Question

一题不定积分题求详解

Answer 1

∫(x+3)/(x^2-5x+6)dx

=∫(x+3)/[(x-2)(x-3)]dx

=∫(x-3+6)/[(x-2)(x-3)]dx

=∫{1/(x-2)+6*[(x-2)-(x-3)]/[(x-2)(x-3)]}dx

=∫[1/(x-2)+6/(x-3)-6/[(x-2)]dx

=∫[6/(x-3)-5/[(x-2)]dx

=6ln|x-3|-5ln|x-2|+C