New posts in closed-form

Interesting Harmonic Sum $\sum_{k\geq 1}\frac{(-1)^{k-1}}{k^2}H_k^{(2)}$

calculus integration sequences-and-series closed-form harmonic-numbers

How to solve homogeneous linear recurrence relations with constant coefficients?

sequences-and-series recurrence-relations closed-form fibonacci-numbers faq

Indefinite integral question: $\int \frac{1}{x\sqrt{x^2+x}}dx$

calculus integration indefinite-integrals closed-form

Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

calculus integration definite-integrals contour-integration closed-form

Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$

calculus definite-integrals special-functions closed-form polylogarithm

Evaluation of $\sum^{\infty}_{n=0}\frac{1}{16^n}\binom{2n}{n}.$

calculus integration sequences-and-series definite-integrals closed-form

Computing $\int_0^1\frac{\ln^3(1-x)\ln(1+x)}{x}dx$ or $\sum_{n=1}^\infty\frac{H_n^{(4)}}{n2^n}$

integration sequences-and-series closed-form harmonic-numbers polylogarithm

Prove that an equation has no elementary solution

abstract-algebra closed-form elementary-functions

Closed-form of integral $\int_0^1 \int_0^1 \frac{\arcsin\left(\sqrt{1-s}\sqrt{y}\right)}{\sqrt{1-y} \cdot (sy-y+1)}\,ds\,dy $

calculus integration definite-integrals closed-form

How to evaluate $\int_{0}^{1}\frac{\arctan x}{x} \log{\left(\frac{ 1+ x}{\sqrt{1+x^2}}\right)}\mathrm dx$

calculus integration definite-integrals closed-form harmonic-numbers

Evaluate $\int\frac{1}{\sin(x-a)\sin(x-b)}\,dx$

calculus integration trigonometry indefinite-integrals closed-form

Solve this integral:$\int_0^\infty\frac{\arctan x}{x(x^2+1)}\mathrm dx$

calculus integration sequences-and-series definite-integrals closed-form

Finding a closed form for $\int_{0}^{1}\frac{\ln\left ( 1-x^{2} \right )\arcsin ^{2}x}{x^{2}}\mathrm{d}x\approx -0.939332$ [duplicate]

calculus integration definite-integrals closed-form

Show this $\int_0^\infty \frac{t\ln(2\sinh t)}{\left(3t^2+\ln^2(2\sinh t)\right)^2}~dt=0$

calculus integration definite-integrals contour-integration closed-form

Closed form of $\int e^{i\csc^2(x)}dx=\int \cos\left(\csc^2(x)\right)dx+i\int \sin\left(\csc^2(x)\right)dx$

special-functions closed-form hypergeometric-function trigonometric-integrals fresnel-integrals

how to calculuate $\int_0^ \pi \sqrt{1+x^2 \sin^2x}dx$

calculus integration definite-integrals closed-form

Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

calculus sequences-and-series summation closed-form

Evaluate$\int\limits_0^1 [\log(x)\log(1-x)+\operatorname{Li}_2(x)]\left[\frac{\operatorname{Li}_2(x)}{x(1-x)}-\frac{\zeta(2)}{1-x}\right]\mathrm dx$

integration definite-integrals closed-form riemann-zeta polylogarithm

Closed form for $\sum^\infty_{n=1}\frac{H_n}{2^n\,(2n+1)^2}$

calculus sequences-and-series closed-form harmonic-numbers polylogarithm

Conjecture $\sum_{n=1}^\infty\frac{n^2}{(-1)^n \cosh(\pi n\sqrt{3})-1}=\frac{1}{12\pi^2}$

calculus sequences-and-series closed-form conjectures