Help! Converting a Riemann Sum to a Definite Integral

Question

Can someone please explain how to convert this into a definite integral in the form

$$\lim _{ n\rightarrow \infty }{ \left\{ \ln { \sqrt [ n ]{ \left( n+1 \right) \left( n+2 \right) \left( n+3 \right) ...\left( 2n \right) } -n\ln { \sqrt [ n ]{ n } } } \right\} } $$

Answer 1

This is nothing but $$\lim_{n \to \infty} \frac{1}{n}\{\log\frac{n+1}{n}+\log\frac{n+2}{n}+...+\log\frac{2n}{n}\}=\lim_{n \to \infty}\frac{1}{n}\sum_{k=1}^n\log \frac{n+k}{n}=\int_0^1 \log (1+x)dx$$