You can easily figure out f

Calculus Level 4

\[ 2f(x) + f(-x) = \frac {1}{x} \ \sin \left ( x - \frac 1 x \right ) \]

Find the value of \(\large \displaystyle \int_{\frac{1}{e}}^{e} f(x) \ \mathrm dx\) if \(f\) satisfies the condition above.

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