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(x^(1 + m)*Sqrt[1 - x^2/a^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, x^2/a^2])/((1 + m)*Sqrt[a^2 - x^2])


Integrate[x^m/Sqrt[a^2 - x^2], x] ==
(x^(1 + m)*Sqrt[1 - x^2/a^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, x^2/a^2])/ ((1 + m)*Sqrt[a^2 - x^2])



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

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

Time to compute: 0.07 second

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