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(x*Sqrt[(-1 + x^3)^4]*(14 - 7*x^3 + 2*x^6))/(14*(-1 + x^3)^2)


Integrate[Sqrt[1 - 4*x^3 + 6*x^6 - 4*x^9 + x^12], x] ==
(x*Sqrt[(-1 + x^3)^4]*(14 - 7*x^3 + 2*x^6))/ (14*(-1 + x^3)^2)



                      3      6      9    12
Integrate[Sqrt[1 - 4 x  + 6 x  - 4 x  + x  ], x] == 

              3 4           3      6
x Sqrt[(-1 + x ) ] (14 - 7 x  + 2 x )
-------------------------------------
                      3 2
            14 (-1 + x )

Time to compute: 0.05 second

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