A different rotation

A solid body rotates with deceleration about a stationary axis with an angular deceleration βω\beta \propto \sqrt{\omega}, where ω\omega is its angular velocity. Find the mean angular velocity of the body averaged over the whole time of rotation if at the initial moment of time its angular velocity was equal to ω0=18 rad/s\omega_0 = 18 \text{ rad/s}.

Problem is not original.
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