Loop antenna $E$ and $H$ modes without approximations as to the distance or wavelength

In Jackson's 9.14 we calculate the expressions for $E$ and $H$ of a loop antenna with current $I=I_0\cos(\omega t)$ in the $x-y$ plane in the radiation zone , where we approximate the distances to be large so: $\frac{1}{|\vec{r}-\vec{r}^{'}|}\approx\frac{1}{\vec{r}}$ $|\vec{r}-\vec{r}^{'}|\approx \vec{r}-\vec{r}.\vec{r}^{'}$ But what if we want to derive an expression that is valid for lower modes of the quadrupole radiation in all distances without approximation? How we should approach the integral with $\frac{1}{|\vec{r}-\vec{r}^{'}|}$ in the denominator? $\vec{A}(\vec{x})=\frac{\mu_0}{4\pi}\int J(\vec{r}')\frac{\exp(ik|\vec{r}-\vec{r}'|)}{|\vec{r}-\vec{r}'|}d\vec{r}'$