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I should determine whether this is a convergent or divergent integral. The problem is that I don't know how to start. $$ \int_{1}^{+\infty} \frac{x\ \sin(x)\ dx}{\sqrt{1+x^5}} $$

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Note that $$\left \vert\dfrac{x \sin(x)}{\sqrt{1+x^5}} \right \vert \leq \dfrac{x}{\sqrt{1+x^5}} \leq \dfrac{x}{x^{5/2}} = \dfrac1{x^{3/2}}$$ Now you should be able to finish it off.

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Garh, I was nearly there, but it felt wrong! Thank you! –  Curtain Nov 20 '12 at 19:21

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