I'm having trouble with the integral $$\iiint_{1\le x^2+y^2+z^2 }\frac{\mathrm{d}x~\mathrm{d}y~\mathrm{d}z}{xyz}$$
this is what I've done so far:
$$\lim_{b\to +\infty}\int_1^b \int_0^{2\pi} \int_0^{\pi}\frac {r^2\sin(\psi)~\mathrm{d}\psi~\mathrm{d}\theta ~\mathrm{d}r}{r^3\cos(\theta)\sin(\theta)\cos(\psi)\sin²(\psi)}$$
but I'm lost. Besides, $\cos(x)$ and $\sin(x)$ are zero in many points of the domain, do I have to consider those too? Any hints please?