Let's go through the mathematical process to solve the given expression: [tex]\( x^3 \sin(\alpha x) \)[/tex].
1. Identify the terms:
- We have [tex]\( x^3 \)[/tex], which is a polynomial term.
- We also have [tex]\( \sin(\alpha x) \)[/tex], a trigonometric function where [tex]\( \alpha \)[/tex] is a constant.
2. Construct the expression:
- We are asked to multiply these two terms together.
3. Combine the terms:
- Multiplying [tex]\( x^3 \)[/tex] with [tex]\( \sin(\alpha x) \)[/tex], we get:
[tex]\[
x^3 \sin(\alpha x)
\][/tex]
Thus, the detailed result of the expression [tex]\( x^3 \sin(\alpha x) \)[/tex] is:
[tex]\[
x^3 \sin(\alpha x)
\][/tex]
This concludes the step-by-step construction and understanding of the given mathematical expression.