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Fungrim entry: 5c9675

0π/41sinc2 ⁣(x)dx=πlog(2)4+Gπ216\int_{0}^{\pi / 4} \frac{1}{\operatorname{sinc}^{2}\!\left(x\right)} \, dx = \frac{\pi \log(2)}{4} + G - \frac{{\pi}^{2}}{16}
TeX:
\int_{0}^{\pi / 4} \frac{1}{\operatorname{sinc}^{2}\!\left(x\right)} \, dx = \frac{\pi \log(2)}{4} + G - \frac{{\pi}^{2}}{16}
Definitions:
Fungrim symbol Notation Short description
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Piπ\pi The constant pi (3.14...)
Loglog(z)\log(z) Natural logarithm
ConstCatalanGG Catalan's constant
Source code for this entry:
Entry(ID("5c9675"),
    Formula(Equal(Integral(Div(1, Pow(Sinc(x), 2)), For(x, 0, Div(Pi, 4))), Sub(Add(Div(Mul(Pi, Log(2)), 4), ConstCatalan), Div(Pow(Pi, 2), 16)))))

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2020-08-27 09:56:25.682319 UTC