The addition problem below shows 4 of the 24 different integers that can be formed by using each of the digits 1, 2, 3, and 4 exactly once in each integer. What is the sum of these 24 integers?

1,234 + 1,243 + 1,324 + x,xxx + x,xxx + 4,321 =

I understand that every x posted must be replaced by one of the given integers. Afterward, I must add all four-digits to obtain a sum. Any ideas?