1. **State the problem:** Evaluate the integral $$\int \frac{dx}{\sqrt{529 + x^2}}$$. 2. **Recall the formula:** The integral of the form $$\int \frac{dx}{\sqrt{a^2 + x^2}}$$ is $$\ln|x + \sqrt{x^2 + a^2}| + C$$, where $a$ is a constant. 3. **Identify $a$:** Here, $a^2 = 529$, so $a = 23$. 4. **Apply the formula:** $$\int \frac{dx}{\sqrt{529 + x^2}} = \ln|x + \sqrt{x^2 + 529}| + C$$ 5. **Final answer:** $$\boxed{\ln|x + \sqrt{x^2 + 529}| + C}$$