Sine of e?

Calculus Level 3

If \( 2f(x) + f(-x) = \frac 1x \sin\left( \frac{x^2-1}x \right) \) for \( x > 0 \), then what is the value of the integral below?

\[ \large \int_{\frac 1e}^e f(x) \, dx \]

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