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Evaluate this integral

  1. Jun 25, 2013 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    [itex] \displaystyle \int^∞_0 \dfrac{dx}{a^2 + \left(x-\frac{1}{x} \right)^2}[/itex] a>=2


    3. The attempt at a solution

    [itex] \displaystyle \int^∞_0 \dfrac{x^2 dx}{x^2a^2 + (x^2-1)^2}[/itex]
     
  2. jcsd
  3. Jun 25, 2013 #2
    Put ##\displaystyle x=\frac{1}{t}## in the given integral. :wink:
     
  4. Jun 26, 2013 #3
    Not sure about Pranav's hint but here is how I would have done it:

    Making a tricky substitution of,

    1/t = x-1/x

    OR

    In your attempt at solution, expand the denominator, then write numerator as x2-1+1, break the denominator, then in each integrand, divide both sides by x2, try making the denominator the perfect square, then in term like Y2 in the denominator, let Y=t...etc..
     
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