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Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis

score 7.5k · Answer 1 · 2026-03-29 10:27:40

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Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis

Published on 29 Mar 2026 - 10:27

score 615 · Answer 2 · 2026-04-11 16:52:20

615

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How to prove $\sqrt[\pi]{e} < \sqrt[\pi]{\pi}<\sqrt[e]{e}< \sqrt[e]{\pi}$

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score 126 · Answer 3 · 2026-04-10 05:42:21

126

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complex logarithms

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score 54 · Answer 4 · 2026-03-29 23:45:03

54

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score 2.9k · Answer 5 · 2026-03-26 19:18:40

2.9k

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How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$

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score 229 · Answer 6 · 2014-11-22 09:21:55

229

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Is there any holomorphic function in a unit ball such that $f(1/n)=\frac{1}{n \ln{n}}$

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score 506 · Answer 7 · 2026-04-11 01:39:00

506

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Math equation problem - fitting wallpapers on a wall

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score 1.3k · Answer 8 · 2026-04-02 16:03:50

1.3k

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Why does my professor say that writing $\int \frac 1x \mathrm{d}x = \ln|x| + C$ is wrong?

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score 251 · Answer 9 · 2026-03-26 02:44:45

251

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how can I publish my log approximation formula

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score 214 · Answer 10 · 2014-11-23 13:40:56

214

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Calculate $\log_{a}(ab)$, when $\log_{ab}(b)$ is known

Published on 23 Nov 2014 - 13:40

score 68 · Answer 11 · 2026-03-27 11:49:04

68

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Let $\gamma$ be the Euler-Mascheroni constant. Can there be natural numbers $a,b,c$ such that $\log a - \log b - \log \log \log c =\gamma$?

Published on 27 Mar 2026 - 11:49

score 190 · Answer 12 · 2014-11-23 22:44:30

190

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Indefinite integrals with natural logs

Published on 23 Nov 2014 - 22:44

score 69 · Answer 13 · 2014-11-24 02:01:05

69

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comparison test to show that $\sum_{n=1}^{\infty}\frac{1}{(n+2)\sqrt{ \ln ^3(n+3)}}$ converges

Published on 24 Nov 2014 - 2:01

score 1.2k · Answer 14 · 2026-04-02 08:18:57

1.2k

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Maximal number of colours in a palette that allows for fewer than 500 mixtures

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score 525 · Answer 15 · 2014-11-24 18:38:37

525

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Does $\log_a b = \log_\sqrt a \sqrt b$ can be a basic logarithm law?

Published on 24 Nov 2014 - 18:38

List Question

Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis

How to prove $\sqrt[\pi]{e} < \sqrt[\pi]{\pi}<\sqrt[e]{e}< \sqrt[e]{\pi}$

complex logarithms

$e^z=-3i$ find $z\in \mathbb C$ check my answer

How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$

Is there any holomorphic function in a unit ball such that $f(1/n)=\frac{1}{n \ln{n}}$

Math equation problem - fitting wallpapers on a wall

Why does my professor say that writing $\int \frac 1x \mathrm{d}x = \ln|x| + C$ is wrong?

how can I publish my log approximation formula

Calculate $\log_{a}(ab)$, when $\log_{ab}(b)$ is known

Let $\gamma$ be the Euler-Mascheroni constant. Can there be natural numbers $a,b,c$ such that $\log a - \log b - \log \log \log c =\gamma$?

Indefinite integrals with natural logs

comparison test to show that $\sum_{n=1}^{\infty}\frac{1}{(n+2)\sqrt{ \ln ^3(n+3)}}$ converges

Maximal number of colours in a palette that allows for fewer than 500 mixtures

Does $\log_a b = \log_\sqrt a \sqrt b$ can be a basic logarithm law?

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