Is there any possibility to simplify the following integral or any function that is equivalent to the following integral?
$$ \frac{1}{2\pi\sqrt{(\sigma_{o_x}^2+\sigma_{p_x}^2)(\sigma_{o_y}^2+\sigma_{p_y}^2)}} \int_0^d \int_0^{2\pi} \exp-\bigg[\frac{(r\cos\theta-\alpha_x)^2}{2(\sigma_{o_x}^2+\sigma_{p_x}^2)} + \frac{(r\sin\theta-\alpha_y)^2}{2(\sigma_{o_y}^2+\sigma_{p_y}^2)} \bigg ] r \; d\theta \;dr $$