
Tricky Integral
I'm trying to show that
$\displaystyle \int_{0}^{\infty}ate^{at}(1e^{at})^{n2}(1ne^{at}) dt = {1 \over {an}} $ for $\displaystyle n \ge 2$
I've tried using induction over n, but I'm not sure this is the best way to go. Is there some substitution I'm missing?

Re: Tricky Integral
I'd be equally glad to know if this is likely to be an unreasonably difficult integral. I obtained the above result using Mathematica and ideally wanted a proof, but it's not essential. Interestingly, the pro online version of Wolfram Alpha runs out of time before being able to evaluate it!

Re: Tricky Integral
Ok I've figured this out, the strategy is simply to do integration by parts to 'kill' the tterm, after which you are left with a much simpler integration which allows the substitution u=exp(at)!