1. The problem is to find the integral of the function $x^2 + x + 3$ with respect to $x$. 2. The formula for integrating a polynomial term $ax^n$ is $$\int ax^n \, dx = \frac{a}{n+1}x^{n+1} + C$$ where $C$ is the constant of integration. 3. Apply the formula to each term: - For $x^2$, $$\int x^2 \, dx = \frac{1}{3}x^3$$ - For $x$, $$\int x \, dx = \frac{1}{2}x^2$$ - For the constant $3$, $$\int 3 \, dx = 3x$$ 4. Combine all results: $$\int (x^2 + x + 3) \, dx = \frac{1}{3}x^3 + \frac{1}{2}x^2 + 3x + C$$ 5. This is the indefinite integral of the given function, where $C$ is an arbitrary constant representing all possible vertical shifts of the antiderivative.