$\int f^{-1}(\frac{1}{x}) dx $, where $f^{-1}$ is inverse function.

Question

I had to changed orginal question because I was too edgy with my different questionsand I can't ask another one

It can by showed that $\int f^{-1}(x) dx=xf^{-1}(x)-F \circ f^{-1}(x)+C$

Is there exists some general solution for $\int f^{-1}(\frac{1}{x}) dx $