Why the negative sign on that line?

Question

First of all, sorry if the question is stupid. I am banging my head to understand that.

As far as I know,

I am trying to understand the following explanation:

On that explanation, the guy does exactly this integral but comes with a negative sign for the natural log...

why?

Answer 1

The variable is $v(t)$, which has a negative sign in the denominator. Use the substitution $u = V - v(t)$.

Also note that $$\int\frac1x\ dx = \begin{cases} \ln(-x) + C_1, & x < 0 \\ \ln x + C_2, & x > 0 \end{cases}$$

Answer 2

He doesn't do exactly that integral. Note the sign in front of $v(t)$ in the denominator.