The result of the integral

$\int_0^9 \frac{dt}{\sqrt{81 + t^2}}$

is $\log(1 + \sqrt{2})$.

Would you like a detailed explanation of how this solution is derived?

Here are 5 related questions for further exploration:

1. What is the general method to evaluate integrals involving square roots?
2. How do logarithms appear in the solutions of integrals like this?
3. Can this integral be solved using a trigonometric substitution?
4. What are some real-world applications of integrals like this one?
5. How would the result change if the limits of integration were different?

Tip: When evaluating integrals with square roots, try substitutions like $t = a \tan(\theta)$, as they simplify the expression.