A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is:

V = ∫dV = ∫(kλdx)/x = ∫(k(Q/L)dx)/x
where the limits of integration are from L to 2L.
Thus, V = (kQ/L)∫(dx/x) from L to 2L
V = (kQ/L)[lnx] from L to 2L
V = (kQ/L)[ln2L - lnL]
V = (kQ/L)ln(2L/L) = (kQ/L)ln2
Since k = 1/(4πε0), we have
V = Qln2/(4πε0L)