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(x*(1 + x^2/c^2)^n*Hypergeometric2F1[1/2, n, 3/2, -(x^2/c^2)])/(c^2 + x^2)^n


Integrate[(c^2 + x^2)^(-n), x] ==
(x*(1 + x^2/c^2)^n*Hypergeometric2F1[1/2, n, 3/2, -(x^2/c^2)])/(c^2 + x^2)^n



            2    2 -n
Integrate[(c  + x )  , x] == 

        2                                 2
       x  n                   1     3    x
x (1 + --)  Hypergeometric2F1[-, n, -, -(--)]
        2                     2     2     2
       c                                 c
---------------------------------------------
                   2    2 n
                 (c  + x )

Time to compute: 0.02 second

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