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I Need help with this definite integral

  1. May 24, 2016 #1
    I'm having a tough time with this integral:

    $$\int_{0}^\infty \frac{x^2 \, dx}{x^4+(a^2+\frac{1}{b^2})x^2+\frac{2a^2}{b^2}}$$
    where $$a, b \in \Bbb R^+$$ I tried using the residue theorem, but the roots of the denominator I found are quite complicated, and I got stuck.

    What contour should I use? Is there an alternative method? I would appreciate any advice.
  2. jcsd
  3. May 24, 2016 #2


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    Homework Helper

    There are no singularities in the region of integration. This looks like partial fractions might be the proper approach.
  4. May 24, 2016 #3


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    Science Advisor

    For partial fractions, the denominator terms will be in terms of [itex]x^2\ not\ x[/itex].
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