..Please help, I'm stuck...

Prove the equality: int[(t^n)(e^-t)] from 0 to infinity = n!, for n=0,1,2,... Mr F says: Proof by induction would be a simple approach (combined with integration by parts).

(Evaluate int(e^(-xt)) dt from 0 to infinity and consider whether repeatedly differentiating under the integral is permitted) Mr F says: Is this a seperate question? Or is it related to the above?