Find the Arc Length of the Curve Defined By $\vec { r } ( t ) = \left\langle e ^ { t } \cos ( t ) , e ^ { t } , e ^ { t } \sin ( t ) \right\rangle$

Essay

Find the arc length of the curve defined by $\vec { r } ( t ) = \left\langle e ^ { t } \cos ( t ) , e ^ { t } , e ^ { t } \sin ( t ) \right\rangle$ over $[ \ln ( 2 ) , \ln ( 5 ) ]$