Hướng dẫn giải

Ta có: \[\begin{array}{l}\int {x{{\left( {x + 2} \right)}^{2019}}dx} = \int {\left[ {\left( {x + 2} \right) - 2} \right]{{\left( {x + 2} \right)}^{2019}}dx} \\ = \int {{{\left( {x + 2} \right)}^{2020}}dx} - 2\int {{{\left( {x + 2} \right)}^{2019}}dx} = \frac{{{{\left( {x + 2} \right)}^{2021}}}}{{2021}} - \frac{{{{\left( {x + 2} \right)}^{2020}}}}{{1010}} + C\end{array}\]

Chọn D.