When I tried to compute the integral $\int \frac 1 {2x-2}dx$, the following was my attempt. $$\int \frac 1 {2x-2}dx=\frac 1 2 \int \frac 1 {x-1}dx=\frac 1 2\ln\left(|x-1|\right)+c$$
But then I saw someone on youtube doing the same integral and getting the answer $$\int \frac 1 {2x-2}dx=\frac 1 2 \ln\left(|2x-2|\right)+c$$
Now I immediately thought that something was wrong, so I tried to put the integral into Symbolab. To my surprise, Symbolab seemed to agree with the second answer. Then I put the integral into Wolfram and I got the answer that I had at first.
After that I decided to input the following into Symbolab. $$\int \frac 1 2 \cdot\frac 1 {x-1}dx$$ and Symbolab seemed to agree with my first answer.
Now, it could be possible that I am missing something very obvious, but I don't know what is it. So, am I wrong or was Symbolab wrong?