Everything But the Kitchen Sink

Calculus Level 4

\[\displaystyle \ln\left[ \lim_{x \rightarrow 0} \left( \dfrac{1}{x} \int_{0}^{x} \left( e^{2t}\cos(3t) + e^{3t}\sinh(2t) \right)^{1/t} \ \mathrm d t \right) \right] \]

Evaluate the above expression.

Image Credit: Wikimedia Kitchen Sink by Tomwsulcer
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