`x log x`

Explanation

`int x log x dx`
`=log x int x dx - int [(d)/(dx)(logx)int x dx ]dx`
`=(x^(2)logx)/(2)-(1)/(2)int(1)/(x)x^(2)dx`
`=(x^(2)logx)/(2)-(1)/(2)int xdx`
`rArr" "I=(x^(2)logx)/(2)-(1)/(4)x^(2)+C`