Multiplex for JEE 2 (no way out)

Calculus Level 4

\[\displaystyle \int_{0}^{1} \left (\prod_{r=1}^{n}(x+r) \right ) \left (\sum_{k=1}^{n}\frac{1}{x+k} \right ) \ dx = \ ? \]

This is a problem of my set Some JEE problems.
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