1. **State the problem:** Evaluate the integral $$\int \frac{\cos x}{\sin x} + 3 \, dx$$. 2. **Rewrite the integral:** Split the integral into two parts: $$\int \frac{\cos x}{\sin x} \, dx + \int 3 \, dx$$. 3. **Recall the formula:** The integral of $$\frac{\cos x}{\sin x}$$ can be rewritten as $$\int \cot x \, dx$$, and the integral of a constant $$a$$ is $$ax + C$$. 4. **Integrate each part:** - $$\int \cot x \, dx = \ln|\sin x| + C$$. - $$\int 3 \, dx = 3x + C$$. 5. **Combine results:** $$\int \frac{\cos x}{\sin x} + 3 \, dx = \ln|\sin x| + 3x + C$$. 6. **Final answer:** $$\boxed{\ln|\sin x| + 3x + C}$$