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Math Help - Improper integrals, converging

  1. #1
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    Improper integrals, converging

    Find all real numbers p such that \int_2^{\infty}\frac{1}{x(\ln x)^p} dx converges
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Find all real numbers p such that \int_2^{\infty}\frac{1}{x(\ln x)^p} dx converges
    Let u = \ln x so your integral becomes

    \int_{\ln 2}^{\infty} \frac{du}{u^p}.

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  3. #3
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    Quote Originally Posted by Danny View Post
    Let u = \ln x so your integral becomes

    \int_{\ln 2}^{\infty} \frac{du}{u^p}.

    Look familar?
    Where did the x go?
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  4. #4
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    Quote Originally Posted by acevipa View Post
    Where did the x go?
    1/x went with the du. du=1/x.

    Also I would prefer first solving the indefinite integral. It's much better approach.
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