integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫
(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
Spread the word: