The integral you've provided is:

$\int \frac{6 \sin x}{x} \, dx$

This is a challenging integral, and there is no elementary function for this expression. However, it's possible to represent the solution in terms of special functions, such as the Sine Integral function ($\text{Si}(x)$).

The solution is expressed as:

$\int \frac{6 \sin x}{x} \, dx = 6 \, \text{Si}(x) + C$

Where:

• $\text{Si}(x) = \int_0^x \frac{\sin t}{t} \, dt$ is the Sine Integral function.
• $C$ is the constant of integration.

This is the most straightforward way to represent the solution since a direct elementary solution does not exist.

Would you like a more detailed explanation of the Sine Integral function or its properties?

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Here are 5 related questions that expand on this topic:

1. What are the properties of the Sine Integral function $\text{Si}(x)$?
2. How can special functions, like the Sine Integral, be used in physics applications?
3. Can this integral be solved using series expansion for small values of $x$?
4. What is the difference between elementary functions and special functions?
5. How would this integral change if the integrand involved $\cos(x)$ instead of $\sin(x)$?

Tip: When an integral doesn't have a solution in terms of elementary functions, special functions like $\text{Si}(x)$ often provide a way to express the result succinctly.