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So I'm trying to understand how to get from F = ∫[(Q*λ)*dL*r]/(r^2) to F=∫q*λ*[(xx+ay)/(a^2+x^2)^(3/2)]*dx

Like I don't understand why the x and y components of r are negative, or why "The horizontal r component is obviously zero: for every element on the right of the midpoint, there is an element on the left whose force magnitude is equal, but whose horizontal component points in the opposite direction."

This was kind of a starting point for trying to understand some of the more "fundamental" Electricity and Magnetism equations and ideas, but I got stuck.