I read that the formula for calculating the time for a capacitor to charge with constant voltage is 5·τ = 5·(R·C) which is derived from the natural logarithm.

In another book I read that if you charged a capacitor with a constant current, the voltage would increase linear with time. Is this true, and if it is, what is the formula used for calculating this? Would a complete voltage charge be possible with a constant current?