integrate[((R/L)*x*(1-Pi/2) + Pi*R/2) * (R/L)*x,{x,0,L}] - Wolfram|Alpha

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Definite integral:

link to /input/?i=1%2F12+L+%284%2B%CF%80%29+R%5E2&lk=1&a=ClashPrefs_*Math-
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Indefinite integral:

link to /input/?i=%28R%5E2+x%5E2+%283+L+%CF%80-2+%28-2%2B%CF%80%29+x%29%29%2F%2812+L%5E2%29&lk=1&a=ClashPrefs_*Math-
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