∫xarctanxdx
=1/2∫arctanx*2xdx
=1/2∫arctanxdx^2
=1/2xarctanx-1/2∫x^2*1/(x^2+1)dx
=1/2xarctanx-1/2∫(x^2+1-1)dx/(x^2+1)
=1/2xarctanx-1/2∫dx+1/2∫dx/(x^2+1)
=1/2xarctanx-x/2+1/2*arctanx+C
=1/2*(xarctanx-x+arctanx)+C