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Fungrim entry: 66fefb

∫01xx dx=∑n=1∞(−1)n+1n−n\int_{0}^{1} {x}^{x} \, dx = \sum_{n=1}^{\infty} {\left(-1\right)}^{n + 1} {n}^{-n}
TeX:
\int_{0}^{1} {x}^{x} \, dx = \sum_{n=1}^{\infty} {\left(-1\right)}^{n + 1} {n}^{-n}
Definitions:
Fungrim symbol Notation Short description
Integral∫abf(x) dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
Sum∑nf(n)\sum_{n} f(n) Sum
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("66fefb"),
    Formula(Equal(Integral(Pow(x, x), For(x, 0, 1)), Sum(Mul(Pow(-1, Add(n, 1)), Pow(n, Neg(n))), For(n, 1, Infinity)))))

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2021-03-15 19:12:00.328586 UTC