Asymptotics of the solution of a differential equation

Let f be twice continuously differentiable function defined on \mathbb{R}, such that f(x)f''(x)=1 for all x\ge 0, f(0)=1 and f'(0)=0.

Find \lim_{x\to\infty} \frac{f(x)}{x\sqrt{\ln(x)}}.

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