# Differentiation and Integration

Calculus Level 3

For a function $$f(x)=ax \ln x + b$$, we know that $$f'(e)=4$$ and $$\displaystyle \int_{1}^{e} f(x)\ dx = \frac{1}{2}e(e+1)$$. What is the value of $$a + b$$?

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