`intlog (1+x^(2))dx.`

Explanation

Integrating by parts, taking log `(1+x^(2))` as the first function and 1 as the second function, we get
`intlog(1+x^(2))dx=int{log(1+x^(2))*1}dx`
`=log(1+x^(2))*intdx-int[(d)/(dx){log(1+x^(2))}*int1dx]dx`
`=log(1+x^(2))*x-int(2x)/((1+x^(2)))*xdx`
`=xlog(1+x^(2))-2int(x^(2))/((1+x^(2)))dx`
`=log(1+x^(2))-2int(1-(1)/(1+x^(2)))dx`
`=xlog(1+x^(2))-2intdx+2int(dx)/((1+x^(2)))`
`=xlog(1+x^(2))-2x+2tan^(-1)x+C`.