∫[1-1/(1+x^2)]arctnxdx
=∫arctanxdx-∫arctanxdarctanx
=xarctanx-∫xdx/(1+x^2)-(1/2)(arctanx)^2+C
=xarctanx-(1/2)ln(1+x^2)-(1/2)(arctanx)^2+C