Which of the following is a valid way to declare an integer variable in Java?

Declaring an integer variable in Java can be done using either the primitive data type int or the wrapper class Integer. The correct way is the usage of the primitive type int followed by the variable name, as shown in the chosen answer.

When you declare an integer variable as int num;, you are specifying that num will hold an integer value and that it is of the primitive type. This is a standard way of variable declaration in Java, designed to consume less memory and provide better performance when working with primitive types.

The option using the wrapper class Integer is also valid, but it is not the selected answer here. It involves slight differences since Integer objects can hold null values and benefit from methods related to object manipulation. However, since the question asks specifically for a valid declaration, int num; is a direct and simple declaration.

The other options presented do not conform to Java's syntax for variable declaration, rendering them invalid. For instance, "num int" incorrectly positions the type after the variable name, and "var num" lacks a type declaration and is not permissible as a keyword at this context in standard Java.