For some integer n, the odd integer is represented in the form of:

An odd integer can be represented in the form of 2n + 1, where n is any integer.

Here's the step-by-step explanation:

1. An integer is a whole number that can be either greater than 0, called positive, less than 0, called negative, or equal to 0.

2. Even integers are multiples of 2, i.e., they can be written in the form 2n where n is an integer.

3. Odd integers are not multiples of 2. They can be written in the form 2n + 1 or 2n - 1, where n is an integer.

4. Therefore, for some integer n, an odd integer can be represented as 2n + 1.

For example, if n = 1, then the odd integer is 21 + 1 = 3. If n = 2, then the odd integer is 22 + 1 = 5, and so on.