1. Simplify the expression:

2. Use symmetry to evaluate the integral:

3. Find the average value of the function:
![\\ \sf\:f(x) = 5 \, \text{on} \, [1, e] \\ \\](https://img.qammunity.org/2024/formulas/mathematics/high-school/e1j6zw0ncip9jq0x9xh9bu6y4e9y81sbuh.png)
Now, let's write the simplified expression, integral, and average value:
1. Simplified expression:

2. Integral using symmetry:

3. Average value of the function:
