The value of \( \int_{0}^{I}\left(\prod_{r=1}^{n}(x+r)\right)\left(\sum_{k=1}^{n} \frac{1}{x+k}\...

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The value of \( \int_{0}^{I}\left(\prod_{r=1}^{n}(x+r)\right)\left(\sum_{k=1}^{n} \frac{1}{x+k}\right) \) equals
(a) \( n \)
(b) \( n \) !
(c) \( (n+1) \) !
(d) \( n \cdot n \) !
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