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ArcTan[x^2/c^2]/(2*c^2)

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

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

        2
       x
ArcTan[--]
        2
       c
----------
      2
   2 c
Time to compute: < 0.01 second
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