Compute the integral of e^x dx.

To compute the integral of ( e^x ) with respect to ( x ), we utilize the fundamental properties of exponential functions. The integration of the exponential function ( e^x ) is particularly straightforward because the derivative of ( e^x ) is itself.

When we integrate ( e^x ), we are essentially looking for a function whose derivative gives us ( e^x ). The only function that satisfies this condition is ( e^x ) itself. Thus, when we integrate ( e^x ), we get ( e^x ) plus a constant of integration, denoted as ( C ). Therefore, the result of the integral is written as:

[

\int e^x , dx = e^x + C

]

This confirms that the correct choice is indeed the integral of ( e^x ), leading us to the conclusion that the expression ( e^x + C ) correctly represents the indefinite integral of ( e^x ).

The other options do not represent the integral of ( e^x ):

• ( e^{-x} + C ) represents the integral of ( e^{-x} ), which is not relevant here.

• (