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Homework Help: Integral of squareroot and exponetial

  1. Sep 15, 2010 #1
    1. The problem statement, all variables and given/known data
    is there a general method of integrating this type of integral:
    [tex] \int \sqrt{x -k} e^{-bx} [/tex]


    2. Relevant equations



    3. The attempt at a solution

    [tex]x-k={u}^{2}[/tex]
    [tex]dx=2udu[/tex]
    [tex] \int u^2 \,{e}^{{-b\left( {u}^{2}-k\right) }}du [/tex]
    [tex] \int {u}^{2}\,{e}^{{-b\,{u}^{2}}+{b\,k}}du [/tex]

    and it seems worse than its starting point
     
    Last edited: Sep 15, 2010
  2. jcsd
  3. Sep 15, 2010 #2
    Actually it's not worse... You can finish the problem by integrating by parts:

    [tex]
    \int u^2\,{e}^{-bu^2}=\int u\cdot u{e}^{-bu^2}
    [/tex]

    I dont know what happened but as I type my message, the browser won't process more tex-code, so I put it in raw form, but I hope, you can understand from it what I'm saying. So:

    =u\cdot \frac{{e}^{-bu^2}}{-2b}+\frac 1{2b}\,\int {e}^{-bu^2}

    And it's done, because the last integral can be calculated explicitly, see the Gauss-distribution at wikipedia.
     
  4. Sep 18, 2010 #3
    here's your code

    [tex]=u\cdot \frac{{e}^{-bu^2}}{-2b}+\frac 1{2b}\,\int {e}^{-bu^2} [/tex]

    thanks
    i was able to do it :)
     
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