\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Establish a recurrence relation for \(I_n = \int_0^1 t^n e^t\,dt\) (\(n \in \mathbb{N}\)) and use it to compute \(I_2\). Hint: IBP with \(u' = e^t\).
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