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Euge

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For ##x\in \mathbb{R}##, let $$A(x) = \frac{1}{2\pi}\, P.V. \int_{-\infty}^\infty e^{i(xy + \frac{y^3}{3})}\, dy$$ Show that the integral defining ##A(x)## exists and ##|A(x)| \le M(1 + |x|)^{-1/4}## for some numerical constant ##M##.

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