Let $\quad f(x)+2 f\left(\frac{1}{x}\right)=x^2+5 \quad$ and $\quad 2 g(x)-3 g\left(\frac{1}{2}\right)=x, x>0$. If $\quad \alpha=\int_1^2 f(x) \mathrm{d} x, \quad$ and $\beta=\int_1^2 \mathrm{~g}(x) \mathrm{d} x$, then the value of $9 \alpha+\beta$ is:
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