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

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

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

           x
-(2 ArcTan[-] + Log[-c + x] - Log[c + x])
           c
-----------------------------------------
                   4 c
Time to compute: < 0.01 second
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