MathNet 2008-part-05 — 164 problems (EN–VI) Question 86

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