Question

Is there a closed-form solution (even approximated) to this inequality?

score 70 · Answer 1 · 2015-07-30 00:59:15

70

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Is there a closed-form solution (even approximated) to this inequality?

Published on 30 Jul 2015 - 0:59

score 3.4k · Answer 2 · 2015-07-30 14:22:02

3.4k

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The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

Published on 30 Jul 2015 - 14:22

score 1.3k · Answer 3 · 2026-03-28 09:57:13

1.3k

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Closed form of $\int_0^\infty \frac{1}{\left(a+\cosh x\right)^{1/n}} \, dx$ for $a=0,1$

Published on 28 Mar 2026 - 9:57

score 451 · Answer 4 · 2026-03-28 09:54:28

451

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Intriguing Poisson sum with hyperbolic function

Published on 28 Mar 2026 - 9:54

score 586 · Answer 5 · 2026-03-27 17:06:03

586

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Closed-form of $\int\limits_0^1\left(\frac{\left(x^2+1\right)\arcsin(x)}{\sqrt{1-x^2}}+2x\ln\left(x^2+1\right)\right)\frac{\ln x}{x^3+x}\,dx$

Published on 27 Mar 2026 - 17:06

score 2.4k · Answer 6 · 2015-08-01 07:39:29

2.4k

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A formula to calculate the partial volume of a capsule or tank?

Published on 01 Aug 2015 - 7:39

score 58 · Answer 7 · 2026-04-03 04:13:29

58

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Simple closed functional form for summed recurrence relation

Published on 03 Apr 2026 - 4:13

score 210 · Answer 8 · 2015-08-01 20:29:05

210

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What is $\int_0^{\pi} \frac{e^{\sin x}\cos(x)}{1+e^{\tan x}} \, dx$?

Published on 01 Aug 2015 - 20:29

score 1.3k · Answer 9 · 2026-03-27 17:06:25

1.3k

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Integral $\int_0^\infty\text{Li}_2\left(e^{-\pi x}\right)\arctan x\,dx$

Published on 27 Mar 2026 - 17:06

score 511 · Answer 10 · 2026-03-26 22:18:12

511

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Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$

Published on 26 Mar 2026 - 22:18

score 252 · Answer 11 · 2015-08-05 00:35:49

252

Views

Closed-form of $\int_0^1 x^n \operatorname{li}(x^m)\,dx$

Published on 05 Aug 2015 - 0:35

score 931 · Answer 12 · 2015-08-05 09:46:36

931

Views

explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$

Published on 05 Aug 2015 - 9:46

score 58 · Answer 13 · 2015-08-05 13:27:40

Calculate in closed form the number of questions to gamble to maximize the probability to get a given score in a multiple choice test

score 1.1k · Answer 14 · 2026-03-31 05:42:41

1.1k

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Closed form for an infinite product: $\displaystyle \prod_{n=2}^\infty\left(1-\frac{1}{n(n-1)}\right)$

Published on 31 Mar 2026 - 5:42

score 11.5k · Answer 15 · 2015-08-06 18:26:32

11.5k

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Generating Functions and closed form

Published on 06 Aug 2015 - 18:26

List Question

Is there a closed-form solution (even approximated) to this inequality?

The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

Closed form of $\int_0^\infty \frac{1}{\left(a+\cosh x\right)^{1/n}} \, dx$ for $a=0,1$

Intriguing Poisson sum with hyperbolic function

Closed-form of $\int\limits_0^1\left(\frac{\left(x^2+1\right)\arcsin(x)}{\sqrt{1-x^2}}+2x\ln\left(x^2+1\right)\right)\frac{\ln x}{x^3+x}\,dx$

A formula to calculate the partial volume of a capsule or tank?

Simple closed functional form for summed recurrence relation

What is $\int_0^{\pi} \frac{e^{\sin x}\cos(x)}{1+e^{\tan x}} \, dx$?

Integral $\int_0^\infty\text{Li}_2\left(e^{-\pi x}\right)\arctan x\,dx$

Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$

Closed-form of $\int_0^1 x^n \operatorname{li}(x^m)\,dx$

explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$

Calculate in closed form the number of questions to gamble to maximize the probability to get a given score in a multiple choice test

Closed form for an infinite product: $\displaystyle \prod_{n=2}^\infty\left(1-\frac{1}{n(n-1)}\right)$

Generating Functions and closed form

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