Which of the following integrals gives the length of the curve $y = \ln x$ from $x = 1$ to $x = 2$ ?
(A) $\int _ { 1 } ^ { 2 } \sqrt { 1 + \frac { 1 } { x ^ { 2 } } } d x$
(B) $\int _ { 1 } ^ { 2 } \left( 1 + \frac { 1 } { x ^ { 2 } } \right) d x$
(C) $\int _ { 1 } ^ { 2 } \sqrt { 1 + e ^ { 2 x } } d x$
(D) $\int _ { 1 } ^ { 2 } \sqrt { 1 + ( \ln x ) ^ { 2 } } d x$
(E) $\int _ { 1 } ^ { 2 } \left( 1 + ( \ln x ) ^ { 2 } \right) d x$