Đáp án:

Gợi ý: \((\ln{x} f(x))' = \frac{1}{x} f(x) + \ln{x} f'(x)\)

\(f(x) + x\ln{x} f'(x) = x^2 + 1\)

\(\Rightarrow \frac{1}{x}f(x) + \ln{x}f'(x) = x + \frac{1}{x}\)

\(\Rightarrow \ln{x}f(x) = \frac{x^2}{2} + \ln{x} + C\)

\(f(e) = \frac{e^2}{2} + 1 \Rightarrow C = 0\)

\(\Rightarrow f(x) = \frac{x^2}{2\ln{x}} + 1  \Rightarrow f(e^2) = \frac{e^4}{4} + 1 \quad \Rightarrow \boxed{\text{D}}\)