不定积分求解 积分符号 (1-X)方 分之X dX

题目

不定积分求解 积分符号 (1-X)方 分之X dX
积分符号 (1-X)方 分之X dX
就是 f x/(x-1)^2 dx

答案

∫[x/(1-x)²]dx
=∫[(x-1)/(x-1)²+1/(x-1)²]dx
=∫[1/(x-1)]dx+∫[1/(x-1)²]dx
=∫[1/(x-1)]d(x-1)+∫[1/(x-1)²]d(x-1)
=ln|x-1|-1/(x-1)+C
C为任意常数