不定积分 ∫ x^2*arctanx*dx

用分步积分法
∫ x^2*arctanx*dx
=1/3∫ arctanx*dx^3
=1/2x^3arctanx-1/3∫ x^3/(1+x^2)dx
=1/2x^3arctanx-1/6∫ x^2/(1+x^2)dx^2
=1/2x^3arctanx-1/6∫[1-1/(1+x^2)]dx^2
=1/2x^3arctanx-1/6x^2+1/6ln(1+x^2)+C