Three Dimensional Fourier transform of a raidal function

Question

Scaling analysis shows that the three dimensional Fourier transform of the function $f(\mathbf{r})=1/r$ is proportional to $1/k^2$. On the other hand, when working with spherical coordinates $(r,\theta ,\varphi )$, after integrating with respect to $\theta$ and $\varphi$, we get $f(\mathbf{k})\propto \int_{-\infty}^{+\infty}e^{(-ikr)}dr$, which is proportional to the delta function instead of a power function. What's the problem?