∫[(ax²+b)×arctan x]/(x²+1)dx=∫[a-（a-b)/(x²+1)*arctan xdx=ax*arctanx-a∫x/(1+x^2) dx -(a-b)/2 *arctan^2x=ax*arctanx-a/2*ln(1+x^2) dx -(a-b)/2 *arctan^2x +C