Here's an undergraduate-level math problem:

Problem:

Evaluate the integral:

$I = \int_0^\infty \frac{e^{-x^2}}{x} \, dx$

Hint: This is a standard improper integral known to converge in a particular manner. You might need to consider techniques like substitution or regularization.

Would you like a detailed explanation of how to approach this, or do you want to try solving it first? Let me know if you have any questions!

---

Related questions for practice:

1. Evaluate the following integral: $\int_0^\infty e^{-x^2} \, dx$.
2. What is the behavior of the function $\frac{e^{-x^2}}{x}$ as $x \to 0$ and $x \to \infty$?
3. Use substitution to compute the integral $\int_0^\infty e^{-ax^2} \, dx$ where $a > 0$.
4. Prove or derive the Gaussian integral: $\int_{-\infty}^\infty e^{-x^2} \, dx = \sqrt{\pi}$.
5. How would you regularize an integral like $\int_0^\infty \frac{e^{-x^2}}{x} \, dx$ to make it convergent?

Tip: Always check the limits of integration carefully, especially when dealing with improper integrals, as they might require special treatment such as regularization or limiting processes.