$\lim _{n \rightarrow \infty} \frac{(2 n(2 n-1) \ldots(n+2)(n+1))^{1 / n}}{n}=$

• A

  $\int_0^1 \log x d x$
• B

  $\int_0^1 x \log x d x$
• C

  $\int_0^1(x+1) \log (x+1) d x$
• Correct answer
  D

  $\int_0^1 \log (1+x) d x$

Hence, the correct answer is option: 'D'.