If the integral ∫ x^3 ln(x) dx is equal to (x^4/4) ln(x) - (x^4/16) + C, what is its simplicity based on integration technique?

The integral ∫ x^3 ln(x) dx resulting in an expression that combines polynomial and logarithmic terms like (x^4/4) ln(x) - (x^4/16) + C signifies that the solution is an elementary function.

Elementary functions include polynomials, exponential functions, logarithmic functions, and trigonometric functions, along with their inverses and combinations of these functions. In this case, the result consists of a polynomial term (specifically, a term involving x^4) and a logarithmic term (ln(x)), both of which are fundamental components of elementary functions.

The combination of these two types of functions in the final result aligns with the definition of an elementary function, indicating that it can be expressed using basic operations and standard functions without involving any transcendental or more complex structures.

The presence of both polynomial and logarithmic components emphasizes that this particular integral and its solution can be represented simply and directly, adhering to the ease associated with elementary functions.