Constantly (well, not really) 0 integral

Level 2

The non-linear relation f(aR+)bf(a\in \mathbb{R}^+)\rightarrow b is a function that takes a value aa and returns a value bb such that ablnxx dx=0\int_a^b\dfrac{\ln x}{x}\text{ }dx=0 What is the minimum value of a+b?a+b\text{?}  \text{ }

Details and Assumptions\textbf{Details and Assumptions}

f(n)f(n) is differentiable over its domain.

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