Tính tích phân I = $I=\int\limits_{1}^{\text{e}}{2x.\ln 2\text{x}.d\text{x}}$

Ta có: $\left\{ \begin{align}  & u=\ln \text{x} \\  & dv=\text{xdx} \\ \end{align} \right.$ $\Rightarrow \left\{ \begin{align}  & du=\frac{1}{x}d\text{x} \\  & v=\frac{1}{2}{{\text{x}}^{2}} \\ \end{align} \right.$

$I=\left. \frac{1}{2}{{\text{x}}^{2}}\ln \text{x} \right|_{1}^{e}-\frac{1}{2}\int\limits_{1}^{e}{x\text{dx}=}\frac{3-{{e}^{2}}}{4}$

chọn D