ok.

\(\displaystyle y = \int ln(3x - 7) dx\)

let \(\displaystyle t = 3x - 7\)

\(\displaystyle \frac{dt}{dx} = 3,\)

so.. \(\displaystyle dx = \frac{1}{3} dt\)

so...

\(\displaystyle y = \frac{1}{3} \int ln t dt\)

let \(\displaystyle u = ln t\), so \(\displaystyle u' = \frac {1}{t}\)

let \(\displaystyle v' = 1 \), so \(\displaystyle v = t\)

so...

\(\displaystyle y = \frac{1}{3} (t ln t - \int \frac{1}{t} dt)\)

\(\displaystyle = \frac{1}{3} (t ln t - ln t) + C\)

\(\displaystyle = \frac{t ln t}{3} - \frac{ln t}{3} + C\)

\(\displaystyle = \frac{(3x - 7) ln (3x - 7)}{3} - \frac{ln(3x - 7)}{3} + C\)

\(\displaystyle = (x - \frac{7}{3})ln(3x - 7) - \frac{ln (3x - 7)}{3} + C\)