Why does the [1,∞]∫ $\displaystyle (5+cos(x))/x$ diverge?

If I broke that up into [1,∞]∫ 5/x + [1,∞]∫cos(x)/x

then [1,∞]∫ 5/x = 0

and [1,∞]∫ cos(x)/x = obviously diverges by I dont know why it does.

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- Feb 27th 2009, 06:36 PMFallen186Improper Integrals Question
Why does the [1,∞]∫ $\displaystyle (5+cos(x))/x$ diverge?

If I broke that up into [1,∞]∫ 5/x + [1,∞]∫cos(x)/x

then [1,∞]∫ 5/x = 0

and [1,∞]∫ cos(x)/x = obviously diverges by I dont know why it does. - Feb 27th 2009, 06:54 PMAbu-Khalil
$\displaystyle \frac{4}{x}\leq \frac{5+\cos x}{x}, \forall x \in [1,\infty)$ and $\displaystyle \int_1^\infty \frac{dx}{x}$ diverges.