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



             2
            x
Integrate[-------, x] == 
           4    4
          c  + x

               Sqrt[2] x                 Sqrt[2] x
(-2 ArcTan[1 - ---------] + 2 ArcTan[1 + ---------] + 
                   c                         c
 
         2                  2
    Log[c  - Sqrt[2] c x + x ] - 
 
         2                  2
    Log[c  + Sqrt[2] c x + x ]) / (4 Sqrt[2] c)

Time to compute: 0.07 second

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