Q:

Is there a rule for integrating $f(x) f(f(x))$?

I am looking through rules/tricks for integration, and there are a lot... but I can't seem to find one specifically applicable to the general form
$$\int_a^b f(x)\,f(f(x)) \,\mathrm dx$$
Is there a nice rule or trick that would generally apply in this situation?

A:

No, but there is a rule for integrating $f'(x)\,f'(f(x))$.

A:

Not in general. If, say, $f(x)=\ln\,x$, one requires a nonelementary function to represent the integral...

