What is the integral of k^2. dk^3

Answer 1

I assume that what is wanted is the 3 space (x,y,z) integral of k²

That is

∫ dk_x dk_y dk_z k²

Going to spherical polar coordinates , this becomes

4 π ∫ (k² dk) k² = (4 π / 5) k⁵ where k is now the upper limit of the integral