`x tan^(-1)x`

Explanation

`int x. tan^(-1) x dx`
`=tan^(-1)x int x dx- int{(d)/(dx)tan^(-1)x int x dx}dx`
`=(x^(2))/(2)tan^(-1)x-int(1)/(1+x^(2)).(x^(2))/(2)dx`
`=(x^(2))/(2)tan^(-1)x-(1)/(2)int(-1(1)/(1+x^(2)))dx`
`=(x^(2))/(2)tan^(-1)x-(1)/(2)(x-tan^(-1)x)+c`
`=((x^(2)+1)/(2))tan^(-1)x-(1)/(2)x+c`