Section 15.8: Triple Integration in Spherical Coordinates

Show that \[ \int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty \sqrt{x^2+y^2+z^2} e^{-(x^2+y^2+z^2)} \, dx \, dy \, dz = 2\pi \] (The improper triple integral is defined as the limit of a triple integral over a solid sphere as the radius of the sphere increases indefinitely.)