Say I have two normal independent random variables with nonzero means - X distributed as N(a,b) and Y as N(c,d). What is the mean of the product XY?

I see that the distribution has been computed (Is the product of two Gaussian random variables also a Gaussian?) as a bessel function in an earlier question if it is 0 mean- but if the mean is not zero, is there a simple expression for E[XY] ?