1. The problem is to find the integral of the function $e^x$ with respect to $x$. 2. The formula for the integral of the exponential function $e^x$ is: $$\int e^x \, dx = e^x + C$$ where $C$ is the constant of integration. 3. Since the derivative of $e^x$ is $e^x$, the integral is the same function plus a constant. 4. Therefore, the solution is: $$\int e^x \, dx = e^x + C$$ This means the antiderivative of $e^x$ is $e^x$ itself, plus an arbitrary constant $C$ because integration is indefinite.