\displaystyle
(supst. \frac{t}{\sqrt{2}} = 2x+1.5y, dx= \frac{\sqrt{2}}{2}dt) = \frac{3\sqrt{3}}{\pi}\cdot \frac{1}{2\sqrt{2}}e^{\frac{27}{4}y}\int_{-\infty}^{\infty}e^{-\frac{t^{2}}{2}}dt=\frac{3\sqrt{3}}{2\sqrt{\pi}}\cdot e^{\frac{27}{4}y}