(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Splitting up exponential terms when integrating

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