Pardon my lack of tex skills, but what is the recommended procedure in the following scenario:
$g(f) = 1+\int_0^{1-f} g\left(\dfrac{f}{1-x}\right)\,dx$
I am not sure how to proceed in such a scenario. My expression is more complicated, but that is the gist of the concept I'm struggling with.
also, we know that g(1) = 1
I'm thinking some sort of Leibniz approach, but I'm an engineer by training so I'm out of my depth.
edit: If the above simplification does not have a solution/doesn't lend itself well to an example, here is the actual thing:
$g(f) = [1-(1-f)^{2}] + 2\int_0^{1-f} (1+g\left(\dfrac{f}{1-x}\right))x\,dx$