Let's denote the three consecutive even integers as $x$, $x+2$, and $x+4$.

The sum of these three consecutive even integers is: $x + (x + 2) + (x + 4)$

Simplifying this expression: $x + x + 2 + x + 4 = 3x + 6$

So, the sum of the three consecutive even integers is $3x + 6$.

Would you like more details or have any other questions?

Here are some related questions:

1. How do you find the individual values of these integers if the sum is given?
2. What is the sum of four consecutive even integers?
3. How does the sum change if you consider consecutive odd integers instead?
4. Can you find the average of these three integers?
5. What is the product of the smallest and largest of these three integers?

Tip: When dealing with consecutive numbers (even or odd), their properties (like sum, product) often follow a pattern that can simplify calculations.