作业帮一题高数不定积分求讲解!第21题.跪谢!
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/08 20:33:15
一题高数不定积分求讲解!第21题.跪谢!
一题高数不定积分求讲解!
第21题.跪谢!
一题高数不定积分求讲解!第21题.跪谢!
∫ [x^2/(x-1)^100] dx
= -(1/99)∫ x^2 d[ 1/(x-1)^99]
=-(1/99) [x^2/(x-1)^99] + (2/99) ∫ [x/(x-1)^99] dx
=-(1/99) [x^2/(x-1)^99] - (1/4851) ∫ x d(1/(x-1)^98)
=-(1/99) [x^2/(x-1)^99] - (...
全部展开
∫ [x^2/(x-1)^100] dx
= -(1/99)∫ x^2 d[ 1/(x-1)^99]
=-(1/99) [x^2/(x-1)^99] + (2/99) ∫ [x/(x-1)^99] dx
=-(1/99) [x^2/(x-1)^99] - (1/4851) ∫ x d(1/(x-1)^98)
=-(1/99) [x^2/(x-1)^99] - (1/4851) [x/(x-1)^98] + (1/4851)∫ [1/(x-1)^98] dx
=-(1/99) [x^2/(x-1)^99] - (1/4851) [x/(x-1)^98] - (1/470547)(1/(x-1)^97) + C
收起