# improper integrals show a beautiful fact [duplicate]

If $$f(x)$$ is a continuous function on $$\mathbb{R}$$ and the improper integral
$$\int_{-\infty}^{\infty} f(x) \,dx$$ converges.
show that : $$\int_{-\infty}^{\infty} f\left(x-\frac{1}{x}\right) \,dx = \int_{-\infty}^{\infty} f(x) \,dx$$