Multiplex for JEE 2 (no way out)

Calculus Level 4

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

n!

(n+1)!

0

n(n!)

1

n(n+1)!

The integral is not solvable

e^{n!}