∫ e^(x²) dx + ln x is: (choose the correct classification)

Elementary function

Algebraic function

Transcendental but integrable in terms of elementary functions

Non-elementary integral

Explanation

$\int e^^{x^^{2}} d x$ cannot be expressed in terms of elementary functions (i.e., polynomials, exponentials, logarithms, trigonometric functions, etc.).

It is a non-elementary integral, though it exists and can be expressed using special functions like the error function:

\int e^^{x^^{2}} d x = not elementary