I'm trying to show that

for

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?

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- Mar 8th 2013, 04:09 AMStaryNightTricky Integral
I'm trying to show that

for

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? - Mar 8th 2013, 01:21 PMStaryNightRe: 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!

- Mar 8th 2013, 03:11 PMStaryNightRe: Tricky Integral
Ok I've figured this out, the strategy is simply to do integration by parts to 'kill' the t-term, after which you are left with a much simpler integration which allows the substitution u=exp(-at)!