Why does C = ln k? (Integration)

Howdy Can someone explain why we can put C = ln k please?
I don't get how it can just have a natural log there now.
What if k was negative?
Thanks

c could be negative so 0<k<1, but k couldnt be negative. But ln(k) is a constant that can take any real value (c), but k must be > 0.
You obviously do it to simpify the result.
Its worth noting that when you remove the abs values, you extend the domain of k to include negative values as well though.

Thanks. I get why it can't be negative but I can't explain to myself why we make C = ln k to begin with. Is it just to make it easier?

Sure, you use ln(k) as the constant as it becomes a multiplier so you "remove" logs. You can write it as c = ln(e^c), and k = e^c.
Though note that k can be negative when you remove the absolute values. The text seems to skip over this.