解答

$${I=\int x\log xdx}$$

$$\begin{eqnarray*} I&=& \int\underbrace{x}_{f'}\underbrace{\log x}_{g}dx\\ &=... ...rac{1}{2}\int xdx\\ &=& \frac{1}{2}x^2\log x-\frac{1}{4}x^2+C \end{eqnarray*}$$