Evaluate : `intxtan^(-1)xdx`

Explanation

Integrating by parts, taking `tan^(-1)` x as the first function, we get
`intxtan^(-1)dx=(tan^(-1)x)*intxdx-int{(d)/(dx)(tan^(-1)x)*intxdx}dx`
`=(tan^(-1)x)*(x^(2))/(2)-int(1)/((1+x^(2)))*(x^(2))/(2)dx`
`=(x^(2)tan^(-1)x)/(2)-(1)/(2)int(1-(1)/(1+x^(2)))dx " "["on dividing "x^(2)" by "1+x^(2)]`
`=(x^(2)tan^(-1))/(2)-(1)/(2)intdx+(1)/(2)int(1)/((1+x^(2)))dx`
`=(x^(2)tan^(-1)x)/(2)-(x)/(2)+(1)/(2)tan^(-1)x+C`
`=(1)/(2)(1+x^(2))tan^(-1)x-(1)/(2)x+C`.