1. Not finding help here? Sign up for a free 30min 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!

Integration of a fraction.

  1. Oct 13, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\displaystyle \int{\frac{dx}{a^2+\left(x-\frac{1}{x} \right)^2}} [/tex]

    2. Relevant equations


    3. The attempt at a solution

    This one looks a bit odd. Had the denominator been a^2 + x^2, it is in one of the standard forms, whose integral is [tex]\frac{1}{a} \atan{\frac{x}{a}} [/tex]. But the denominator is in the form of a^2 + u^2 (where u is a function of x). I did try some manipulations, but to no avail. I tried putting x as sin(theta), but got something like cos(theta)d(theta)/(a^2+cos^4(theta)/sin^2(theta)), which seems even more complex. If someone can just point me into the direction to look, I'll attempt the solution.

    Thank you,
  2. jcsd
  3. Oct 13, 2007 #2

    Gib Z

    User Avatar
    Homework Helper

    Expand the brackets, simplify, multiply the entire integral by x^2/x^2, factor the denominator and partial fractions.
  4. Oct 13, 2007 #3
    Thanks for the quick reply, I'm currently here,

    [tex]\displaystyle \int{\frac{x^2dx}{x^2(a^2-2)+x^4+1} [/tex]

    I don't see how I can factorize/simplify the denominator or the expression...?

    Last edited: Oct 13, 2007
  5. Oct 13, 2007 #4

    Gib Z

    User Avatar
    Homework Helper

    Well let [itex]a^2-2 =b[/itex] and [itex]u=x^2[/itex]. Now it resembles a nice quadratic equation =]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integration of a fraction.