**Explanation:**

The integral of log(x) with respect to x, denoted as ∫log(x)dx, cannot be expressed in terms of elementary functions (such as polynomials, exponential functions, trigonometric functions, etc.). Therefore, the correct answer is option D, which states "none of these".

To understand why the integral of log(x) cannot be expressed in terms of elementary functions, we need to consider the properties of the logarithm function and the concept of integration.

**Properties of the Logarithm Function:**
1. log(a * b) = log(a) + log(b)
2. log(a / b) = log(a) - log(b)
3. log(a^n) = n * log(a)

**Concept of Integration:**
Integration is the process of finding the antiderivative (or primitive) of a function. The antiderivative of a function F(x) is another function f(x) whose derivative is equal to F(x). In other words, if F'(x) = f(x), then ∫f(x)dx = F(x) + C, where C is the constant of integration.

**Integration of log(x):**
The integral of log(x) with respect to x is denoted as ∫log(x)dx. Since log(x) is not an elementary function, we cannot find its antiderivative using the standard rules of integration (such as power rule, product rule, etc.).

However, we can express the integral of log(x) using a special function called the logarithmic integral (Li(x)). The logarithmic integral is defined as:

Li(x) = ∫[1 / log(t)]dt, where the integral is taken from 2 to x.

Therefore, the integral of log(x) can be expressed as:

∫log(x)dx = Li(x) + C

where C is the constant of integration.

In conclusion, the integral of log(x) cannot be expressed in terms of elementary functions. The correct answer to the given question is option D, "none of these".

Xlogx - x + k