对(x+1)/(x^2-4x+3)求不定积分

问题描述:

对(x+1)/(x^2-4x+3)求不定积分

∫(x+1)/(x^2-4x+3)dx=∫(x+1)/(x-3)(x-1)dx=∫(x-1+2)/(x-3)(x-1)dx=∫[1/(x-3)+2/(x-3)(x-1)]dx=∫{1/(x-3)+[1/(x-3)-1/(x-1)]}dx=∫[2/(x-3)-1/(x-1)]dx=2ln(x-3)-ln(x-1)+C