Question

$$ int \frac { 4 } { 3 x - 2 } d x $$

Explanation:

Step1: Use substitution

Let \(u = 3x - 2\), then \(du=3dx\), and \(dx=\frac{1}{3}du\).
The integral becomes \(\int\frac{4}{u}\cdot\frac{1}{3}du=\frac{4}{3}\int\frac{1}{u}du\).

Step2: Integrate \(\frac{1}{u}\)

We know that \(\int\frac{1}{u}du=\ln|u| + C\).
So \(\frac{4}{3}\int\frac{1}{u}du=\frac{4}{3}\ln|u|+C\).

Step3: Substitute back \(u = 3x - 2\)

We get \(\frac{4}{3}\ln|3x - 2|+C\).

Answer:

\(\frac{4}{3}\ln|3x - 2|+C\)