I'm trying to show that
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?
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!