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!