用两次分部积分
∫(x-1)^2(x-4)^12dx
=((x-1)^2*(x-4)^13)/13 - (2/13)∫(x-1)(x-4)^13dx
= (1/13)*(x-1)^2(x-4)^13 - (2/(13*14))(x-1)*(x-4)^14 +(1/(13*7))∫(x-4)^14dx
= (1/13)*(x-1)^2(x-4)^13 - (1/91)(x-1)(x-4)^14 +(1/91*15))(x-4)^15 + C
用两次分部积分
∫(x-1)^2(x-4)^12dx
=((x-1)^2*(x-4)^13)/13 - (2/13)∫(x-1)(x-4)^13dx
= (1/13)*(x-1)^2(x-4)^13 - (2/(13*14))(x-1)*(x-4)^14 +(1/(13*7))∫(x-4)^14dx
= (1/13)*(x-1)^2(x-4)^13 - (1/91)(x-1)(x-4)^14 +(1/91*15))(x-4)^15 + C