Recall that in 3 dimensions, the Fourier transforms are defined as following:
$$ \tilde{f}(\textbf{k})= \frac{1}{(2\pi)^{3/2}} \int_{0}^{\infty}f(\textbf{x}) e^{-i\textbf{k}\cdot\textbf{x}} d^3x$$
$$f(\textbf{x}) = \frac{1}{(2\pi)^{3/2}} \int_{0}^{\infty} \tilde{f}(\textbf{k}) e^{i\textbf{k}\cdot\textbf{x}} d^3k$$
Suppose we have a function such that its Fourier transform is
$$\tilde{f}(\textbf{k}) = \frac{1}{|\textbf{k}|^2}$$
Find the original function f (x); the use of spherical coordinates in k space might be helpful. You can pick the z-axis to point anywhere, and in particular you can make it point along the direction of x. You may also find this integral useful:
$$\int_{0}^{\infty} \frac{\sin u}{u} du = \frac{\pi}{2}$$
I attempted this and it seemed straightforward, but I ended up getting lost around the hint to make the z-axis point along the direction of x. What is that supposed to mean?