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Integrate (xe^(2x))/(1+2x)^2

  1. Feb 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Integrate [tex]\frac{xe^{2x}}{(1+2x)^2}[/tex] with respect to x

    Didn't get anywhere with integration by parts or substitution using u=xe^(2x)
    A push in the right direction would be much appreciated.
     
  2. jcsd
  3. Feb 17, 2013 #2
    Try v = 1 + 2x.
     
  4. Feb 17, 2013 #3
    As a second substitution?
     
  5. Feb 17, 2013 #4
    No, just start with it.
     
  6. Feb 17, 2013 #5
    Ok, I now have the following:

    [tex]\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}[/tex]
     
  7. Feb 17, 2013 #6
    Allow me to fix that for you:

    ##\displaystyle \frac{1}{4} \int \frac{(u-1)e^{(u-1)}}{u^2} \ du##
     
    Last edited: Feb 17, 2013
  8. Feb 17, 2013 #7
    where is du?
     
  9. Feb 17, 2013 #8

    ehild

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    Integrate by parts

    ∫uv'dx=uv-∫u'vdx,

    using u=xe2x and v'=1/(1+2x)2.

    ehild
     
  10. Feb 17, 2013 #9
    Parts requires u,v to be continuous.
     
  11. Feb 17, 2013 #10
    Now that we have reinstated du, observe that e^(u - 1) = (e^u)/e; the 1/e constant goes outside, and what's inside can be simplified into ((e^u)/u - (e^u)/u^2).
     
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