How can I show that$$\sqrt[3]6>\int_1^\infty\frac{(1+x)^{1/3}}{x^2}\mathrm dx?$$
Proving an estimate for this integral
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integration
measure-theory
inequality
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0Perhaps you can try to use a Taylor expansion on $(1+x)^{1/3}$ and use a suitable convergence theorem (e.g. Monotone convergence theorem, Fatou's lemma or the Dominated convergence theorem) – 2012-08-03