What is the integral of the constant 7 with respect to x?

The integral of a constant can be determined using the basic principle of integration. When you integrate a constant 'k' with respect to a variable 'x', the result is k times the variable, plus a constant of integration, typically denoted as C.

In this case, since the constant is 7, the integral can be calculated as follows:

[

\int 7 , dx = 7x + C

]

This matches the correct answer, as it captures the essence of integrating a constant by multiplying it by the variable (x) and adding the constant of integration (C).

The other options present alternative forms that do not correspond to the process of integrating a constant with respect to x. For instance, the second option suggests a division by x, which is not relevant in this context. The third option merely adds a constant to 7 without involving x, while the fourth option introduces a natural logarithm, which is entirely unrelated to the integration of a constant. Thus, the first option accurately reflects the correct method of integrating a constant, making it the right choice.