# Math Help - Improper Integrals Question

1. ## Improper Integrals Question

Why does the [1,∞]∫ $(5+cos(x))/x$ 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.

2. $\frac{4}{x}\leq \frac{5+\cos x}{x}, \forall x \in [1,\infty)$ and $\int_1^\infty \frac{dx}{x}$ diverges.