Find the Length of the Curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 6 }$

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 6 }$ . Select the correct answer.

A) $e ^ { 12 }$
B) $e ^ { 6 } + 5$
C) $e ^ { 6 }$
D) $e ^ { 12 } + 5$