Exponential Integral (Possibly integration by parts)

[staceybiomed]

Homework Statement

Integrate the following equation for average energy from -infinity to infinity
\int(c*x^4)*(e^(-c*x^4)/KT)dx

Homework Equations

c, K, T are constants
\int(e^(-c*x^4/KT)) = (KT/c)^(1/4)*(2\Gamma(5/4))

The Attempt at a Solution

I tried using integration by parts \intu dv = uv - \intv du 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!

 

[LogicalTime]

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:

<br /> \int(c*x^4)*(e^{(-c*x^4)/KT})dx<br />

 

[weejee]

subsitute t = c*x^4/KT and use the definition of the gamma function \Gamma(x) = \int t^{x-1} e^t dt

 

[staceybiomed]

subsitute t = c*x^4/KT and use the definition of the gamma function \Gamma(x) = \int t^{x-1} e^t dt

thanks - i will give this a try!

 

[bbsaad]

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