$14$

Let $R$ be the region in the first quadrant of the $xy-$plane bounded by the hyperbolas $xy=1,xy=9$ and the lines $y=x,y=4x.$ Use the transformation $x=\frac{u}{v},y=uv$ with $u>0$ and $v>0$ to rewrite

${}_R(\sqrt[\phantom{2}]{\frac{y}{x}}+\sqrt[\phantom{2}]{xy})dxdy$