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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^(1/4)*b^(3/4))


Integrate[1/(-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^(1/4)*b^(3/4))



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

Time to compute: 0.03 second

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