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Homework Help: Exponential integration

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data

    how would you integrate, int (-ik - 2ax)*exp(-2ax^2) dx with limits infinity - infinity

    2. Relevant equations

    i think i can use the result int exp(-x^2) dx = sqrt (pi). But I am stumped.

    3. The attempt at a solution

    i thought about multiplying it out

    int -ik*exp(-2ax^2) - 2ax*exp(-2ax^2) dx with limits infinity and - infinity

    but it looks more complex now. would you use integration by substitution

    Thank you
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 1, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi ronaldoshaky! Welcome to PF! :smile:

    (have an integral: ∫ and an infinity: ∞ and a pi: π and try using the X2 tag just above the Reply box :wink:)

    Just do the two parts separately …

    -∞ ik e-2ax2 dx you know how to do;

    and ∫ 2ax e-2ax2 dx you can do by substitution. :wink:
     
  4. Feb 2, 2010 #3
    Thank you!
     
  5. Feb 3, 2010 #4
    Hi tiny-tim

    Can I evaluate this integral ∫-∞∞ (ik-2ax) exp(-2ax2) dx without multiplying it out,
    using integration by parts because it is a product?

    I get


    ∫-∞∞ (ik-2ax) exp(-2ax2) dx = f(x)g(x) - ∫ f '(x)g(x) = - ik (sqrt (pi/2a)) + ikx (sqrt (pi/2a))

    Is that any way correct?
     
  6. Feb 3, 2010 #5

    tiny-tim

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    No. :redface:
     
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