New posts in closed-form

Is $K\left(\frac{\sqrt{2-\sqrt3}}2\right)\stackrel?=\frac{\Gamma\left(\frac16\right)\Gamma\left(\frac13\right)}{4\ \sqrt[4]3\ \sqrt\pi}$

calculus special-functions gamma-function closed-form conjectures

On the integral $\int_0^\infty \eta^2(i x) \,dx = \ln(1+\sqrt{3}+\sqrt{3+2 \sqrt{3}})$ and its cousins

integration sequences-and-series definite-integrals closed-form modular-forms

An integral by O. Furdui $\int_0^1 \log^2(\sqrt{1+x}-\sqrt{1-x}) \ dx$

calculus real-analysis integration definite-integrals closed-form

A closed form for $\int_0^1\frac{\ln(-\ln x)\ \operatorname{li}^2x}{x}dx$

calculus integration special-functions logarithms closed-form

A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$

calculus integration definite-integrals improper-integrals closed-form

Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$

calculus real-analysis integration definite-integrals closed-form

Integral involving Clausen function ${\large\int}_0^{2\pi}\operatorname{Cl}_2(x)^2\,x^p\,dx$

calculus integration definite-integrals closed-form polylogarithm

A closed form for $\int_0^\infty\frac{\sin(x)\ \operatorname{erfi}\left(\sqrt{x}\right)\ e^{-x\sqrt{2}}}{x}dx$

integration definite-integrals closed-form elementary-functions error-function

Closed form for $\int_{-\infty}^0\operatorname{Ei}^3x\,dx$

calculus integration definite-integrals special-functions closed-form

How to compute $\int_{-\infty}^\infty\exp\left(-\frac{(x^2-13x-1)^2}{611x^2}\right)\ dx$

calculus integration definite-integrals improper-integrals closed-form

Closed form expression for the product $\prod\limits_{k=1}^{n}\left(1 - \frac{1}{ak}\right)$

sequences-and-series products closed-form

A Challenging Euler Sum $\sum\limits_{n=1}^\infty \frac{H_n}{\tbinom{2n}{n}}$

sequences-and-series special-functions definite-integrals closed-form

Closed form for $\int_0^{\infty}\frac{\arctan x\ln(1+x^2)}{1+x^2}\sqrt{x}\,dx$

definite-integrals improper-integrals closed-form

The positive root of the transcendental equation $\ln x-\sqrt{x-1}+1=0$

special-functions logarithms mathematica closed-form transcendental-equations

Is any closed-form representation known for the sum $\sum\limits_{n=1}^{\infty}\frac{\mu(n)\log n}{n^2}$?

sequences-and-series number-theory prime-numbers closed-form

Integral $\int_0^1\frac{\ln x}{x-1}\ln\left(1+\frac1{\ln^2x}\right)dx$

calculus integration definite-integrals logarithms closed-form

Integral $\int_0^\infty x^2\,e^{-x^2}\operatorname{erf}(x)\,\log(x)\,dx$

integration definite-integrals improper-integrals closed-form hypergeometric-function

How to solve $\int_0^\infty J_0(x)\ \text{sinc}(\pi\,x)\ e^{-x}\,\mathrm dx$?

special-functions definite-integrals improper-integrals closed-form

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

calculus integration definite-integrals improper-integrals closed-form

Crazy $\int_0^\infty{_3F_2}\left(\begin{array}c\tfrac58,\tfrac58,\tfrac98\\\tfrac12,\tfrac{13}8\end{array}\middle|\ {-x}\right)^2\frac{dx}{\sqrt x}$

calculus integration definite-integrals closed-form hypergeometric-function