what's:[integral sign] e^(2z) * sqrt(1-e^(4z)) dz?

Answer 1

let x = e^(2z)

dx = 2 e^(2z) dz then intergand becomes:

1/2*dx/(sqrt(1-x^2)) --> this integrates to 1/2*arcsin(x) = 1/2*arcsin(e^(2z))

Answer 2

☻ start with exp(2z) = sin x;