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问题: 求不定积分

∫(x+1)/(x-1)^3 dx

解答:

解:原式=∫[(x-1)+2]dx/(x-1)^3
=∫d(x-1)/(x-1)^2+2∫d(x-1)/(x-1)^3
=-1/(x-1)-1/(x-1)^2+C