Compute the double integral

$$\int\!\int_D 2 xy^2 \, dx \, dy$$
over the region $D$ bounded by

$$xy = 1, \ xy = 9, \ \ \ xy^2 = 1, \ xy^2 = 36$$
in the first quadrant of the $xy$-plane. Hint: make a change of variables $T : \mathbb{R}^2 \to \mathbb{R}^2$ that converts a rectangular region $D^*$ in the $uv$-plane into the region of integration $D = T(D^*)$ in the $xy$-plane.

Double integral =