Compute the integral of e^x dx.

Compute the integral of e^x dx.

• A. e^x + C
• B. e^(-x) + C
• C. ln(x) + C
• D. xe^x + C

Answer: (A)

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. - \(

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.

• (