In my calculus book, (not for homework, I was just looking around), I was given the following equality and was told to find all valid functions that fit it.
Find all families of functions that satisfy the following equality: $$\bigg(\int f(t)dt\bigg)\bigg(\int {1\over f(t)}dt\bigg)=-1$$
My two failed attempts to solve this yielded $f(x)=e^x+C$ and $f(x)=e^{-x}+C$ depending on my methods.
What families of functions satisfies this relationship?