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Incorrect answer for the integral of -1/(x-1)?

Posted 10 years ago

Hello,

I was playing around with Wolfram Alpha and I performed the following query:

integral of 1/(x-1) dx

The answer it returned was ln(x - 1) as you would expect.

I then tried to integrate the function multiplied by -1 expecting to get the original answer times -1 (as per integration rules for a function multiplied by a constant):

integral of -1/(x-1) dx

The answer it returned was -ln(1-x) instead of the expected -ln(x-1).

I did a quick, lazy check to see if our answers were the same with the following query:

-ln(1-x) / -ln(x-1)

However, they are not equivalent. They do have the same real value for x >= 1, though.

Am I doing something wrong? Have I simply forgotten some of my integral or log rules? Is this a limitation of the free version of WolframAlpha? Any help would be much appreciated!

POSTED BY: Deryk Morrish
4 Replies
POSTED BY: Sean Clarke
Posted 10 years ago

Thank you! My understanding of calculus is only at an undergrad engineering level. And that was 6 years ago. And I didn't do very well at the time! I'm just getting myself back to where I left off and hopefully farther. Thanks!

POSTED BY: Deryk Morrish
POSTED BY: S M Blinder
Posted 10 years ago

I really wish I saw this myself. Very simple explanation. Thanks!

POSTED BY: Deryk Morrish
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