Original formula = (1/2) (xarctanx) 2-∫ [(x2/(1+x2)] arctan xdx = (1/2) (xarctanx) 2-∫.

And ∫ [1-1(1+x 2)] arctan xdx = ∫ arctan xdx-(1/2) (arctan x) 2 = xarctanx-(6544)

∴ Original formula = (1/2) (1+x 2) (arctanx) 2-xarctanx+(1/2) ln (1+x 2)+C.

For reference.