There exists a unique, positive-valued, non-constant, continuous and differentiable function $y = f(x)$ such that

- over any specified interval, the area between $f(x)$ and the $x$-axis is equal to the arc length of the curve, and
- $f(0) = 1.$

If $\displaystyle \int_{\ln2}^{\ln5} f(x) \, dx = \dfrac{a}{b}$, where $a$ and $b$ are coprime positive integers, then find $a + b$.

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