I know this is a very naive question but during my quantum optics study, I often come across the following kind of integrals. Sometimes there is an identity to get it solved but other times there is no identity. Could someone guide me how these are solved like I really want to understand how we evaluate integrals with powers like $d^2 \alpha$?
$$a=\int d^2 \alpha \exp[-\alpha \gamma^* + \alpha^* \gamma]$$