"Commonly, the basic functions that are allowed in closed forms are nth root, exponential function, logarithm, and trigonometric functions.[a] However, the set of basic functions depends on the context. For example, if one adds polynomial roots to the basic functions, the functions that have a closed form are called elementary functions."
It's only maths, don't expect things to be so black and white.
https://en.wikipedia.org/wiki/Closed-form_expression
"Commonly, the basic functions that are allowed in closed forms are nth root, exponential function, logarithm, and trigonometric functions.[a] However, the set of basic functions depends on the context. For example, if one adds polynomial roots to the basic functions, the functions that have a closed form are called elementary functions."
It's only maths, don't expect things to be so black and white.