\frac{1}{\pi}\int_{-\pi}^{\pi}x/\pi \sin(nx)\, dx - Wolfram|Alpha

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    Exact result:

    link to /input/?i=%28-2+n+%CF%80+cos%28n+%CF%80%29%2B2+sin%28n+%CF%80%29%29%2F%28n%5E2+%CF%80%5E2%29&lk=1&a=ClashPrefs_*Math-
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    Computation result:

    link to /input/?i=%28-2+n+%CF%80+cos%28n+%CF%80%29%2B2+sin%28n+%CF%80%29%29%2F%28n%5E2+%CF%80%5E2%29&lk=1&a=ClashPrefs_*Math-
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    Series expansion of the integral at n=0:

    link to /input/?i=%282+n+%CF%80%29%2F3-%28n%5E3+%CF%80%5E3%29%2F15%2B%28n%5E5+%CF%80%5E5%29%2F420&lk=1&a=ClashPrefs_*Math-
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