- #1
leviathanX777
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1. Relevant problem
integrate from 0 to infinity of r^2exp^(-r/a0)dr
I'm also given; integral from 0 to infinity of x^nexp^-x dx = n!
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 a lot of times. As there's two other terms with higher powers of r to go through.
integrate from 0 to infinity of r^2exp^(-r/a0)dr
Homework Equations
I'm also given; integral from 0 to infinity of x^nexp^-x dx = n!
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 a lot of times. As there's two other terms with higher powers of r to go through.