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Integrate[Sqrt[3 - 2*x - x^3], x] ==
(-2*Sqrt[3 + x + x^2]*((-1 + x)*x*Sqrt[3 + x + x^2] + ((2*I)*Sqrt[2]*(-1 + x)*EllipticE[ ArcSin[Sqrt[-I + Sqrt[11] - (2*I)*x]/ (Sqrt[2]*11^(1/4))], (2*Sqrt[11])/ (-3*I + Sqrt[11])])/ Sqrt[(I*(-1 + x))/(-3*I + Sqrt[11])] - (5*I)*Sqrt[2]*Sqrt[(I*(-1 + x))/(-3*I + Sqrt[11])]* EllipticF[ArcSin[Sqrt[-I + Sqrt[11] - (2*I)*x]/ (Sqrt[2]*11^(1/4))], (2*Sqrt[11])/ (-3*I + Sqrt[11])]))/(5*Sqrt[3 - 2*x - x^3])



                          3
Integrate[Sqrt[3 - 2 x - x ], x] == 

                  2                            2
(-2 Sqrt[3 + x + x ] ((-1 + x) x Sqrt[3 + x + x ] + 
 
      ((2 I) Sqrt[2] (-1 + x) 
 
         EllipticE[ArcSin[
 
            Sqrt[-I + Sqrt[11] - (2 I) x]
            -----------------------------], 
                              1/4
                    Sqrt[2] 11
 
            2 Sqrt[11]               I (-1 + x)
          ---------------]) / Sqrt[---------------] - 
          -3 I + Sqrt[11]          -3 I + Sqrt[11]
 
                           I (-1 + x)
      (5 I) Sqrt[2] Sqrt[---------------] 
                         -3 I + Sqrt[11]
 
       EllipticF[ArcSin[
 
          Sqrt[-I + Sqrt[11] - (2 I) x]
          -----------------------------], 
                            1/4
                  Sqrt[2] 11
 
          2 Sqrt[11]                            3
        ---------------])) / (5 Sqrt[3 - 2 x - x ])
        -3 I + Sqrt[11]

Time to compute: 0.58 second

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