Question

x^2/(x-1)^10 dx求不定积分详细过程 急

Answer 1

x^2/(x-1)^10

说明：x^2=(x-1+1)^2=(x-1)^2+2(x-1)+1

x^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)^(-10)]d(x-1)

=-[1/[7(x-1)^7]-[2/[8(x-1)^(-8)]-[1/[9(x-1)^(-9)] + C

=-1/[7(x-1)^7]-1/[4(x-1)^8]-1/[9(x-1)^9]+C