Question

Integration $I_n=\int_{0}^{1}\frac{dx}{(x^n+1)(\sqrt[n]{x^n+1})}$

score 182 · Answer 1 · 2014-10-23 11:47:24

182

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Integration $I_n=\int_{0}^{1}\frac{dx}{(x^n+1)(\sqrt[n]{x^n+1})}$

Published on 23 Oct 2014 - 11:47

score 79 · Answer 2 · 2014-10-23 22:31:44

79

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Decomposition of $_1F_2(1+n;1,2+n;x)$

Published on 23 Oct 2014 - 22:31

score 282 · Answer 3 · 2014-10-24 12:28:14

282

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Closed formula for the asymptotic limit of a definite integral

Published on 24 Oct 2014 - 12:28

score 2.4k · Answer 4 · 2014-10-24 12:36:55

2.4k

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Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$

Published on 24 Oct 2014 - 12:36

score 1.5k · Answer 5 · 2014-10-24 17:04:30

1.5k

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Closed form of $I=\int_{0}^{\pi/2} \tan^{-1} \bigg( \frac{\cos(x)}{\sin(x) - 1 - \sqrt{2}} \bigg) \tan(x)\;dx$

Published on 24 Oct 2014 - 17:04

score 993 · Answer 6 · 2014-10-24 19:41:08

993

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Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

Published on 24 Oct 2014 - 19:41

score 1.1k · Answer 7 · 2026-03-26 02:47:51

1.1k

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Closed-forms of real parts of special value dilogarithm identities from inverse tangent integral function

Published on 26 Mar 2026 - 2:47

score 472 · Answer 8 · 2026-03-28 22:13:47

472

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Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

Published on 28 Mar 2026 - 22:13

score 1.4k · Answer 9 · 2026-03-25 14:25:30

1.4k

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Expressing the integral $\int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{\left(1-x^3\right)\left(1-a^6x^3\right)}}$ in terms of elliptic integrals

Published on 25 Mar 2026 - 14:25

score 533 · Answer 10 · 2014-10-27 00:06:09

533

Views

Three integral involving polylogarithm function

Published on 27 Oct 2014 - 0:06

score 288 · Answer 11 · 2014-10-27 08:35:56

288

Views

How to calculate the closed form of the series

Published on 27 Oct 2014 - 8:35

score 230 · Answer 12 · 2014-10-27 16:18:39

230

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generalization of geometric series $ \sum_{k=0}^\infty x^{p(k)} $

Published on 27 Oct 2014 - 16:18

score 266 · Answer 13 · 2026-03-26 14:43:17

266

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Value of a Sine-Like Infinite Product

Published on 26 Mar 2026 - 14:43

score 605 · Answer 14 · 2026-03-28 01:07:21

605

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Prove this closed-form of sum of ${_4F_3}$ hypergeometric functions

Published on 28 Mar 2026 - 1:07

score 417 · Answer 15 · 2014-10-28 01:16:37

417

Views

Write $\sum_{k=1}^nk\sin(kx)^2$ in closed form

Published on 28 Oct 2014 - 1:16

List Question

Integration $I_n=\int_{0}^{1}\frac{dx}{(x^n+1)(\sqrt[n]{x^n+1})}$

Decomposition of $_1F_2(1+n;1,2+n;x)$

Closed formula for the asymptotic limit of a definite integral

Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$

Closed form of $I=\int_{0}^{\pi/2} \tan^{-1} \bigg( \frac{\cos(x)}{\sin(x) - 1 - \sqrt{2}} \bigg) \tan(x)\;dx$

Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

Closed-forms of real parts of special value dilogarithm identities from inverse tangent integral function

Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

Expressing the integral $\int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{\left(1-x^3\right)\left(1-a^6x^3\right)}}$ in terms of elliptic integrals

Three integral involving polylogarithm function

How to calculate the closed form of the series

generalization of geometric series $ \sum_{k=0}^\infty x^{p(k)} $

Value of a Sine-Like Infinite Product

Prove this closed-form of sum of ${_4F_3}$ hypergeometric functions

Write $\sum_{k=1}^nk\sin(kx)^2$ in closed form

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