# Gamma function

1. May 10, 2005

### splitendz

Hi. I'm having some trouble solving the following gamma function:

Evaluate the integral e^(4u) * e^(-e^u)du. The upper limit is inifinity and the lower limit is 0.

I'm letting x = e^(u) or u = 1 in the hope to have the function looking similar to the gamma function. But i'm having no luck as du/dx will be equal to zero in this case.

2. May 11, 2005

### James R

You want

$$\int \limits_0^\infty e^{4u}e^{-e^u} du$$

Put $x=e^u$, so that $dx=e^u du$ and you get:

$$\int \limits_1^\infty x^3 e^{-x} dx$$

Can you go from there?

3. May 11, 2005

### PhysicsinCalifornia

How do you write those sophisticated symbols?

I want to be able to write it, but don't know how

(Sorry its not helping your problem dude)

4. May 11, 2005

### splitendz

Thanks James. I'm right to continue now but shouldn't it be x^4 not x^3?

5. May 11, 2005

### Moo Of Doom

Actually, dx=e^u du, so one of the e^u's is in the dx, leaving only e^3u, or x^3.

6. May 11, 2005

### splitendz

Of course. Thanks for your help guys :) :)

7. May 11, 2005

### dextercioby

I think part integrating will do it.Three times,i guess.

Daniel.

8. May 11, 2005

### HallsofIvy

Staff Emeritus
If you go to the "general physics" forum you will find a "sticky" on Latex formatting.