Examples of interesting integrable functions with at least 2 fixed points and an explicit inverse What are some interesting functions I can use to demonstrate this integration trick:
$$\int_a^b [f(x)+f^{-1}(x)]=b^2-a^2$$
I would like to know of some interesting functions where this trick is not obvious. EDIT: The functions I am receiving are the obvious ones like $f(x)=x$, which I don't want. :)

Let $a$ and $b$ be greater than or equal to 1. $\int_a^b{e^{x^2}+\sqrt{\ln{x}}dx}=b^2-a^2$
