Giải thích các bước giải:
$\begin{array}{l}
\int {x\ln xdx} \\
= \dfrac{1}{2}\int {\ln x} d\left( {{x^2}} \right)\\
= \dfrac{1}{2}\left( {{x^2}\ln x - \int {{x^2}.\dfrac{1}{x}dx} } \right)\\
= \dfrac{1}{2}\left( {{x^2}\ln x - \int {xdx} } \right)\\
= \dfrac{1}{2}\left( {{x^2}\ln x - \dfrac{1}{2}{x^2}} \right)+C\\
= \dfrac{1}{2}{x^2}\left( {\ln x - \dfrac{1}{2}} \right)+C
\end{array}$
