求一个不定积分∫ln(x
∫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。