Electrial potential energy

Suppose charge Q is located at the origin of a Cartesian Coordinate System, and charge q is at distance r from the origin on the +ve x-axis.

Then work done by an external force W = integral{=(-Qq/4pi er^2)*dr}, limts from a to b, say

Since r is measured from the origin, i.e. postion of chrage Q, towards the charge q, it is clear that r is pointing in the +ve x-direction, hence, its defferential dr is +ve.

After integration, W = (Qq/4.pi.e).(1/b - 1/a)
That is, the force does +ve work when a > b (W is +ve), as work needs to be done against the repulsive force.
When a < b, the force does -ve work ( W is -ve), as the force prevents the charge q moves away by electrostatic repulsion.

Why we use dr but not -dr since the displacement is towards left which is the negative direction.

Maybe I am wrong, but as I know,dr is already define as the direction toward Q which is already pointing inward.

Let dx be the displacement pointing outward(as your direction of E-force), in this case,-dx is the displacement of the charge q.