k \int_{-\infty}^{\infty}e^{\frac{b^2}{4a}y^2-cy^2}\sqrt{\frac{\pi}{a}}\int_{-\infty}^{\infty}\frac{1}{\sqrt{2\pi}\frac{1}{\sqrt{2a}}}e^{-\frac{(x-by/2a)^2}{2\cdot \frac{1}{2a}}}dx dy