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Integral problem

  1. Oct 7, 2008 #1
    The problem is given as
    [tex]\int\frac{x*e^x}{(x+1)^2}dx[/tex]

    I did u substitution with u=(x+1) and du=dx

    which gives me [tex]\int\frac{(u-1)*e^{u-1}}{u^2}[/tex]

    simplifies to [tex]\int\frac{u*e^{u-1}-e^{u-1}}{u^2}[/tex]

    Then I separated it into two integrals

    [tex]\int\frac{e^{u-1}}{u}-\int\frac{e^{u-1}}{u^2}[/tex]


    Now I'm stuck. I tried doing these separate integrals by parts, but it doesn't seem to be working for me. Am I going in the complete wrong direction with this? Any help would be appreciated.
     
  2. jcsd
  3. Oct 7, 2008 #2

    gabbagabbahey

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    Everything looks good to me so far, what do you get when you integrate the second term by parts once?
     
  4. Oct 7, 2008 #3
    Oh wow. I got caught up on the fact that I couldn't do the first term and didn't realize that I don't have to! The integral of the second term takes care of that for me. Thank you.
     
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