Rewriting an integral involving an exponential

[Repetit]

Can someone help me show the following:

\int_0^{\infty}r^k e^{-a r} dr=\frac{k!}{a^{k+1}}

I tried to use the polynomial expansion of e^x:

\sum_{n=0,1...} \frac{x^n}{n!}

...but I get stuck pretty fast. Can someone give me a few hints?


Thanks!

 

[matt grime]

Just do integration by parts and apply one more well known technique of proof (it might help if you let that integral be I(k), 'cos then what is I(k-1), and how does that link up with the hint to do things by parts?)

 

[Repetit]

I got it now! I wasn't really as difficult as it first seemed. Thanks a lot! :-)