Find the length of the curve $\boldsymbol{\vec{r}}(t) = \left<e^{\frac{t}{6}}\cos\!\left(\frac{t}{6}\right),e^{\frac{t}{6}}\sin\!\left(\frac{t}{6}\right),e^{\frac{t}{6}}\right>$ for $0 \leq t \leq 3$.

Arc length =