∫x/(1-x)dx的不定积分

问题描述:

∫x/(1-x)dx的不定积分

答:
∫ [x/(1-x)] dx
=∫ [(x-1+1)/(1-x)] dx
=∫ [-1+1/(1-x)] dx
=-∫ dx-∫ [1/(x-1)] d(x-1)
=-x-ln |x-1| +C