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Calculus II - Partial Fractions - Evaluate integral dx/(x^4-10x^2+9)

  1. Aug 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Evaluate integral dx/(x^4-10x^2+9)

    2. Relevant equations

    3. The attempt at a solution

    Ok so I'm trying to solve this problem for my calculus II course as a homework problem and am lost.

    The first attachment you'll see how I attempted to evaluate the integral by setting u = x^2, which resulted in

    1/2 integral dx/(sqrt(u)(u^2-16u+9))

    I then factored u^2-16u+9 by finding the solution of what u is equal to using the quadratic formula and got this as my new resulting integral

    1/2 integral du/(sqrt(u)(u-8+sqrt(55))(u-8-sqrt(55)))

    I then tried to result this into partial fractions in order to evaluate the integral in form

    A/sqrt(u) + B/(u-8+sqrt(55)) + C/(u-8-sqrt(55))

    When I solved for A, B, and C, I got

    A = 1/9
    B = -1/(2 sqrt(55) sqrt(8+sqrt(55)) )
    C = 1/(2 sqrt(55) sqrt(8 + sqrt(55) )

    When I then tried to evaluate each separate integral I got

    x/9 - 1/(4 sqrt(55) sqrt(8 + sqrt(55))) ln|x^2 - 8 + sqrt(55)| + 1/(4 sqrt(55) sqrt(8 + sqrt(55) ) ) ln|x^2 - 8 - sqrt(55)| + c

    I guess I did something wrong...

    I than tried to evaluate the integral using trig substitution as you will see in the the second attachment, i crossed off my first attempt and just got to the point were i decided it was getting to complicated for calculus II I had to make two trig substitutions using two different triangles.

    I'm lost thanks for any help.

    Attached Files:

    • try.jpg
      File size:
      30.1 KB
    • try2.jpg
      File size:
      54.7 KB
  2. jcsd
  3. Aug 6, 2011 #2


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    Homework Helper

    Factor x^4-10*x^2+9. It splits completely into linear factors. Then use partial fractions.
  4. Aug 6, 2011 #3
    oh wow thanks =) i over complicated it a bit much
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