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:

Substituting K back into our expression:

Rearranging:

Multiplying throughout by -R:

Collecting the logarithm parts together:

Taking e to both sides:

Subtracting 1 from both sides:

Multiplying both sides by -(V/R):