Question

How to evaluate$J(k) = \int_{0}^{1} \frac{\ln^2x\ln\left ( \frac{1-x}{1+x} \right ) }{(x-1)^2-k^2(x+1)^2}\text{d}x$

score 459 · Answer 1 · 2021-09-11 08:09:57

459

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How to evaluate$J(k) = \int_{0}^{1} \frac{\ln^2x\ln\left ( \frac{1-x}{1+x} \right ) }{(x-1)^2-k^2(x+1)^2}\text{d}x$

Published on 11 Sep 2021 - 8:09

score 360 · Answer 2 · 2021-10-16 07:35:03

360

Views

Evaluate two integrals involving $\operatorname{Li}_3,\operatorname{Li}_4$

Published on 16 Oct 2021 - 7:35

score 235 · Answer 3 · 2021-10-22 16:37:20

235

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Closed form evaluation of a trigonometric integral in terms of polylogarithms

Published on 22 Oct 2021 - 16:37

score 176 · Answer 4 · 2021-11-03 02:27:48

176

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Prove $\int_0^1\frac{\text{Li}_2(-x^2)}{\sqrt{1-x^2}}\,dx=\pi\int_0^1\frac{\ln\left(\frac{2}{1+\sqrt{1+x}}\right)}{x}\,dx$

Published on 03 Nov 2021 - 2:27

score 351 · Answer 5 · 2021-11-04 13:21:11

351

Views

Evaluating $\int_0^\infty\frac{\tan^{-1}av\cot^{-1}av}{1+v^2}\,dv$

Published on 04 Nov 2021 - 13:21

score 340 · Answer 6 · 2021-11-07 02:15:00

340

Views

Evaluating $\int_0^1\frac{\operatorname{Li}_2(x)\ln(1+x)}x\,dx$

Published on 07 Nov 2021 - 2:15

score 123 · Answer 7 · 2021-11-08 07:34:34

123

Views

Evaluate $\int_{{\frac {\pi}{8}}}^{{\frac {7\,\pi}{8}}}\!{\frac {\ln \left( 1- \cos \left( t \right) \right) }{\sin \left( t \right) }}\,{\rm d}t$

Published on 08 Nov 2021 - 7:34

score 128 · Answer 8 · 2021-11-11 15:23:47

128

Views

Conjectured closed form for ${\it {Li_2}} \left( 1-{\frac {\sqrt {2}}{2}}-i \left( 1-{\frac {\sqrt { 2}}{2}} \right) \right)$

Published on 11 Nov 2021 - 15:23

score 480 · Answer 9 · 2021-11-19 14:45:59

480

Views

Is the closed form of $\int_0^1 \frac{x\ln^a(1+x)}{1+x^2}dx$ known in the literature?

Published on 19 Nov 2021 - 14:45

score 78 · Answer 10 · 2021-11-29 20:06:07

78

Views

How to solve a Non-algebraic equation?

Published on 29 Nov 2021 - 20:06

score 328 · Answer 11 · 2021-12-06 18:46:08

328

Views

Different ways to evaluate $\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{(n+1)(n+2)(n+3)}$

Published on 06 Dec 2021 - 18:46

score 72 · Answer 12 · 2021-12-07 17:13:00

72

Views

Asymptotics of Geometric Distribution Moments

Published on 07 Dec 2021 - 17:13

score 105 · Answer 13 · 2021-12-15 14:53:01

105

Views

Identity involving PolyLog functions

Published on 15 Dec 2021 - 14:53

score 57 · Answer 14 · 2021-12-23 13:25:30

57

Views

Difference of polylogarithms of complex conjugate arguments

Published on 23 Dec 2021 - 13:25

score 481 · Answer 15 · 2026-03-25 10:25:08

481

Views

Finding $\int_{1}^{\infty} \frac{1}{1+x^2} \frac{\operatorname{Li}_2\left ( \frac{1-x}{2} \right ) }{\pi^2+\ln^2\left(\frac{x-1}{2}\right)}\text{d}x$

Published on 25 Mar 2026 - 10:25

List Question

How to evaluate$J(k) = \int_{0}^{1} \frac{\ln^2x\ln\left ( \frac{1-x}{1+x} \right ) }{(x-1)^2-k^2(x+1)^2}\text{d}x$

Evaluate two integrals involving $\operatorname{Li}_3,\operatorname{Li}_4$

Closed form evaluation of a trigonometric integral in terms of polylogarithms

Prove $\int_0^1\frac{\text{Li}_2(-x^2)}{\sqrt{1-x^2}}\,dx=\pi\int_0^1\frac{\ln\left(\frac{2}{1+\sqrt{1+x}}\right)}{x}\,dx$

Evaluating $\int_0^\infty\frac{\tan^{-1}av\cot^{-1}av}{1+v^2}\,dv$

Evaluating $\int_0^1\frac{\operatorname{Li}_2(x)\ln(1+x)}x\,dx$

Evaluate $\int_{{\frac {\pi}{8}}}^{{\frac {7\,\pi}{8}}}\!{\frac {\ln \left( 1- \cos \left( t \right) \right) }{\sin \left( t \right) }}\,{\rm d}t$

Conjectured closed form for ${\it {Li_2}} \left( 1-{\frac {\sqrt {2}}{2}}-i \left( 1-{\frac {\sqrt { 2}}{2}} \right) \right)$

Is the closed form of $\int_0^1 \frac{x\ln^a(1+x)}{1+x^2}dx$ known in the literature?

How to solve a Non-algebraic equation?

Different ways to evaluate $\sum_{n=1}^\infty\frac{H_nH_n^{(2)}}{(n+1)(n+2)(n+3)}$

Asymptotics of Geometric Distribution Moments

Identity involving PolyLog functions

Difference of polylogarithms of complex conjugate arguments

Finding $\int_{1}^{\infty} \frac{1}{1+x^2} \frac{\operatorname{Li}_2\left ( \frac{1-x}{2} \right ) }{\pi^2+\ln^2\left(\frac{x-1}{2}\right)}\text{d}x$

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