I want to solve this wave equation in $3$-D using Kirchhoff's formula but all I've done it doesn't work. In particular I'm not able to compute the integral in Kirchhoff's formula.
$$\begin{cases} \frac{\partial^2u}{\partial t^2}-\Delta u=0&\text{in $\mathbb R^3 \times(0,+\infty)$}\\ u(x,0)=|x|^2 &u_t(x,0)=0, x \in\mathbb R^3. \end{cases}$$
It is this the classical one (homogeneous problem) with $c=1$ and $F=0$ (no external force) and $u(x,0)=|x|^2$ and $u_ t(x,0)=0$.