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Math Help - Find covergence

  1. #1
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    Find covergence

    Find if the improper integral converges. 1 / infinity lnx/x^2
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Link88 View Post
    Find if the improper integral converges. 1 / infinity lnx/x^2
    Consider that

    \frac{\ln(x)}{x^2}\leqslant\frac{\sqrt{x}}{x^2}=\f  rac{1}{x^{\frac{3}{2}}}

    So what can we conclude?
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  3. #3
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    do we have to use integration by parts? thats what my professor told us is the way to solve it.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Link88 View Post
    do we have to use integration by parts? thats what my professor told us is the way to solve it.
    If you are trying to actually find the value of the integral then integration by parts is the correct method. To make it a little easier first try making the substitution \ln(x)=z
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  5. #5
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    using subst. method i get u = lnx and then du = 1/x dx and substituting in i get u/x^2 = ln/x
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