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Fungrim entry: bd3faa

π=355113−13164∫01x8(1−x)8(25+816x2)1+x2 dx\pi = \frac{355}{113} - \frac{1}{3164} \int_{0}^{1} \frac{{x}^{8} {\left(1 - x\right)}^{8} \left(25 + 816 {x}^{2}\right)}{1 + {x}^{2}} \, dx
References:
  • https://mathworld.wolfram.com/PiFormulas.html
TeX:
\pi = \frac{355}{113} - \frac{1}{3164} \int_{0}^{1} \frac{{x}^{8} {\left(1 - x\right)}^{8} \left(25 + 816 {x}^{2}\right)}{1 + {x}^{2}} \, dx
Definitions:
Fungrim symbol Notation Short description
Piπ\pi The constant pi (3.14...)
Integral∫abf(x) dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
Source code for this entry:
Entry(ID("bd3faa"),
    Formula(Equal(Pi, Sub(Div(355, 113), Mul(Div(1, 3164), Integral(Div(Mul(Mul(Pow(x, 8), Pow(Sub(1, x), 8)), Add(25, Mul(816, Pow(x, 2)))), Add(1, Pow(x, 2))), For(x, 0, 1)))))),
    References("https://mathworld.wolfram.com/PiFormulas.html"))

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2021-03-15 19:12:00.328586 UTC