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Integral Problem

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data

    integral[x*exp(iax + b)] dx



    2. Relevant equations



    3. The attempt at a solution

    I know there is a an integral for this I can pull out from a table, but is there any direct analytical way to solve it? Perhaps by parts?

    Thanks.
     
  2. jcsd
  3. Oct 5, 2009 #2

    jbunniii

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    Gold Member

    You can use

    [tex]e^{iax + b} = e^{iax} e^b[/tex]

    to simplify the integrand. Yes, integration by parts looks promising.
     
  4. Oct 6, 2009 #3
    What if I had [tex]\int^{\infty}_{-\infty}x exp(-ax^{2})exp(bx) dx[/tex]
     
  5. Oct 6, 2009 #4

    lanedance

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    haven't tried it... but how about combining the exponetial terms, then complete the square in the exponential, substitute for y = x+c in the square, then use another substitution u = y^2

    the only problem i can see is in you integration limits... may have to have a think about those & maybe split the integral
     
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