Why is Anti Derivative of (1/x-3) Equal to -ln|x+3|?

[elitespart]

Why is the anti derivative of 1/(x-3) equal to -ln\left|x+3\right|. Why isn't it just ln\left|x-3\right|. Does it have something to do with the absolute value? Thanks.

 

[rootX]

for negative x?

using just log |x-3| defines the differentiation function for pos x only

 

[exk]

it's not -ln|x+3| and is in fact ln|x-3| . Take the derivative of your first answer and second and see which one works.

 

[elitespart]

Alright so I'm guessing there was a typo. Thanks for your help.

 

[rootX]

d/dx (log |x-3|) != 1/(x-3)
for x element of (-inf, inf) for sure! edit: wrong

ooops.. my mistake. I was ignoring the absolute part

 

[rock.freak667]

d/dx (log |x-3|) != 1/(x-3)
for x element of (-inf, inf) for sure!

For x \neq 3

 

[exk]

the original function is undefined for x=3 also btw.