Suppose that the function $f$ is given by its two-sided Laplace transform: $$ \int_{\mathbb R} f(x)e^{-sx} \, dx = e^{as^2+bs}\frac{1}{1+cs} $$ where $a,b,c>0$ are positive real numbers. I want to find out what $f$ is but I'm struggeling to invert in the above Laplace transform.
Is there a simple way to find out what $f$ is?