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Exponential Integral (Possibly integration by parts)

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Integrate the following equation for average energy from -infinity to infinity
    [tex]\int(c*x^4)*(e^(-c*x^4)/KT)dx[/tex]


    2. Relevant equations
    c, K, T are constants
    [tex]\int(e^(-c*x^4/KT))[/tex] = (KT/c)^(1/4)*(2[tex]\Gamma[/tex](5/4))


    3. The attempt at a solution
    I tried using integration by parts [tex]\intu dv[/tex] = uv - [tex]\intv du[/tex] but either way i do (with u as the exponential term and dv = cx^4 dx or the other way around), i can't seem to get the answer. Can anyone help me out?

    Thanks!!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 23, 2008 #2
    might want to repost this in a simpler form without all the constants and then add those back in later, also your exponents are kinda messed up I'm guessing you wanted:

    [tex]
    \int(c*x^4)*(e^{(-c*x^4)/KT})dx
    [/tex]
     
  4. Nov 23, 2008 #3
    subsitute t = c*x^4/KT and use the definition of the gamma function [tex] \Gamma(x) = \int t^{x-1} e^t dt [/tex]
     
  5. Nov 23, 2008 #4
    thanks - i will give this a try!
     
  6. Apr 11, 2011 #5
    Hi all

    I would like to integrate

    the integrale from o to t of (1/(1-k*exp(alpha*t))) dt where alpha and k are constant. I tried integration by part but it didnt work :s. Any help is much appreciated.

    S
     
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