We start with:


Subtracting Ri from both sides:


Divide both sides by L:


Multiply both sides by dt and divide both by (V - Ri):


Integrate (see Integration: Basic Logarithm Form):



Now, since `i = 0` when `t = 0`, we have:

`K=-(ln\ V)/R`

Substituting K back into our expression:

`-(ln(V-Ri))/R=1/Lt-(ln V)/R`


`(ln\ V)/R-(ln(V-Ri))/R=1/Lt`

Multiplying throughout by -R:

`-ln\ V+ln(V-Ri)=-R/Lt`

Collecting the logarithm parts together:


Taking "e to both sides":



Subtracting 1 from both sides:


Multiplying both sides by `-(V/R)`: