A positive integer \( n \leq 5 \) such that
\( \int_{0}^{1} e^{2 x-1}(x-1)^{n} d x=\frac{1}{4}\l....
A positive integer \( n \leq 5 \) such that
\( \mathrm{P} \)
\( \int_{0}^{1} e^{2 x-1}(x-1)^{n} d x=\frac{1}{4}\left(\frac{7}{e}-e\right) \) is
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