https://file.aiquickdraw.com/mathbot/file/172745662691733u01r4q.jpg

The expression in the image is:

\[
\int \frac{\sin x}{x^2} \, dx
\]

This integral cannot be solved in terms of elementary functions. However, we can solve it in terms of a series expansion or using special functions. One of the common ways to approach this integral is by recognizing that it is related to the *sine integral function* and the *exponential integral function*.

1. **Series expansion:** For small values of \(x\), we can use the Taylor series expansion for \(\sin x\) to approximate the integral. 

2. **Special functions:** This integral is closely related to the sine integral function \( \text{Si}(x) \), which is defined as:

\[
\text{Si}(x) = \int_0^x \frac{\sin t}{t} \, dt
\]

The integral given, however, involves \(x^2\) in the denominator, which makes it more complex. Therefore, the exact solution would involve advanced techniques or numerical integration.

Would you like to proceed with a specific approach like a series solution, or should I show how it can be numerically integrated?

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### Related questions:
1. What is the series expansion for \( \sin x \)?
2. How do we derive the sine integral function \( \text{Si}(x) \)?
3. What are special functions in mathematics and how are they used in solving integrals?
4. How can integrals be approximated using numerical methods?
5. What are the methods for solving non-elementary integrals?

**Tip:** Always consider numerical or series-based methods when dealing with complex integrals that lack elementary solutions.

Explore the solution for the integral of sin(x) divided by x^2. This problem involves the use of special functions such as the sine integral and series expansions. Suitable for advanced calculus students.

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