先分部积分把ln去掉
原式=1/3*x^3*ln(1+x^2)-∫1/3*x^3*(2x/(1+x^2))dx
=1/3*x^3*ln(1+x^2)-2/3*∫(x^2-x^2/(1+x^2))dx
=1/3*x^3*ln(1+x^2)-2/3*(1/3*x^3-x+arctanx)
=1/3*x^3*ln(1+x^2)-2/9*x^3+2/3*x-2/3*arctanx