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Integrate[1/(x^(3/2)*Sqrt[25 - 4*x^2]), x] ==
(2*(-(Sqrt[25 - 4*x^2]/Sqrt[x]) + Sqrt[10]*(-EllipticE[ArcSin[Sqrt[2/5]*Sqrt[x]], -1] + EllipticF[ArcSin[Sqrt[2/5]*Sqrt[x]], -1])))/25



                   1
Integrate[--------------------, x] == 
           3/2              2
          x    Sqrt[25 - 4 x ]

                   2
      Sqrt[25 - 4 x ]
(2 (-(---------------) + 
          Sqrt[x]
 
                                       2
      Sqrt[10] (-EllipticE[ArcSin[Sqrt[-] Sqrt[x]], 
                                       5
 
                                       2
           -1] + EllipticF[ArcSin[Sqrt[-] Sqrt[x]], 
                                       5
 
          -1]))) / 25

Time to compute: 0.21 second

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