Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gamma function

  1. May 10, 2005 #1
    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.

    Help please! :)
  2. jcsd
  3. May 11, 2005 #2

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You want

    [tex]\int \limits_0^\infty e^{4u}e^{-e^u} du[/tex]

    Put [itex]x=e^u[/itex], so that [itex]dx=e^u du[/itex] and you get:

    [tex]\int \limits_1^\infty x^3 e^{-x} dx[/tex]

    Can you go from there?
  4. May 11, 2005 #3
    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)
  5. May 11, 2005 #4
    Thanks James. I'm right to continue now but shouldn't it be x^4 not x^3?
  6. May 11, 2005 #5
    Actually, dx=e^u du, so one of the e^u's is in the dx, leaving only e^3u, or x^3.
  7. May 11, 2005 #6
    Of course. Thanks for your help guys :) :)
  8. May 11, 2005 #7


    User Avatar
    Science Advisor
    Homework Helper

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

  9. May 11, 2005 #8


    User Avatar
    Science Advisor

    If you go to the "general physics" forum you will find a "sticky" on Latex formatting.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook