Trying to integrate the following integral.
$$\int_{-\infty}^\infty dx \int_{-\infty}^\infty dy e^{-(x-y)^2}$$.
I've tried pulling out $x$ from the square and setting $s=\frac{y}{x}$ gives me the integral $$\int_{-\infty}^\infty ds \int_{-\infty}^\infty dx -xe^{-x^2(1-s)^2}/2$$
However, it becomes zero when the integral over $x$ is taken and I know that my answer should be nonzero so I don't know what I'm doing wrong.
Let $u=x-y$ $$\int_{-\infty}^\infty dx \int_{-\infty}^\infty dy e^{-(x-y)^2}=\int_{-\infty}^\infty dx \int_{-\infty}^\infty du e^{-u^2}=\int_{-\infty}^\infty dx \sqrt\pi=\infty. $$