1. We are asked to evaluate the integral $$\int \frac{1}{(x+3) \ln(x+3)} \, dx.$$ 2. This integral involves a logarithmic function in the denominator, suggesting a substitution related to the inner function of the logarithm. 3. Let us use the substitution $$u = \ln(x+3).$$ 4. Then, the derivative is $$\frac{du}{dx} = \frac{1}{x+3}$$ or equivalently $$du = \frac{1}{x+3} dx.$$ 5. Notice that the integral can be rewritten as $$\int \frac{1}{(x+3) \ln(x+3)} dx = \int \frac{1}{\ln(x+3)} \cdot \frac{1}{x+3} dx.$$ 6. Using the substitution, this becomes $$\int \frac{1}{u} du.$$ 7. The integral of $$\frac{1}{u}$$ with respect to $$u$$ is $$\ln|u| + C.$$ 8. Substituting back for $$u$$, the final answer is $$\ln|\ln(x+3)| + C.$$