1. **State the problem:** Evaluate the improper integral $$\int_0^\infty 2 \ln(x) \, dx$$. 2. **Analyze the integral:** The integral involves the natural logarithm function multiplied by 2, integrated from 0 to infinity. 3. **Check convergence:** The integral $$\int_0^\infty \ln(x) \, dx$$ does not converge because $\ln(x)$ tends to $-\infty$ as $x \to 0^+$ and grows slowly as $x \to \infty$. Multiplying by 2 does not change convergence. 4. **Conclusion:** The integral $$\int_0^\infty 2 \ln(x) \, dx$$ diverges and does not have a finite value. Therefore, the integral does not converge to any finite number.