分类：教育/科学-理工学科-数学
问题：求一个不定积分∫ln(x
回答：∫ln(x-1)dx
=∫ln(x-1)d(x-1)
=(x-1)ln(x-1)-∫(x-1)d[ln(x-1)]
=(x-1)ln(x-1)-∫[(x-1)·1/|(x-1)|]d(x-1)
=(x-1)ln(x-1)-∫|1|d(x-1)
=(x-1)ln(x-1)-|x-1|+C。