To integrate \( e^{0.45t^2} \), we can approach the problem, but this integral does not have a solution in terms of elementary functions. However, it is related to the **Gaussian integral** and often expressed in terms of the **error function (erf)**.

### Solution:
The integral of \( e^{kt^2} \), where \( k \) is a constant, typically requires special functions to represent the result. Unfortunately, the constant in front of \( t^2 \), here \( 0.45 \), doesn't allow for a straightforward antiderivative.

Thus, we can express it as:

\[
\int e^{0.45 t^2} \, dt
\]

This is closely related to the error function for integrals of the form \( \int e^{ax^2} dx \), but it needs to be solved numerically or left in terms of a special function.

If we look for a numerical solution, that would require defining limits.

Would you like more details on using numerical methods or working with error functions?

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Here are 5 questions to expand on this:
1. Would you like to evaluate this integral with specific limits for a numerical result?
2. Are you familiar with the error function and how it's used in integrals?
3. Do you need the integral evaluated in terms of a power series expansion?
4. Would you like an example of a related integral that does have an elementary solution?
5. How does this integral fit into your larger problem?

**Tip:** Special functions like the error function often arise in integrals involving exponentials and squares, and are frequently used in probability and statistics.

Explore the integration of e^(0.45t^2), a challenging problem related to the Gaussian integral and error function. Understand why this integral does not have a solution in elementary functions and learn how to approach it using special functions. Suitable for undergraduate students studying calculus.

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