Constantly (well, not really) 0 integral

Level pending

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

\(\textbf{Details and Assumptions}\)

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

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