- #1

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## Homework Statement:

- Solve the following integral

## Relevant Equations:

- ∫dx/(1-x)

I solved the integral by two different methods and I get different answers.

Method 1:

∫dx/(1-x) = -∫-dx/(1-x), u=1-x, du=-dx

∫dx/(1-x) = -∫du/u = -ln|u| = -ln|1-x|

Method 2:

∫-dx/(x-1) = -∫dx/(x-1), u=x-1, du=dx

∫-dx/(x-1) = -∫du/u = -ln|u| = -ln|x-1|

What am I doing wrong?

Method 1:

∫dx/(1-x) = -∫-dx/(1-x), u=1-x, du=-dx

∫dx/(1-x) = -∫du/u = -ln|u| = -ln|1-x|

Method 2:

∫-dx/(x-1) = -∫dx/(x-1), u=x-1, du=dx

∫-dx/(x-1) = -∫du/u = -ln|u| = -ln|x-1|

What am I doing wrong?