HMMT 2008 K8

Let $T=\int_{0}^{\ln 2} \frac{2 e^{3 x}+e^{2 x}-1}{e^{3 x}+e^{2 x}-e^{x}+1} d x$ . Evaluate $e^{T}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{11}{4}

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