Tích phân \(I = \int\limits_1^2 {x\ln xdx} \) có g...

D

- Hướng dẫn giải

Đặt \(\left\{ \begin{array}{l}u = \ln x\\dv = xdx\end{array} \right. \Rightarrow \left\{ \begin{array}{l}du = \frac{1}{x}dx\\v = \frac{{{x^2}}}{2}\end{array} \right.\).

\( \Rightarrow I = \left. {\left( {\frac{{{x^2}}}{2}.\ln x} \right)} \right|_1^2 - \int\limits_1^2 {\frac{x}{2}dx} \\= \left. {\left( {\frac{{{x^2}}}{2}.\ln x} \right)} \right|_1^2 - \left. {\left( {\frac{{{x^2}}}{4}} \right)} \right|_1^2 \\= 2\ln 2 - \frac{3}{4}\)