dx/(x-1)乘以(x-2)乘以(x-3)的不定积分

Question

dx/(x-1)乘以(x-2)乘以(x-3)的不定积分

Answer 1

let1/[(x-1)(x-2)(x-3)]≡A/(x-1)+B/(x-2)+C/(x-3)=>1≡A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2)x=1,A= 1/2x=2,B= -1/2x=3,C=1/2∫ dx/[(x-1)(x-2)(x-3)]=(1/2)∫ [1/(x-1) -1/(x-2)+1/(x-3)] dx=(1/2)ln|(x-1)(x-3)/(x...