∫(1/(-(m/c) g + 
              v)) \[DifferentialD]v

Clear[g, m, c, v, t, 
      const]

    c = 12, 5; m = 68, 1; g = 9, 
    8



    Solve[
Log[Abs[-g m + c v]] =  -(c/m) t + 
          const
, 
v]