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Math Help - Improper Integrals

  1. #1
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    Improper Integrals

    the problem is: int(x/((x^2+2)^2)dx) from 0 to infinite

    I just have to tell whether it's convergent or divergent. I set it to the
    lim as t-> infinite of the integral from 0 to t. I'm having trouble integrating it. I started using partial fractions but can't anywhere with that. Any help would be appreciated.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by LINKJ6 View Post
    the problem is: int(x/((x^2+2)^2)dx) from 0 to infinite

    I just have to tell whether it's convergent or divergent. I set it to the
    lim as t-> infinite of the integral from 0 to t. I'm having trouble integrating it. I started using partial fractions but can't anywhere with that. Any help would be appreciated.
    Make the substitution u=x^2+2\implies \,du=2x\,dx

    The integral transforms from \int_0^{\infty}\frac{x}{\left(x^2+2\right)^2}\,dx\  implies \tfrac{1}{2}\int_2^{\infty}\frac{\,du}{u^2}

    Can you take it from here?

    --Chris
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