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Math Help - converges

  1. #1
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    converges

    how do you show that intergrate from 0 to infinity of

    1/ (x^2 + sq root x) dx converges?

    i tried to do comparison test by saying that it is less than integrate from 0 to infinity of
    1/ sq root x but it doesnt show that it converges.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    If f(x) is the integrand function, we have

    \displaystyle\lim_{x \to{+}\infty}{\frac{f(x)}{1/x^2}}=\ldots=1\neq 0

    \displaystyle\lim_{x \to 0^+}{\frac{f(x)}{1/\sqrt{x}}}=\ldots=1\neq 0

    So,

    \int_0^1 f(x)dx\;,\quad \int_1^{+\infty} f(x)dx

    are convergent
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