求不定积分

Question

如题所述

Answer 1

∫ (x² - 5x + 9)/(x² - 5x + 6) dx
= ∫ [(x² - 5x + 6) + 3]/(x² - 5x + 6) dx
= ∫ [1 + 3/(x² - 5x + 6)] dx
= ∫ dx + 3∫ dx/[(x - 3)(x - 2)]
= ∫ dx + 3∫ [(x - 2) - (x - 3)]/[(x - 3)(x - 2)] dx
= ∫ dx + 3∫ [1/(x - 3) - 1/(x - 2)] dx
= x + 3[ln|x - 3| - ln|x - 2|] + C
= x + 3ln|(x - 3)/(x - 2)| + C

Answer 2

原式=∫1dx+∫4/(x-3)(x-2)dx
=x+4[∫1/(x-3)-1/(x-2)]dx
=x+4ln|x-3|-4ln|x-2|+c