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Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$

The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

On the integral $\int_{e}^{\infty}\frac{t^{1/2}}{\log^{1/2}\left(t\right)}\alpha^{-t/\log\left(t\right)}dt,\,\alpha>1.$

Closed form of an integral involving Lambert function

Challenging identity regarding Bell polynomials

Dilogarithm identity containing the tribonacci constant

Closed-forms of infinite series with factorial in the denominator

What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?

Known exact values of the $\operatorname{Li}_3$ function

Generalized FoxTrot Series $F(a,b,q,x) = \sum_{k=q}^{\infty} \dfrac {(-1)^{k+1} k^a}{k^b+x}$

Compute this following integral without Fourier series : $\int_0^{\pi/4}x\ln(\tan x)dx$

Conjecture $\sum_{m=1}^\infty\frac{y_{n+1,m}y_{n,k}}{[y_{n+1,m}-y_{n,k}]^3}\overset{?}=\frac{n+1}{8}$, where $y_{n,k}=(\text{BesselJZero[n,k]})^2$

Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$

Packing an infinite sequence of disks

Proof of a dilogarithm identity

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^5 2^n}$

New posts in closed-form

Solving $x + 3^x < 4$ analytically

Solve $-2^x-x/2=0$ analytically

Closed form of $\sum\limits_{i=1}^n\left\lfloor\frac{n}{i}\right\rfloor^2$?

Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$

The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

On the integral $\int_{e}^{\infty}\frac{t^{1/2}}{\log^{1/2}\left(t\right)}\alpha^{-t/\log\left(t\right)}dt,\,\alpha>1.$

Closed form of an integral involving Lambert function

Challenging identity regarding Bell polynomials

Dilogarithm identity containing the tribonacci constant

Closed-forms of infinite series with factorial in the denominator

What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?

Known exact values of the $\operatorname{Li}_3$ function

Generalized FoxTrot Series $F(a,b,q,x) = \sum_{k=q}^{\infty} \dfrac {(-1)^{k+1} k^a}{k^b+x}$

Compute this following integral without Fourier series : $\int_0^{\pi/4}x\ln(\tan x)dx$

Conjecture $\sum_{m=1}^\infty\frac{y_{n+1,m}y_{n,k}}{[y_{n+1,m}-y_{n,k}]^3}\overset{?}=\frac{n+1}{8}$, where $y_{n,k}=(\text{BesselJZero[n,k]})^2$

Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$

Packing an infinite sequence of disks

Proof of a dilogarithm identity

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^5 2^n}$