Question

Prove $ \int_{5\pi/36}^{7\pi/36} \ln (\cot t )dt +\int_{\pi/36}^{3\pi/36} \ln (\cot t )dt = \frac49G $

score 497 · Answer 1 · 2026-03-25 07:16:34

497

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Prove $ \int_{5\pi/36}^{7\pi/36} \ln (\cot t )dt +\int_{\pi/36}^{3\pi/36} \ln (\cot t )dt = \frac49G $

Published on 25 Mar 2026 - 7:16

score 573 · Answer 2 · 2026-03-25 07:15:11

573

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Beautiful monster: Catalan's constant and the Digamma function

Published on 25 Mar 2026 - 7:15

score 371 · Answer 3 · 2026-03-25 07:15:09

371

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Is there an integral for $\frac{\pi}{\mathrm{G}}$?

Published on 25 Mar 2026 - 7:15

score 436 · Answer 4 · 2026-03-25 07:21:57

436

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Compute $\int_{0}^{1}\frac{\ln(1+x)\ln(1+x^2)}{x}\,dx=\frac{\pi}{2}G-\frac{33}{32}\zeta(3)$

Published on 25 Mar 2026 - 7:21

score 267 · Answer 5 · 2026-03-25 07:15:14

267

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How do I solve this ominous integral?

Published on 25 Mar 2026 - 7:15

score 540 · Answer 6 · 2026-03-25 07:16:35

540

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Computation of $\int_0^1 \frac{\arctan^2 x\ln x}{1+x}dx$

Published on 25 Mar 2026 - 7:16

score 89 · Answer 7 · 2026-03-25 07:15:34

89

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Question on Difference Root representations of $\eta(2 n+1)$ and $\beta(2n)$ where $n\in\mathbb{N}$

Published on 25 Mar 2026 - 7:15

score 791 · Answer 8 · 2026-03-25 07:23:00

791

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Catalan constant's integral representation

Published on 25 Mar 2026 - 7:23

score 121 · Answer 9 · 2026-03-25 07:15:32

121

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Question related to potential closed-form representation of Catalan's constant

Published on 25 Mar 2026 - 7:15

score 801 · Answer 10 · 2026-03-25 07:15:33

801

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Finding $\int_0^{\frac{\pi}{2}} \frac{x}{\sin x} dx $

Published on 25 Mar 2026 - 7:15

score 216 · Answer 11 · 2026-03-25 07:15:32

216

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How do I evaluate $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}H_n}{2n+1}?$

Published on 25 Mar 2026 - 7:15

score 236 · Answer 12 · 2026-03-25 07:21:56

236

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How many ways to deal with the integral $\int_{0}^{\frac{\pi}{4}} \ln (\tan x) d x$ and $\int_{0}^{\frac{\pi}{4}} \ln (\sin x) d x$?

Published on 25 Mar 2026 - 7:21

score 306 · Answer 13 · 2026-03-25 07:15:34

306

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Integral $\int_0^{\pi/3}\frac{x}{\cos(x)}\,dx$

Published on 25 Mar 2026 - 7:15

score 117 · Answer 14 · 2026-03-25 07:21:57

117

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How do we prove that $\int_{0}^{\frac{\pi}{4}} x\cot xd x= \frac{\pi}{8} \ln 2+\frac{G}{2},$ where G is the Catalan’s constant?

Published on 25 Mar 2026 - 7:21

score 108 · Answer 15 · 2026-03-25 07:16:34

108

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How many ways are there to prove that $ \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin x} d x=2 G?$

Published on 25 Mar 2026 - 7:16

List Question

Prove $ \int_{5\pi/36}^{7\pi/36} \ln (\cot t )dt +\int_{\pi/36}^{3\pi/36} \ln (\cot t )dt = \frac49G $

Beautiful monster: Catalan's constant and the Digamma function

Is there an integral for $\frac{\pi}{\mathrm{G}}$?

Compute $\int_{0}^{1}\frac{\ln(1+x)\ln(1+x^2)}{x}\,dx=\frac{\pi}{2}G-\frac{33}{32}\zeta(3)$

How do I solve this ominous integral?

Computation of $\int_0^1 \frac{\arctan^2 x\ln x}{1+x}dx$

Question on Difference Root representations of $\eta(2 n+1)$ and $\beta(2n)$ where $n\in\mathbb{N}$

Catalan constant's integral representation

Question related to potential closed-form representation of Catalan's constant

Finding $\int_0^{\frac{\pi}{2}} \frac{x}{\sin x} dx $

How do I evaluate $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}H_n}{2n+1}?$

How many ways to deal with the integral $\int_{0}^{\frac{\pi}{4}} \ln (\tan x) d x$ and $\int_{0}^{\frac{\pi}{4}} \ln (\sin x) d x$?

Integral $\int_0^{\pi/3}\frac{x}{\cos(x)}\,dx$

How do we prove that $\int_{0}^{\frac{\pi}{4}} x\cot xd x= \frac{\pi}{8} \ln 2+\frac{G}{2},$ where G is the Catalan’s constant?

How many ways are there to prove that $ \int_{0}^{\frac{\pi}{2}} \frac{x}{\sin x} d x=2 G?$

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