高数，这题不定积分怎么求？谢谢。 5
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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
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
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