To solve the integral $\int \frac{dx}{2 - 3x}$, we'll use the method of substitution. Here are the steps:

1. Substitute: Let $u = 2 - 3x$.

2. Differentiate: $\frac{du}{dx} = -3 \implies du = -3 \, dx \implies dx = -\frac{1}{3} \, du$

3. Rewrite the integral in terms of $u$: $\int \frac{dx}{2 - 3x} = \int \frac{-\frac{1}{3} \, du}{u} = -\frac{1}{3} \int \frac{du}{u}$

4. Integrate: $-\frac{1}{3} \int \frac{du}{u} = -\frac{1}{3} \ln |u| + C$

5. Substitute back $u$: $-\frac{1}{3} \ln |2 - 3x| + C$

Therefore, the solution to the integral $\int \frac{dx}{2 - 3x}$ is: $-\frac{1}{3} \ln |2 - 3x| + C$

Would you like more details or have any questions about this solution?

Here are 5 questions you might want to ask next:

1. How do you solve integrals involving trigonometric functions?
2. Can you explain integration by parts with an example?
3. How do you solve definite integrals?
4. What is the method of partial fractions in integration?
5. Can you show me how to solve a complex integral step by step?

Tip: When solving integrals, identifying the correct method (substitution, integration by parts, partial fractions, etc.) is crucial for simplifying the process.