# Exponential Integral (Possibly integration by parts)

1. Nov 23, 2008

### staceybiomed

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

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

3. 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!!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 23, 2008

### 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:

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

3. Nov 23, 2008

### weejee

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

4. Nov 23, 2008

### staceybiomed

thanks - i will give this a try!

5. Apr 11, 2011