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Homework Help: Improper Integral

  1. Apr 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Evaluate the integral: [tex]\int[/tex][tex]\frac{dx}{x^{3}+x^{2}+x+1}[/tex]
    from infinity to zero

    2. Relevant equations
    lim t--> infinity [/tex] [tex]\int[/tex] [tex]\frac{dx}{x^{3}+x^{2}+x+1}[/tex]

    3. The attempt at a solution

    lim t-->infinity [/tex] [tex]\int[/tex] [tex]\frac{dx}{(x+1)(x^{2}+1}[/tex]

    I'm stuck on where to go from here. I tried partial fractions, but can't seem to get it. any hints would be a great help!
  2. jcsd
  3. Apr 3, 2008 #2
    partial fractions, yes.


    So you must have

    Comparing coefficients of the same powers of x you get the equation:


    which you can easily solve, I assume :smile:

    Do you know to integrate the partial fractions?
    Last edited: Apr 3, 2008
  4. Apr 3, 2008 #3
    Oh! I see, i must have miswritten something when i was doing partial fractions. Thank you so much for the help!

    I 'll give it a shot and see what comes up
  5. Apr 3, 2008 #4
    alright, so I've worked on solving this problem up to:

    a=1/2 b=1/2 c=-1/2

    so my integral terms would be:

    taking the antiderivative:
    i have, [tex]\frac{1}{2}[/tex]ln|x+1| for the first term
    as for the second, i know one of the terms will be tan[tex]^{-1}[/tex]x because of the denominator, but i'm having troubles with the numerator since I can't use substitution for it.
  6. Apr 3, 2008 #5
    Split the second term into two. For the one with the x in the numerator you can use the substitution


    The first term (with the constant numerator).. well..you know how to do it:smile:
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