A particle moves in a line so that the velocity v m/s is given by v = 1 + e^(−2x). Find the position, x m , in terms of time t seconds ( t ≥ 0 ), given that x = 0 when t = 0.

I've tried various methods but I can't seem to get the answer

x = (1/2) ln [2e^(2t)-1].

Could the question be wrong? Any hints for my first step?

I know that I should be equating dx/dt = 1 + e^(−2x). And then, integrate both sides wrt t?