Here comes 2016!

Calculus Level 4

\[\large \lim _{ n\rightarrow \infty }{ \ln\left( n\int _{ 0 }^{ 1 }{ { \left( x+\frac { { 2016x }^{ 2 } }{ n } \right) }^{ n } \, dx } \right) } = \, ? \]

Inspired by Satyajit Mohanty