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Math Help - convergence problem

  1. #1
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    convergence problem

    \int_{0}^\infty \frac{ln (1+x)} {x^{1/2}+x^{2}}dx
    the answer book gives us is convergence
    but i think it diverges in (0,1)
    so can anyone help me to solve the problem?
    show it!
    Last edited by chialin4; January 27th 2010 at 07:10 PM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    for x < 1

    ln(1+x) < 1

    and 1/(x^(1/2) +x^2) < 1/(x^(1/2)


    ln(1+x)/[(x^(1/2) +x^2)] < 1/(x^)1/2))


    the integral [1/(x^)1/2))]dx can easily be shown to converge on (0,1]
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    for x < 1

    ln(1+x) < 1

    and 1/(x^(1/2) +x^2) < 1/(x^(1/2)


    ln(1+x)/[(x^(1/2) +x^2)] < 1/(x^)1/2))


    the integral [1/(x^)1/2))]dx can easily be shown to converge on (0,1]

    thx for ur help!
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