对(x+1)/(x^2-4x+3)求不定积分

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对(x+1)/(x^2-4x+3)求不定积分对(x+1)/(x^2-4x+3)求不定积分对(x+1)/(x^2-4x+3)求不定积分∫(x+1)/(x^2-4x+3)dx=∫(x+1)/(x-3)(x

对(x+1)/(x^2-4x+3)求不定积分
对(x+1)/(x^2-4x+3)求不定积分

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

原式=∫(x+1)/[(x-1)(x-3)]dx=∫(-1/(x-1)+2/(x-3))dx=-∫d(x-1)/(x-1)+2∫d(x-3)/(x-3)=-ln|x-1|+2ln|x-3|+C

哎 高数基本忘了