不定积分求解 积分符号 (1-X)方 分之X dX

_Fashion_yoyo 2023-03-18 05:22

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  ___一休___

  2023-03-18 06:14

  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

  ∫[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

  把题目写清楚一点？

  x/(x-1)^2=(x-1)/(x-1)^2+1/(x-1)^2=1/(x-1)+1/(x-1)^2.

  原式=ln(x-1)-1/(x-1)+C
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