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

Splitting up exponential terms when integrating

  1. Oct 9, 2011 #1
    1. Relevant problem

    integrate from 0 to infinity of r^2exp^(-r/a0)dr

    2. Relevant equations

    I'm also given; integral from 0 to infinity of x^nexp^-x dx = n!

    3. The attempt at a solution

    I'm just wondering if I can split up the exponential to make it look like this form. Eg;

    integrate from 0 to infinity of (r^2e^(-r/a0)dr becomes; integrate from 0 to infinity of (r^2e^(-r)dr times integrate from 0 to infinity of (e^(1/a0)dr however I'm pretty sure when I split up the integral, the second term isn't correct. Can anyone help? I just don't want to integration by parts alot of times. As there's two other terms with higher powers of r to go through.
  2. jcsd
  3. Oct 9, 2011 #2


    Staff: Mentor

    It looks like you are thinking that e-r/a = e-r * e1/a, which is not true. Review the properties of exponents. This wikipedia page has a summary.

    The fastest approach to your integral, I believe, is by integration by parts. One application should get you to a form similar to the one you show in your relevant equations.
  4. Oct 9, 2011 #3
    I did it already using integration by parts. First time I did it didn't yield something similar to the hint I was given. Had to do integration by parts twice and the exponential was still divided by ao all the way through.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook