A Naturally Limited Integrand

Calculus Level 4

Evaluate \[\lim_{x\to 0} \left (\frac{1}{x^{5}}\left(\int_{0}^{x}e^{-t^{2}}\, dt\right)-\frac{1}{x^{4}} +\frac{1}{3x^{2}}\right ). \]

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