Let's say that I'm integrating a composite function, say $f(g(x))$, that is in a form to which I can apply the substitution rule. Is it true to say that both $f$ and $g$ must be differentiable?
I understand that the substitution rule requires $g$ to be differentiable and that the substitution rule relies on the chain rule, and the chain rule requires both f and g to be differentiable.