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(Sqrt[(1 + x^2)^3]*(x*Sqrt[1 + x^2]*(5 + 2*x^2) + 3*ArcSinh[x]))/(8*(1 + x^2)^(3/2))


Integrate[Sqrt[1 + 3*x^2 + 3*x^4 + x^6], x] ==
(Sqrt[(1 + x^2)^3]*(x*Sqrt[1 + x^2]*(5 + 2*x^2) + 3*ArcSinh[x]))/(8*(1 + x^2)^(3/2))



                      2      4    6
Integrate[Sqrt[1 + 3 x  + 3 x  + x ], x] == 

            2 3               2          2
(Sqrt[(1 + x ) ] (x Sqrt[1 + x ] (5 + 2 x ) + 
 
                                2 3/2
      3 ArcSinh[x])) / (8 (1 + x )   )

Time to compute: 0.07 second

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