New posts in definite-integrals

Proof of an Elliptic Integral Relation

integration definite-integrals special-functions pi elliptic-integrals

Does $\int_0^\infty\frac{\ln(1+x)}{x(1+x^n)}dx$ have a general form?

calculus integration definite-integrals

Find the value of $a$ such that $F(a)=\int^{\frac \pi 2}_{0}{|\sin x-a\cos x|} \space dx$ is minimised

proof-verification definite-integrals

Closed-Form solution for nested integrals of this polynomial?

calculus integration definite-integrals recurrence-relations closed-form

Beautiful monster: Catalan's constant and the Digamma function

integration definite-integrals fourier-series digamma-function catalans-constant

Evaluate $\iint_D xy$ [closed]

calculus integration definite-integrals

Proving that $\int_0^1\frac{x \log^2(1-x)}{1+x^2} \ dx = \frac{35}{32}\zeta(3)+\frac{1}{24}\log^3(2) -\frac{5}{96} \pi^2 \log(2)$

calculus real-analysis integration definite-integrals

A probabilistic integral $\int_{-\infty}^{\infty}e^{-x^2/2\sigma^2}\arcsin\left(1-2\left|\lfloor x\rceil-x\right|\right)\,dx$

integration definite-integrals improper-integrals

Having fun integral $\int_0^{\pi/4} \cos x \arctan(\cos x)\, dx$

calculus integration trigonometry definite-integrals alternative-proof

A limit evaluating to $2 K$ (Catalan's constant)

real-analysis calculus limits definite-integrals catalans-constant

Integrate $\left(\frac{\cos^3x\>+\>\sin^3x}{\cos^4x\>+\>\sin^4x}\right)^2$ over $[-\frac\pi4,\frac\pi4]$

integration definite-integrals

Challenging integral $\int_{0}^{1}\frac{x\operatorname{li}(x)}{x^2+1}dx$

definite-integrals logarithms power-series improper-integrals

Showing $\int_{-1}^1\frac{m(2m-1)x^{2m-2}(1-x^{2m})+m^2x^{4m-2}}{(m^2x^{4m-2}+1-x^{2m})\sqrt{1-x^{2m}}}dx=\pi$, algebraically

differential-geometry definite-integrals curvature

integration of a function

calculus integration definite-integrals

Integral-Summation inequality.

calculus real-analysis integration inequality definite-integrals

Closed form for ${\large\int}_0^\infty\frac{\arctan(x)\,\operatorname{arccot}(x+1)}{x}dx$

calculus integration definite-integrals closed-form trigonometry

How to prove that $\int_{0}^{1}\ln{(x/(1-x))}\ln{(1+x-x^2)}\frac{dx}{x}=-\frac{2}{5}\zeta{(3)}$

calculus integration definite-integrals

Find $\int\limits^{\infty}_{0}\frac{1}{(x^8+5x^6+14x^4+5x^2+1)^4}dx$

calculus integration definite-integrals closed-form

Closed form of $\int_{0}^{1} \frac{\log(1+x)\log(2+x) \log(3+x)}{1+x}\,dx$

integration definite-integrals logarithms

Bessel function integral and Mellin transform

special-functions definite-integrals integral-transforms