The worksheet involves solving integrals using trigonometric substitution or methods yielding inverse trigonometric functions. I will solve one of the integrals as an example. Let me know which specific one you want me to solve or if you'd like all of them worked through step-by-step!

Would you like to proceed with solving a specific problem, or should I start from the first one and work sequentially?

Here are related questions to deepen understanding:

1. What are the steps to select the appropriate substitution for these problems?
2. How does trigonometric substitution simplify the given integrals?
3. Why are some integrals linked to inverse trigonometric functions?
4. How do you differentiate between substitutions for different forms of $\sqrt{a^2 - x^2}$, $\sqrt{a^2 + x^2}$, and $\sqrt{x^2 - a^2}$?
5. What strategies can be used to check the correctness of your solution?

Tip: Always rewrite the integral in terms of substitution variables and back-substitute at the end to return to the original variable.