New posts in definite-integrals

What was the largest ratio (result size)/(integrand size) you have seen?

integration definite-integrals calculus soft-question big-list

An exercise from my brother: $\int_{-1}^1\frac{\ln (2x-1)}{\sqrt[\large 6]{x(1-x)(1-2x)^4}}\,dx$

calculus real-analysis integration definite-integrals improper-integrals

Proving that $ \int_{0}^{\pi/2} \frac{\mathrm{d}{x}}{\sqrt{a^{2} {\cos^{2}}(x) + b^{2} {\sin^{2}}(x)}} = \frac{\pi}{2 \cdot \text{AGM}(a,b)} $.

integration complex-analysis definite-integrals

Integral $ \int_{0}^{\infty} \ln x\left[\ln \left( \frac{x+1}{2} \right) - \frac{1}{x+1} - \psi \left( \frac{x+1}{2} \right) \right] \mathrm{d}x $

real-analysis definite-integrals improper-integrals special-functions

Prove that:$\int_{0}^{1}{x+x^2+\cdots+x^{2n}-2nx\over (1+x)\ln{x}}dx=\ln{\left[\left({2\over \pi}\right)^n(2n)!!\right]}$

integration definite-integrals

How to demonstrate the equality of these integral representations of $\pi$?

calculus integration definite-integrals improper-integrals pi

Closed form for ${\large\int}_0^\pi\frac{x\,\cos\frac x3}{\sqrt[3]{\sin x}}dx$

calculus integration trigonometry definite-integrals closed-form

Evaluate $3\int_{0}^{2\pi} \sin(t) \cos(t) \,{\rm d}t$

calculus integration definite-integrals

Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$

definite-integrals special-functions conjectures hypergeometric-function elliptic-integrals

Why the answer for double integral is coming as zero?

multivariable-calculus definite-integrals multiple-integral

How to perform integration by parts when the upper integral limit is infinity?

calculus integration definite-integrals self-learning

For what values of $\alpha$, does this integral converge? [closed]

calculus real-analysis limits convergence-divergence definite-integrals

How to find the derivative of an integral where both, the limit and the integrand, are functions of x?

integration derivatives definite-integrals

Approximation of a summation by an integral

definite-integrals summation numerical-methods approximation summation-method

How can we show that $\int_{0}^{\pi/2}x\cos(8x)\ln\left(1+\tan x\over 1-\tan x\right)\mathrm dx={\pi\over 12}?$

calculus integration definite-integrals

Evaluating $\int_0^1 \frac{1}{\sqrt{\Gamma(x)}} dx$

integration definite-integrals improper-integrals special-functions

Difficult infinite integral involving a Gaussian, Bessel function and complex singularities

integration definite-integrals special-functions bessel-functions

Superscript of an integral of a marginal probability

definite-integrals conditional-probability

Interesting integral: $I=\int_0^1 \int_0^1 \log\left( \cos(\pi x)^2 + \cos(\pi y)^2 \right)dxdy$

integration sequences-and-series multivariable-calculus definite-integrals

Some interesting integrals with dilogarithm

calculus integration complex-analysis definite-integrals special-functions