If $\int_{-\infty}^\infty f(x) dx = 1$, then what is the value of $\int_{-\infty}^\infty f\left(x-\frac1{x}\right)dx$?
How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$