3次分部积分法解 用!代表积分号
=!(x^3-x+1)（1-cos2x）/2dx
=(x^3-x+1)（x/2-sin2x/4）-!(3x^2-1)（x/2-sin2x/4）dx+c
= -!(3x^2-1)（x/2）dx +!(3x^2-1)(sin2x)/4）dx+c
= -!（3/2)x^3-x/2 dx +!(3x^2-1)(sin2x)/4）dx+c
= -(3/8)x^4+(x^2)/4 +(-(3x^2-1)(cos2x)/8+!(6x)(cos2x)/8dx)+c
= -(3x^2-1)(cos2x)/8+!(6x)(cos2x)/8dx+c
= +(6xsin2x)/16-!6sin2x/16dx +c
= +(3/16)cos2x+c
=(x^3-x+1)（x/2-sin2x/4）-(3/8)x^4+(x^2)/4 -(3x^2-1)(cos2x)/8 +(6xsin2x)/16+(3/16)cos2x+c