I recently learned how to calculate the field from a cylinder (inside and outside the cylinder) using Gauss's law. I was wondering how I would be able to derive the same formula without using Gauss's law (just for practice). My idea is that you would need to integrate the electric field from cylindrical shells of a radius 0 to R (where R is the radius of the cylinder), and to find the electric field of a cylindrical shell, you would need to integrate the field from rings along the length of the cylinder. The field from a ring is easy to calculate along its axis, but how would you calculate it in a less symmetric situation? Or is there a better way of doing this?