I have to find v in terms of t so I used the substitution
I'm not terribly fond of the "ArcTanh" result... is there another way to do this?
(by the way if this is supposed to be motion under gravity in a resisting
medium this is only valid if the axis system is positive downwards and the
intial velocity is zero or positive - but assuming high Reynold's number,
a sky diver perhaps).