Quick! What's its antiderivative?

Calculus Level 2

\[ \large \int_{2y}^{y^2} x^{x^{x^x}} e \cdot \ln | 9 | \ dx \]

Find the value of the integral above if \( \displaystyle y = \lim_{n \to \infty} \frac {6n-2}{3n+3} \).

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