HMMT 2009 K3

Compute $e^{A}$ where $A$ is defined as

$\int_{3 / 4}^{4 / 3} \frac{2 x^{2}+x+1}{x^{3}+x^{2}+x+1} d x$

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{16}{9}

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