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pisco
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44
Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$
Jul 20, 2020
39
Prove $\sum_{n=1}^\infty\frac{\cot(\pi n\sqrt{61})}{n^3}=-\frac{16793\pi^3}{45660\sqrt{61}}$
Nov 30, 2018
33
Closed Form for $~\int_0^1\frac{\text{arctanh }x}{\tan\left(\frac\pi2~x\right)}~dx$
Aug 1, 2015
30
Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$
Oct 29, 2019
27
Prove $n! +5$ is not a perfect square for $n\in\mathbb{N}$
Aug 12, 2017
27
Prove: $\int_0^2 \frac{dx}{\sqrt{1+x^3}}=\frac{\Gamma\left(\frac{1}{6}\right)\Gamma\left(\frac{1}{3}\right)}{6\Gamma\left(\frac{1}{2}\right)}$
Aug 6, 2020
26
Prove $\int_0^{\infty }\frac1{\sqrt{x}}\left(\frac{\cos(\pi x^2)}{\sinh (\pi x)}-\frac1{\pi x}\right)dx=\frac{1}{\sqrt{2}}\zeta(\frac{1}{2})$
Sep 15, 2020
23
Proving $\int_{\sqrt{5/7}}^1 \frac{(\pi-3\arctan\sqrt{\frac{2x^2-1}{3x^2-2}})\arctan x}{\sqrt{2x^2-1}(3x^2-1)} dx = \frac{\pi^3}{672}$
Mar 8, 2020
23
Evaluating $\int_0^1 \sqrt{1 + x ^4 } \, d x $
Jun 6, 2017
21
Evaluate $\int_0^1\arcsin^2(\frac{\sqrt{-x}}{2}) (\log^3 x) (\frac{8}{1+x}+\frac{1}{x}) \, dx$
Dec 6, 2022
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7
Series for $\frac{\log m}{\pi}$ with summands involving harmonic numbers
7
Three conjectural series for $\pi^2$ and related identities
5
Epstein zeta function for non-fundamental discriminant to L-series
5
How to prove the identity $L(2,(\frac{\cdot}3))=\frac2{15}\sum\limits_{k=1}^\infty\frac{48^k}{k(2k-1)\binom{4k}{2k}\binom{2k}k}$?