Haven't done much integration for a couple of years and am a bit rusty,

have this differential equation and have to integrate but can't get my head around the suggested substitution any help would be great, cheers.

After seperating vars i get;

(1/γv^2 - g).dv/dt = 1

then it asks me to integrate both sides given v(0) = 0 , using the substitution;

u= tanh^-1(sqrt(γ/g).v))

can someone please explain next step for me, would be greatly appreciated, thanks.

(γ is just a constant as is g for gravity)