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.