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(2*ArcTan[(a^(1/4)*x)/b^(1/4)] + Log[-b^(1/4) + a^(1/4)*x] - Log[b^(1/4) + a^(1/4)*x])/(4*a^(3/4)*b^(1/4))


Integrate[x^2/(-b + a*x^4), x] ==
(2*ArcTan[(a^(1/4)*x)/b^(1/4)] + Log[-b^(1/4) + a^(1/4)*x] - Log[b^(1/4) + a^(1/4)*x])/(4*a^(3/4)*b^(1/4))



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

           1/4
          a    x          1/4    1/4
(2 ArcTan[------] + Log[-b    + a    x] - 
            1/4
           b
 
         1/4    1/4           3/4  1/4
    Log[b    + a    x]) / (4 a    b   )

Time to compute: 0.03 second

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