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Tricky Integral

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]\int\frac{xe^{2x}}{(2x+1)^2}dx[/tex] where "e" is the natural number

    2. Relevant equations

    3. The attempt at a solution
    I tried many ways to solve this problem, but to no avail.
    the hint on the book said to use substitution and make [tex]u=xe^{2x}[/tex] and [tex]du=2xe^{2x}+e^{2x}dx[/tex] but I don't see how that would work out; there is no way to change all the x's into u's.
  2. jcsd
  3. Feb 4, 2010 #2


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    I don't think they meant a simple substitution. They meant to integrate by parts with u=x*exp(2x). Pick dv=dx/(2x+1)^2. That works.
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