Find the exact area of the surface obtained by rotating the curve about the x-axis.

$Find the exact area of the surface obtained by rotating the curve about the $ x $-axis. \[ y=\frac{x^{3}}{2}+\frac{1}{6 x},$

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Find the exact area of the surface obtained by rotating the curve about the x-axis.

$Find the exact area of the surface obtained by rotating the curve about the $ x $-axis. \[ y=\frac{x^{3}}{2}+\frac{1}{6 x},$

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