1. The problem is to solve the integral $$\int Ne^x \, dx$$ where $N$ is a constant. 2. The formula for integrating an exponential function multiplied by a constant is: $$\int a e^x \, dx = a e^x + C$$ where $a$ is a constant and $C$ is the constant of integration. 3. Applying this formula, since $N$ is a constant, we have: $$\int Ne^x \, dx = N \int e^x \, dx = N e^x + C$$ 4. Therefore, the solution to the integral is: $$N e^x + C$$ This means the antiderivative of $Ne^x$ with respect to $x$ is $N e^x$ plus an arbitrary constant $C$ because integration is indefinite.