x^2⼀(x-1)^10 dx不定积分 求详细解答步骤

2025-03-07 05:09:59
推荐回答(1个)
回答1:

因为x^2=(x-1)^2 + 2(x-1) + 1

∫x^2/(x-1)^10=[(x-1)^2 + 2(x-1) + 1]/(x-1)^10 dx
=∫[(x-1)^(-8) + 2(x-1)^(-9) + (x-1)^(-10)]dx
=-[(x-1)^(-7)/7 + (x-1)^(-8)/4 + (x-1)^(-9)/9]