Compute the integrals: `int_(1/e)^e1/xsin(x-1/x)dx`

Explanation

To compute the integral

\[ I = \int_{1/e}^{e} \frac{1}{x} \sin\left(x - \frac{1}{x}\right) \, dx, \]

we will use a substitution method. Let's follow the steps:

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