Let $\left. \vec { F } = \left( e ^ { y } + 5 x \right) \right) \vec { i } + \left( 4 y + z \cos x ^ { 5 } \right) \vec { j } + ( 2 z + 5 x ) \vec { k }$

Essay

Let $\left. \vec { F } = \left( e ^ { y } + 5 x \right) \right) \vec { i } + \left( 4 y + z \cos x ^ { 5 } \right) \vec { j } + ( 2 z + 5 x ) \vec { k }$ Calculate the flux $\int _ { S } \vec { F } \cdot \vec { d A }$ , where S is the sphere (x-2)² + (y-3)² + z² = $4$ oriented inward.