Question

What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

score 1.6k · Answer 1 · 2026-03-26 02:45:52

1.6k

Views

What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

Published on 26 Mar 2026 - 2:45

score 194 · Answer 2 · 2026-03-25 21:00:12

194

Views

Log integrals II

Published on 25 Mar 2026 - 21:00

score 790 · Answer 3 · 2014-10-14 19:15:23

790

Views

How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$

Published on 14 Oct 2014 - 19:15

score 468 · Answer 4 · 2014-10-15 11:08:35

468

Views

Can we consider a hypergeometric function as a closed-form?

Published on 15 Oct 2014 - 11:08

score 1.1k · Answer 5 · 2026-03-28 09:57:40

1.1k

Views

Sum of Bessel functions and integral of exponential of sine or cosine

Published on 28 Mar 2026 - 9:57

score 1.3k · Answer 6 · 2014-10-16 13:41:05

1.3k

Views

Prove $\int_{0}^{\pi/2} x\csc^2(x)\arctan \left(\alpha \tan x\right)\, dx = \frac{\pi}{2}\left[\ln\frac{(1+\alpha)^{1+\alpha}}{\alpha^\alpha}\right]$

Published on 16 Oct 2014 - 13:41

score 3.5k · Answer 7 · 2014-10-17 17:50:32

3.5k

Views

Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$

Published on 17 Oct 2014 - 17:50

score 465 · Answer 8 · 2014-10-17 22:20:38

465

Views

Closed-form of $\int_0^{\pi/4} \sin(\sin(x)) \, dx$

Published on 17 Oct 2014 - 22:20

score 665 · Answer 9 · 2014-10-17 23:18:26

665

Views

Closed-form of $\int_0^1 B_n(x)\psi(x+1)\,dx$

Published on 17 Oct 2014 - 23:18

score 279 · Answer 10 · 2026-03-28 18:16:58

279

Views

Non-recursive closed-form of the coefficients of Taylor series of the reciprocal gamma function

Published on 28 Mar 2026 - 18:16

score 459 · Answer 11 · 2026-03-28 02:42:56

459

Views

Closed-form of the sequence ${_2F_1}\left(\begin{array}c\tfrac12,-n\\\tfrac32\end{array}\middle|\,\frac{1}{2}\right)$

Published on 28 Mar 2026 - 2:42

score 287 · Answer 12 · 2014-10-18 19:48:41

287

Views

Closed-form of $\sum_{k=0}^{\infty} \frac{k^a\,b^k}{k!}$

Published on 18 Oct 2014 - 19:48

score 1.1k · Answer 13 · 2014-10-18 22:58:42

1.1k

Views

Integral ${\large\int}_0^1\frac{\ln^2\ln\left(\frac1x\right)}{1+x+x^2}dx$

Published on 18 Oct 2014 - 22:58

score 433 · Answer 14 · 2026-03-26 02:45:41

433

Views

Closed-form of a special value dilogarithm identity

Published on 26 Mar 2026 - 2:45

score 129 · Answer 15 · 2014-10-19 07:55:32

129

Views

Inverse Laplace transform of $\frac{s^2-4s-2}{\left(s^2+2\right)^2}$

Published on 19 Oct 2014 - 7:55

List Question

What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

Log integrals II

How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$

Can we consider a hypergeometric function as a closed-form?

Sum of Bessel functions and integral of exponential of sine or cosine

Prove $\int_{0}^{\pi/2} x\csc^2(x)\arctan \left(\alpha \tan x\right)\, dx = \frac{\pi}{2}\left[\ln\frac{(1+\alpha)^{1+\alpha}}{\alpha^\alpha}\right]$

Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$

Closed-form of $\int_0^{\pi/4} \sin(\sin(x)) \, dx$

Closed-form of $\int_0^1 B_n(x)\psi(x+1)\,dx$

Non-recursive closed-form of the coefficients of Taylor series of the reciprocal gamma function

Closed-form of the sequence ${_2F_1}\left(\begin{array}c\tfrac12,-n\\\tfrac32\end{array}\middle|\,\frac{1}{2}\right)$

Closed-form of $\sum_{k=0}^{\infty} \frac{k^a\,b^k}{k!}$

Integral ${\large\int}_0^1\frac{\ln^2\ln\left(\frac1x\right)}{1+x+x^2}dx$

Closed-form of a special value dilogarithm identity

Inverse Laplace transform of $\frac{s^2-4s-2}{\left(s^2+2\right)^2}$

Trending Questions

Popular # Hahtags

Popular Questions