
                         1 - Sqrt[3]
 
                     1 - Sqrt[3] + 2 Sqrt[2] x
    2 Sqrt[3] ArcTan[-------------------------] + 
                            1 + Sqrt[3]
 
                     -1 + Sqrt[3] + 2 Sqrt[2] x
    2 Sqrt[3] ArcTan[--------------------------] - 
                            1 + Sqrt[3]
 
                     1 + Sqrt[3] + 2 Sqrt[2] x
    2 Sqrt[3] ArcTan[-------------------------] - 
                           -1 + Sqrt[3]
 
                           2
    2 Log[1 - Sqrt[2] x + x ] - 
 
                           2
    2 Log[1 + Sqrt[2] x + x ] + 
 
                                       2
    Log[2 + Sqrt[2] x - Sqrt[6] x + 2 x ] + 
 
                                          2
    Log[2 + Sqrt[2] (-1 + Sqrt[3]) x + 2 x ] + 
 
                                       2
    Log[2 - (Sqrt[2] + Sqrt[6]) x + 2 x ] + 
 
                                       2
    Log[2 + (Sqrt[2] + Sqrt[6]) x + 2 x ]) / 24

Time to compute: 0.40 second

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