Question

How to find $I=\int_0^1\frac{\arctan^2x}{1+x}\left(\frac{\ln x}{1-x}+\ln(1+x)\right)dx$

score 445 · Answer 1 · 2026-03-26 08:02:28

445

Views

How to find $I=\int_0^1\frac{\arctan^2x}{1+x}\left(\frac{\ln x}{1-x}+\ln(1+x)\right)dx$

Published on 26 Mar 2026 - 8:02

score 746 · Answer 2 · 2026-03-26 07:59:06

746

Views

Challenging Sum: compute $\sum_{n=1}^\infty\frac{H_n}{2n+1}\left(\zeta(3)-H_n^{(3)}\right)$

Published on 26 Mar 2026 - 7:59

score 799 · Answer 3 · 2026-03-26 08:02:36

799

Views

On the relationship between $\Re\operatorname{Li}_n(1+i)$ and $\operatorname{Li}_n(1/2)$ when $n\ge5$

Published on 26 Mar 2026 - 8:02

score 521 · Answer 4 · 2026-03-26 07:59:02

521

Views

Compute $\int_0^1\frac{\ln^2(1+x)\operatorname{Li}_2(-x)}{x}dx$

Published on 26 Mar 2026 - 7:59

score 445 · Answer 5 · 2026-03-26 08:00:29

445

Views

Calculating $\int_0^1\frac{1}{1+x}\operatorname{Li}_2\left(\frac{2x}{1+x^2}\right)dx$

Published on 26 Mar 2026 - 8:00

score 72 · Answer 6 · 2026-03-26 08:03:23

72

Views

Elementary proof that $\sum \frac1{n^s} = \sum \frac1{s^n}$ has no solutions $s>1$.

Published on 26 Mar 2026 - 8:03

score 316 · Answer 7 · 2026-03-26 08:02:38

316

Views

How to evaluate: $\int_0^1 \frac{\frac{\pi^2}{6}-\operatorname{Li}_2(1-x)}{1-x}\cdot \ln^2(x) \, \mathrm dx$

Published on 26 Mar 2026 - 8:02

score 465 · Answer 8 · 2026-03-26 08:04:23

465

Views

Prove closed expression for $\int_0^1 \log(x) \log(1+x) \log(2+x)\,dx$

Published on 26 Mar 2026 - 8:04

score 568 · Answer 9 · 2026-05-10 18:27:53

568

Views

Closed form for the skew-harmonic sum $\sum_{n = 1}^\infty \frac{H_n \overline{H}_n}{n^2}$

Published on 10 May 2026 - 18:27

score 411 · Answer 10 · 2026-03-26 08:00:51

411

Views

Is there a closed form function for the integral $\int_{0}^{z} \frac{1}{x}\log(1-x)\log(x)\log(1+x)\,dx$?

Published on 26 Mar 2026 - 8:00

score 144 · Answer 11 · 2026-03-26 07:59:00

144

Views

Evaluating the indefinite integral $\int x^k \log (1-x) \log (x) \log (x+1) \, dx$

Published on 26 Mar 2026 - 7:59

score 318 · Answer 12 · 2026-03-26 07:56:41

318

Views

Properties of Polylogarithm functions

Published on 26 Mar 2026 - 7:56

score 201 · Answer 13 · 2026-03-26 08:00:43

201

Views

Verifying $\int_0^1 \ln^2x\ln(1+x)\operatorname{Li}_3\left(\frac1x\right)\ dx$

Published on 26 Mar 2026 - 8:00

score 139 · Answer 14 · 2026-05-11 05:16:34

139

Views

polylogarithm integrating by parts and expanding

Published on 11 May 2026 - 5:16

score 62 · Answer 15 · 2026-03-26 08:00:48

62

Views

How can we show that the multi-polylogarithmic function $L_{\underbrace{1,\ldots,1}_n}(z)=\frac{1}{n!}(L_1(z))^n$

Published on 26 Mar 2026 - 8:00

List Question

How to find $I=\int_0^1\frac{\arctan^2x}{1+x}\left(\frac{\ln x}{1-x}+\ln(1+x)\right)dx$

Challenging Sum: compute $\sum_{n=1}^\infty\frac{H_n}{2n+1}\left(\zeta(3)-H_n^{(3)}\right)$

On the relationship between $\Re\operatorname{Li}_n(1+i)$ and $\operatorname{Li}_n(1/2)$ when $n\ge5$

Compute $\int_0^1\frac{\ln^2(1+x)\operatorname{Li}_2(-x)}{x}dx$

Calculating $\int_0^1\frac{1}{1+x}\operatorname{Li}_2\left(\frac{2x}{1+x^2}\right)dx$

Elementary proof that $\sum \frac1{n^s} = \sum \frac1{s^n}$ has no solutions $s>1$.

How to evaluate: $\int_0^1 \frac{\frac{\pi^2}{6}-\operatorname{Li}_2(1-x)}{1-x}\cdot \ln^2(x) \, \mathrm dx$

Prove closed expression for $\int_0^1 \log(x) \log(1+x) \log(2+x)\,dx$

Closed form for the skew-harmonic sum $\sum_{n = 1}^\infty \frac{H_n \overline{H}_n}{n^2}$

Is there a closed form function for the integral $\int_{0}^{z} \frac{1}{x}\log(1-x)\log(x)\log(1+x)\,dx$?

Evaluating the indefinite integral $\int x^k \log (1-x) \log (x) \log (x+1) \, dx$

Properties of Polylogarithm functions

Verifying $\int_0^1 \ln^2x\ln(1+x)\operatorname{Li}_3\left(\frac1x\right)\ dx$

polylogarithm integrating by parts and expanding

How can we show that the multi-polylogarithmic function $L_{\underbrace{1,\ldots,1}_n}(z)=\frac{1}{n!}(L_1(z))^n$

Trending Questions

Popular # Hahtags

Popular Questions