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Integrate[1/(7 + 3*x^4), x] ==
(-2*ArcTan[1 - (3/7)^(1/4)*Sqrt[2]*x] + 2*ArcTan[1 + (3/7)^(1/4)*Sqrt[2]*x] - Log[7 - Sqrt[2]*3^(1/4)*7^(3/4)*x + Sqrt[21]*x^2] + Log[7 + Sqrt[2]*3^(1/4)*7^(3/4)*x + Sqrt[21]*x^2])/ (4*Sqrt[2]*3^(1/4)*7^(3/4))



             1
Integrate[--------, x] == 
                 4
          7 + 3 x

                3 1/4
(-2 ArcTan[1 - (-)    Sqrt[2] x] + 
                7
 
                  3 1/4
    2 ArcTan[1 + (-)    Sqrt[2] x] - 
                  7
 
                     1/4  3/4               2
    Log[7 - Sqrt[2] 3    7    x + Sqrt[21] x ] + 
 
                     1/4  3/4               2
    Log[7 + Sqrt[2] 3    7    x + Sqrt[21] x ]) / 
 
              1/4  3/4
  (4 Sqrt[2] 3    7   )

Time to compute: 0.14 second

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