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Conjectured value of $\int_{0}^{\infty}\left(\frac{x-1}{\ln^2 x}-\frac{1}{\ln x}\right)\frac{\mathrm{d}x}{x^2+1}$

integration definite-integrals asked Jul 18, 2016 at 16:32

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14 votes

Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

calculus sequences-and-series summation closed-form asked Jul 21, 2016 at 14:18

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8 votes

Closed form for $\sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{n^2+a^2}}$

calculus summation asked Jul 21, 2016 at 1:36

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7 votes

General formula for $\int^1_0 x^\alpha \log(1-x)\operatorname{Li}_2 (x)\, \mathrm dx$

integration definite-integrals special-functions mathematica asked Feb 7, 2021 at 12:36

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6 votes

When you can look through a forest?

probability poisson-distribution asked Aug 15, 2020 at 8:06

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6 votes

Integrate $\int_{a}^1 \frac{\left(1-t^2\right) \tanh^{-1}t }{t^6} \ln \left(\frac{t+\sqrt{-1+t^2/a^2}}{t-\sqrt{-1+t^2/a^2}}\right) dt$

integration definite-integrals asked Nov 20, 2020 at 15:22

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5 votes

Exact symbolic area of an intersection of two polygons with parameters

regions polygons geometric-computation asked Dec 14, 2020 at 21:50

mathematica.stackexchange.com

Top Answers

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

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Sum the series $\sum_{n = 1}^{\infty}\{\coth (n\pi x) + x^{2}\coth(n\pi/x)\}/n^{3}$

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Interesting triple integral

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Proof of $\sum_{n=1}^{\infty}\frac1{n^3}\frac{\sinh\pi n\sqrt2-\sin\pi n\sqrt2}{{\cosh\pi n\sqrt2}-\cos\pi n\sqrt2}=\frac{\pi^3}{18\sqrt2}$

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Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

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The Basel problem

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Calculate $\sum\limits_{n=1}^{\infty} \frac{a\cos(nx)}{a^2+n^2}$

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How was the normal distribution derived?

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