Question

Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $

score 2k · Answer 1 · 2013-06-13 04:50:02

2k

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Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $

Published on 13 Jun 2013 - 4:50

score 561 · Answer 2 · 2013-06-15 06:20:34

561

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Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$

Published on 15 Jun 2013 - 6:20

score 111 · Answer 3 · 2013-06-15 10:43:30

111

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Proof for closed form approximation of e

Published on 15 Jun 2013 - 10:43

score 703 · Answer 4 · 2026-03-29 20:51:54

703

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Integral of polylogarithms and logs in closed form: $\int_0^1 \frac{du}{u}\text{Li}_2(u)^2(\log u)^2$

Published on 29 Mar 2026 - 20:51

score 8.3k · Answer 5 · 2013-06-19 21:45:21

8.3k

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Find closed form for $1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, \ldots$

Published on 19 Jun 2013 - 21:45

score 125 · Answer 6 · 2013-06-19 22:25:56

125

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How to solve $a \frac{d^2 y}{d x}+b \frac{d y}{d x} = f(y)$?

Published on 19 Jun 2013 - 22:25

score 180 · Answer 7 · 2013-06-20 11:17:19

180

Views

Find a number $A$ so that $\lfloor A^{3^n} \rfloor$ are always odd

Published on 20 Jun 2013 - 11:17

score 40k · Answer 8 · 2026-03-30 01:29:49

40k

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Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

Published on 30 Mar 2026 - 1:29

score 1.7k · Answer 9 · 2013-06-22 10:01:17

1.7k

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A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$

Published on 22 Jun 2013 - 10:01

score 848 · Answer 10 · 2026-03-26 11:08:42

848

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The positive root of the transcendental equation $\ln x-\sqrt{x-1}+1=0$

Published on 26 Mar 2026 - 11:08

score 450 · Answer 11 · 2013-06-24 22:43:50

450

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Closed form of $\sum\limits_{i=1}^n k^{1/i}$ or asymptotic equivalent when $n\to\infty$

Published on 24 Jun 2013 - 22:43

score 62 · Answer 12 · 2013-06-25 08:56:01

Closed form for the definite integral $\int_3^5\exp\left[\frac{-3.91}{V}\left(\frac{\lambda}{0.55}\right)^{-q}R\right]\,\mathrm d\lambda$

score 261 · Answer 13 · 2013-06-25 10:10:42

261

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Explicit formula for the series $ \sum_{k=1}^\infty \frac{x^k}{k!\cdot k} $

Published on 25 Jun 2013 - 10:10

score 148 · Answer 14 · 2013-06-29 16:26:43

148

Views

Converting from Closed Form

Published on 29 Jun 2013 - 16:26

score 489 · Answer 15 · 2013-07-01 21:51:31

489

Views

Telescoping series of form $\sum (an+1) ..(an+k)$

Published on 01 Jul 2013 - 21:51

List Question

Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $

Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$

Proof for closed form approximation of e

Integral of polylogarithms and logs in closed form: $\int_0^1 \frac{du}{u}\text{Li}_2(u)^2(\log u)^2$

Find closed form for $1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, \ldots$

How to solve $a \frac{d^2 y}{d x}+b \frac{d y}{d x} = f(y)$?

Find a number $A$ so that $\lfloor A^{3^n} \rfloor$ are always odd

Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$

The positive root of the transcendental equation $\ln x-\sqrt{x-1}+1=0$

Closed form of $\sum\limits_{i=1}^n k^{1/i}$ or asymptotic equivalent when $n\to\infty$

Closed form for the definite integral $\int_3^5\exp\left[\frac{-3.91}{V}\left(\frac{\lambda}{0.55}\right)^{-q}R\right]\,\mathrm d\lambda$

Explicit formula for the series $ \sum_{k=1}^\infty \frac{x^k}{k!\cdot k} $

Converting from Closed Form

Telescoping series of form $\sum (an+1) ..(an+k)$

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