Calculus problem #2198

Calculus Level 3

For a function f(x)=axlnx+bf(x)=ax \ln x + b, we know that f(e)=4f'(e)=4 and 1ef(x) dx=12e(e+1)\displaystyle \int_{1}^{e} f(x)\ dx = \frac{1}{2}e(e+1). What is the value of a+b a + b ?

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