# What on Earth is going on?

Calculus Level 2

Given a polynomial $$f: \mathbb{R}^+ \rightarrow \mathbb{R}^+$$ that satisfies $$f(0) = 1, f(1) = e, f(e) =\pi$$.

Let $$\displaystyle I = \int_1^e \frac{ f'(x) } { f(x) } \, dx$$. Find the value of $$\text{sgn}(I)$$.

Notation: $$\text{sgn}(x)$$ denote the signum function, where $$\text{sgn}(x) = \begin{cases} \dfrac{x}{|x|} , x \ne 0 \\ 0 , x = 0 \end{cases}$$.

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