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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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