1. **State the problem:** We need to evaluate the integral $$\int \frac{1 + \ln x}{x \ln x} \, dx.$$\n\n2. **Rewrite the integral:** Split the integral into two parts:\n$$\int \frac{1}{x \ln x} \, dx + \int \frac{\ln x}{x \ln x} \, dx = \int \frac{1}{x \ln x} \, dx + \int \frac{1}{x} \, dx.$$\n\n3. **Evaluate the second integral:**\n$$\int \frac{1}{x} \, dx = \ln |x| + C.$$\n\n4. **Evaluate the first integral:** Use substitution. Let $$u = \ln x,$$ then $$du = \frac{1}{x} dx.$$\nRewrite the integral:\n$$\int \frac{1}{x \ln x} \, dx = \int \frac{1}{u} du = \ln |u| + C = \ln |\ln x| + C.$$\n\n5. **Combine results:**\n$$\int \frac{1 + \ln x}{x \ln x} \, dx = \ln |\ln x| + \ln |x| + C.$$\n\n6. **Final answer:**\n$$\boxed{\ln |\ln x| + \ln |x| + C}.$$