plot 1/ln(2) (1/2)e^(-g)/(1-(1/2)e^(-g)) dg/dx substitute g=ln(1+sqrt(1/2)) (sqrt(1+arctanh(x)^2) arctanh(x))/(sqrt(1+arctanh(0.5)^2) arctanh(0.5)) from x=0..1 y=0..1.3