Newbetuts

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

Closed-forms of real parts of special value dilogarithm identities from inverse tangent integral function

Trilogarithm $\operatorname{Li}_3(z)$ and the imaginary golden ratio $i\,\phi$

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

Indefinite integral $\int \arcsin \left(k\sin x\right) dx$

Is it true that $\left\lfloor\sum_{s=1}^n\operatorname{Li}_s\left(\frac 1k \right)\right\rfloor\stackrel{?}{=}\left\lfloor\frac nk \right\rfloor$

Evaluation of a dilogarithmic integral

A twisted hypergeometric series $\sum_{n=1}^\infty\frac{H_n}{n}\left(\frac{(2n)!}{4^n(n!)^2}\right)^2$

How to integrate the dilogarithms?

Prove $\int_{0}^{1} \frac{\sin^{-1}(x)}{x} dx = \frac{\pi}{2}\ln2$

Prove $\int_{\frac{\pi}{20}}^{\frac{3\pi}{20}} \ln \tan x\,\,dx= - \frac{2G}{5}$

A reason for $ 64\int_0^1 \left(\frac \pi 4+\arctan t\right)^2\cdot \log t\cdot\frac 1{1-t^2}\; dt =-\pi^4$ ...

How to solve a Non-algebraic equation?

A peculiar Euler sum

Is the following Harmonic Number Identity true?

Equating the integrals of 1/(1-xy) and 2/(1+xy) by elementary calculus?

New posts in polylogarithm

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

Integral $\int_0^1 \frac{\log^4(x)}{(1-x)^4}dx$

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

Closed-forms of real parts of special value dilogarithm identities from inverse tangent integral function

Trilogarithm $\operatorname{Li}_3(z)$ and the imaginary golden ratio $i\,\phi$

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

Indefinite integral $\int \arcsin \left(k\sin x\right) dx$

Is it true that $\left\lfloor\sum_{s=1}^n\operatorname{Li}_s\left(\frac 1k \right)\right\rfloor\stackrel{?}{=}\left\lfloor\frac nk \right\rfloor$

Evaluation of a dilogarithmic integral

A twisted hypergeometric series $\sum_{n=1}^\infty\frac{H_n}{n}\left(\frac{(2n)!}{4^n(n!)^2}\right)^2$

How to integrate the dilogarithms?

Prove $\int_{0}^{1} \frac{\sin^{-1}(x)}{x} dx = \frac{\pi}{2}\ln2$

Prove $\int_{\frac{\pi}{20}}^{\frac{3\pi}{20}} \ln \tan x\,\,dx= - \frac{2G}{5}$

A reason for $ 64\int_0^1 \left(\frac \pi 4+\arctan t\right)^2\cdot \log t\cdot\frac 1{1-t^2}\; dt =-\pi^4$ ...

How to solve a Non-algebraic equation?

A peculiar Euler sum

Is the following Harmonic Number Identity true?

Equating the integrals of 1/(1-xy) and 2/(1+xy) by elementary calculus?