$\lim _{n \rightarrow \infty} \ln \sqrt[n]{\left(1+\frac{1}{n}\right)^2\left(1+\frac{2}{n}\right)^2 \cdots\left(1+\frac{2}{n}\right)^2}$ 等于
A
$\int_1^2 \ln ^2 x \mathrm{~d} x$
B
$2 \int_1^2 \ln x \mathrm{~d} x$
C
$2 \int_1^2 \ln (1+x) d x$
D
$\int_1^2 \ln ^2(1+x) \mathrm{d} x$
E
F