The longest imaginable

Calculus Level 4

Evaluate lim⁡n→∞∫01∫01…∫01nx1+x2+⋯+xn dx1dx2…dxn. \lim_{n \to \infty} \displaystyle \int_0^1 \int_0^1 \ldots \int_0^1 \dfrac{n}{x_1+x_2+\dots+x_n}\, dx_1 dx_2 \ldots dx_n.

Clarification: In the answer options, e (≈2.71828)e \, (\approx 2.71828) is the Euler's number.

Note: This problem is a generalization of my previous problem.
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Efren Medallo by Efren Medallo
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