How to integrate ((1 -y/(y^2+R^2)^(1/2)) dy) limit from 0 to infinity

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\frac{d^{2} x}{d y^{2}} - x = k

k

y = 0

y

lim x \to \infty \frac{x}{\sqrt{{4 x}^{2} + 1}} = \frac{1}{2}

((\sqrt{x^{3}}) + 1) + ((\sqrt[3]{x^{2}}) + 2)

x = 0

x = 2

lim x \to \infty \frac{{3 x}^{- 1} + {4 x}^{- 2}}{{5 x}^{- 1} + 6 x^{- 2}} = \frac{3}{5}

lim x \to \infty \frac{(3 x - 1) (4 x - 2)}{(x + 8) (x - 1)} [12]

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