∫x arctanxdx =1/2∫ arctanxdx^2 =x^2arctanx/2-1/2∫x^2darctanx =x^2arctanx/2-1/2∫x^2/(1+x^2)dx =x^2arctanx/2-1/2∫(1-1/(1+x^2))dx =x^2arctanx/2-x/2+arctanx/2+C.
