1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluate this integral

  1. Jun 25, 2013 #1


    User Avatar
    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


    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..
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted