Do not get Logarithmic antiderivatives

[muzialis]

Dear All,

the antiderivative of $$\frac{1}{x}$$ is $$ln \vert x \vert $$.
If I then consider the expression $$ (x-a) ln (\vert x-a\vert)-x $$ and compute the first derivative I obtain $$ ln (\vert x-a \vert)$$.
If I then consider the equivalent expression $$ (x-a) ln (\vert a -x\vert)-x $$ I do not get the same result, where is my mistake??

 

[pwsnafu]

If I then consider the equivalent expression $$ (x-a) ln (\vert a -x\vert)-x $$ I do not get the same result, where is my mistake??

We can't answer that unless you show us what answer you got. And your working.