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Integrate[x^2*Sqrt[a - b^4*x^2], x] ==
Sqrt[a - b^4*x^2]*(-(a*x)/(8*b^4) + x^3/4) + (a^2*ArcTan[(b^2*x)/Sqrt[a - b^4*x^2]])/(8*b^6)

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

                           3
          4  2   -(a x)   x
Sqrt[a - b  x ] (------ + --) + 
                     4    4
                  8 b
 
                  2
   2             b  x
  a  ArcTan[---------------]
                      4  2
            Sqrt[a - b  x ]
  --------------------------
                6
             8 b