2nd derivative -2/pi * atan (pi/2 * x) - Wolfram|Alpha

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Derivative:

link to /input/?i=%288+%CF%80%5E2+x%29%2F%284%2B%CF%80%5E2+x%5E2%29%5E2&lk=1&a=ClashPrefs_*Math-
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Alternate form:

link to /input/?i=%288+%CF%80%5E2+x%29%2F%2816%2Bx%5E2+%288+%CF%80%5E2%2B%CF%80%5E4+x%5E2%29%29&lk=1&a=ClashPrefs_*Math-
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Expanded form:

link to /input/?i=%288+%CF%80%5E2+x%29%2F%2816%2B8+%CF%80%5E2+x%5E2%2B%CF%80%5E4+x%5E4%29&lk=1&a=ClashPrefs_*Math-
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Root:

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Series expansion at x=0:

link to /input/?i=%28%CF%80%5E2+x%29%2F2-%28%CF%80%5E4+x%5E3%29%2F4%2B%283+%CF%80%5E6+x%5E5%29%2F32&lk=1&a=ClashPrefs_*Math-
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Series expansion at x=∞:

link to /input/?i=-64%2F%28%CF%80%5E4+x%5E5%29%2B8%2F%28%CF%80%5E2+x%5E3%29&lk=1&a=ClashPrefs_*Math-
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Indefinite integral:

link to /input/?i=-4%2F%284%2B%CF%80%5E2+x%5E2%29&lk=1&a=ClashPrefs_*Math-
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