x^2/(x-1)^10 dx求不定积分详细过程急_数学解答

x^2/(x-1)^10 dx求不定积分详细过程急

人气：104 ℃　时间：2020-02-06 01:35:32

解答

x^2/(x-1)^10 说明：x^2=(x-1+1)^2=(x-1)^2+2(x-1)+1x^2/(x-1)^10=((x-1)^2+2(x-1)+1)/(x-1)^10=1/(x-1)^8+(2(x-1)+1)/(x-1)^10=(x-1)^(-8) +2 (x-1)^(-9) +(x-1)^(-10)原式=∫[(x-1)^(-8) +2 (x-1)^(-9) +(x-1)^(-1...