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


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



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

           x
-(2 ArcTan[-] + Log[-a + x] - Log[a + x])
           a
-----------------------------------------
                   4 a

Time to compute: < 0.01 second

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