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Calc II Improper Integrals

  1. Sep 27, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]\int\frac{x}{(x^2+2)(x^2+2)}[/tex] dx from 0 to infinity

    2. Relevant equations
    Improper integrals

    3. The attempt at a solution
    Lim[tex]_{t->\infty}[/tex] [tex]\int[/tex][tex]\frac{t}{0}[/tex] ([tex]\frac{x}{(x^2+2)(x^2+2)}[/tex])

    I tried integrating this by parts and also by partial fractions but neither seemed to lend itself nicely to the problem. (Choosing dv = (x^2+2)^(-2) made finding v ugly and based on the rules for choosing u shouldn't I choose x to be u?) And partial fractions didn't seem to work either. Any suggestions?
    Last edited: Sep 27, 2008
  2. jcsd
  3. Sep 27, 2008 #2


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    That's a pretty ugly tex post but if you mean the integral of x*dx/(x^2+2) try u=x^2+2.
  4. Sep 27, 2008 #3
    I am still trying to play with the formatting, sorry, I will write it out in words in the mean time: the integral of x over (x^2+2)^2 dx.

    But, yes, it seems like that simple u-substitution will work! Thank you ... I feel so silly for overcomplicating the problem!
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