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This question already has an answer here:

If $f(x)$ is a continuous function on $\mathbb{R}$ and the improper integral

$\int_{-\infty}^{\infty} f(x) \,dx$ converges.

show that : $$\int_{-\infty}^{\infty} f\left(x-\frac{1}{x}\right) \,dx = \int_{-\infty}^{\infty} f(x) \,dx $$

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marked as duplicate by Sameer Kailasa, Nosrati, Morgan Rodgers, saz, Lord Shark the Unknown Sep 26 '18 at 17:04

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