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Does x/(x^2 - 1)^2 converge or diverge?

  1. Jan 13, 2010 #1
    Does the integral from 2 to infinity of x/(x^2 - 1)2 converge or diverge, if it converges, state its value.

    I got up to the point where i know the integral converges using the direct comparison test and comparing the original integral with the integral from 2 to infinity of 1/x3.

    First, i "FOILed" the bottom to get:

    x/[x4 - 2x2 + 1]

    Using my FOILed integral i took out an x/x4 which is = to 1/x3 and then used the direct comparison test to find out that the integral from 2 to infinity of 1/x3 reaches a value of 1/2 (converging), thus allowing us to assume that the original integral converges as well.

    Now, i just don't know how to calculate the value of convergence for x/(x^2 - 1)2. Any advice to lead me in the right direction?
     
  2. jcsd
  3. Jan 13, 2010 #2
    Hint: The numerator is proportional to the derivative of the contents of the brackets in the denominator.
     
  4. Jan 13, 2010 #3
    u-sub ;)
     
  5. Jan 13, 2010 #4

    Hurkyl

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    Don't do it this way* -- but is there any reason why you did not consider partial fractions?

    *: unless you want to.
     
  6. Jan 14, 2010 #5
    i just realized you have to use u-substitution. partial fractions take much too long for a problem like this.
     
  7. Jan 14, 2010 #6

    Hurkyl

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    I bet you could have done it in the half hour between your previous two posts. :wink:
     
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