Question

Integral $\int_0^1 \frac{\ln(1+x+x^2)\ln(1-x+x^2)}{x}dx$

score 894 · Answer 1 · 2019-06-03 00:16:30

894

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Integral $\int_0^1 \frac{\ln(1+x+x^2)\ln(1-x+x^2)}{x}dx$

Published on 03 Jun 2019 - 0:16

score 226 · Answer 2 · 2026-03-25 12:50:48

226

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Relating $\int_0^1\frac{(\ln x)^{n-1}(\ln(1-z\,x))^p}{x}dx$ and $\int_0^1\frac{(\ln x)^{n}(\ln(1-z\,x))^{p-1}}{1-z\,x}dx$

Published on 25 Mar 2026 - 12:50

score 292 · Answer 3 · 2019-06-03 10:16:09

292

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Closed form for $\sum_{n=1}^\infty \frac{4^n}{n^p\binom{2n}{n}}$

Published on 03 Jun 2019 - 10:16

score 431 · Answer 4 · 2026-03-25 12:50:08

431

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Closed forms of Nielsen polylogarithms $\int_0^1\frac{(\ln t)^{n-1}(\ln(1-z\,t))^p}{t}dt$?

Published on 25 Mar 2026 - 12:50

score 200 · Answer 5 · 2019-06-03 16:40:49

200

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Integral $E_n(a_1,...,a_n;t)=\int_{-\infty}^{\infty}\frac{x^2\cos(tx)}{\prod_{k=1}^{n}(x^2+a_k^2)}dx$

Published on 03 Jun 2019 - 16:40

score 198 · Answer 6 · 2019-06-03 22:15:21

198

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Show that : $\displaystyle\int_0^{\infty}\frac{\ln(1+x^2)\operatorname{arc\,cot} x}{x}=\frac{π^3}{12}$

Published on 03 Jun 2019 - 22:15

score 240 · Answer 7 · 2019-06-05 23:38:34

240

Views

Integrable subbundle

Published on 05 Jun 2019 - 23:38

score 501 · Answer 8 · 2019-06-06 13:42:48

501

Views

Sum of reciprocal binomial coefficients

Published on 06 Jun 2019 - 13:42

score 117 · Answer 9 · 2019-06-06 14:06:16

117

Views

Do I have a chance to get a closed form for this integral?

Published on 06 Jun 2019 - 14:06

score 61 · Answer 10 · 2019-06-06 15:01:30

61

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How to analytically compute $\iiint \frac{1}{\sqrt{a+b \sin c}}\,da\,db\,dc$

Published on 06 Jun 2019 - 15:01

score 320 · Answer 11 · 2026-03-25 06:06:49

320

Views

Integral $\int_0^1 \sqrt{\frac{x^2-2}{x^2-1}}\, dx=\frac{\pi\sqrt{2\pi}}{\Gamma^2(1/4)}+\frac{\Gamma^2(1/4)}{4\sqrt{2\pi}}$

Published on 25 Mar 2026 - 6:06

score 566 · Answer 12 · 2019-06-06 17:59:13

566

Views

Closed form of series $z^n/n$.

Published on 06 Jun 2019 - 17:59

score 76 · Answer 13 · 2026-03-25 03:01:37

76

Views

Closed form of $\eta^{(k)}(i)$.

Published on 25 Mar 2026 - 3:01

score 370 · Answer 14 · 2026-03-25 11:00:58

370

Views

A bug in Wolfram Alpha about an infinite series?

Published on 25 Mar 2026 - 11:00

score 294 · Answer 15 · 2019-06-10 12:55:41

294

Views

Double integrals involving incomplete beta function

Published on 10 Jun 2019 - 12:55

List Question

Integral $\int_0^1 \frac{\ln(1+x+x^2)\ln(1-x+x^2)}{x}dx$

Relating $\int_0^1\frac{(\ln x)^{n-1}(\ln(1-z\,x))^p}{x}dx$ and $\int_0^1\frac{(\ln x)^{n}(\ln(1-z\,x))^{p-1}}{1-z\,x}dx$

Closed form for $\sum_{n=1}^\infty \frac{4^n}{n^p\binom{2n}{n}}$

Closed forms of Nielsen polylogarithms $\int_0^1\frac{(\ln t)^{n-1}(\ln(1-z\,t))^p}{t}dt$?

Integral $E_n(a_1,...,a_n;t)=\int_{-\infty}^{\infty}\frac{x^2\cos(tx)}{\prod_{k=1}^{n}(x^2+a_k^2)}dx$

Show that : $\displaystyle\int_0^{\infty}\frac{\ln(1+x^2)\operatorname{arc\,cot} x}{x}=\frac{π^3}{12}$

Integrable subbundle

Sum of reciprocal binomial coefficients

Do I have a chance to get a closed form for this integral?

How to analytically compute $\iiint \frac{1}{\sqrt{a+b \sin c}}\,da\,db\,dc$

Integral $\int_0^1 \sqrt{\frac{x^2-2}{x^2-1}}\, dx=\frac{\pi\sqrt{2\pi}}{\Gamma^2(1/4)}+\frac{\Gamma^2(1/4)}{4\sqrt{2\pi}}$

Closed form of series $z^n/n$.

Closed form of $\eta^{(k)}(i)$.

A bug in Wolfram Alpha about an infinite series?

Double integrals involving incomplete beta function

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