：依题意：∫x^3/(1+x^2)dx =∫（x^2 * arctanx）dx ＝1/3*∫arctanxd(x^3)dx ＝1/3*x^3*arctanx－1/3*∫x^3/(1+x^2)dx ＝1/3*x^3*arctanx－1/3*∫(x^3+x-x)/(1+x^2)dx ＝1/3*x^3*arctanx－1/3*∫xdx＋1/3*∫x/(1+x^2)dx ＝1/3*x^3*arctanx－1/6*x^2..
