Step-by-Step Solution
Key Concept: General
$$\int x^2 e^x \, dx = x^2(e^x) - \int \underset{I}{2x} \underset{II}{e^x} \, dx$$ $$= x^2(e^x) - \left[ 2x e^x - \int 2 e^x \, dx \right]$$ $$= x^2 e^x - 2x e^x + 2e^x + C$$
Correct Answer: $x^2 e^x - 2x e^x + 2e^x + C$