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(x^(2 + 2*m)*Sqrt[1 - x^2/a^2]*Hypergeometric2F1[1/2, 1 + m, 2 + m, x^2/a^2])/(2*(1 + m)*Sqrt[-a^2 + x^2])


Integrate[x^(1 + 2*m)/Sqrt[-a^2 + x^2], x] ==
(x^(2 + 2*m)*Sqrt[1 - x^2/a^2]*Hypergeometric2F1[1/2, 1 + m, 2 + m, x^2/a^2])/ (2*(1 + m)*Sqrt[-a^2 + x^2])



              1 + 2 m
             x
Integrate[--------------, x] == 
                 2    2
          Sqrt[-a  + x ]

                    2
  2 + 2 m          x
(x        Sqrt[1 - --] 
                    2
                   a
 
                                        2
                      1                x
    Hypergeometric2F1[-, 1 + m, 2 + m, --]) / 
                      2                 2
                                       a
 
                    2    2
  (2 (1 + m) Sqrt[-a  + x ])

Time to compute: 0.07 second

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