More Corrections For Nothing

From the post "We Have A Problem, Coulomb's Law" dated 20 Nov 14,

$F_v=2\cfrac { qc^{ 2 } }{ x } e^{i\pi/2}$

and from "Wrong, Wrong, Wrong" dated 25 May 15,

$F=\int{F_v}\,d\,x$

The force in the field due to a particle is,

$F=2\int{\cfrac { qc^{ 2 } }{ x } }\,d\,x.={2{ qc^{ 2 } }{ ln(x) } }+C$

where we have dropped the phase information,  $e^{i\pi/2}$.

but $F=-\psi$, so,

$\psi=-2{ qc^{ 2 } }{ ln(x) }+A$

However, $\psi$ cannot be less than zero.  So, both $F$ and $\psi$ is valid up till $\psi=0$.

This is not the inverse square law!  And what happens to $F$ after $\psi=0$?