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Math Help - Improper Integrals Question

  1. #1
    Junior Member
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    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.
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  2. #2
    Member Abu-Khalil's Avatar
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    \frac{4}{x}\leq \frac{5+\cos x}{x}, \forall x \in [1,\infty) and \int_1^\infty \frac{dx}{x} diverges.
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