New posts in definite-integrals

periodic function antiderivative

calculus integration derivatives definite-integrals solution-verification

Evaluating a double integral by using $\int\arctan (1+\sin 2t)\ dt/(1+\sin 2t)$

calculus integration multivariable-calculus definite-integrals

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

definite-integrals closed-form gamma-function bessel-functions elliptic-integrals

Solving the integral $\int_{0}^{1} d{v} \frac{e^{-y^2(1+v^2)}}{1+v^2}e^{\frac{2 t v^2}{v^2+1}}$

calculus integration definite-integrals error-function

Closed-form expression for an iterated integral

integration multivariable-calculus definite-integrals hypergeometric-function elliptic-integrals

How to find this integral $I=\int_{0}^{+\infty}\frac{\{t\}(\{t\}-1)}{1+t^2}dx$?

integration definite-integrals improper-integrals

Area interpretation of integrals

calculus integration definite-integrals area

Nontrivial integral representations for $e$

definite-integrals exponential-function

The integral of an elliptic integral: $\int_{0}^{1}\frac{x\mathbf{K}^2\left ( x \right )}{\sqrt{1-x^{2}}}\mathrm{d}x$

calculus integration definite-integrals hypergeometric-function elliptic-integrals

How would you prove $\int^8_0\frac1{\sqrt{x+\frac1{\sqrt{x}}}}dx<4-\frac1{2019}$?

calculus integration inequality definite-integrals nested-radicals

How to evaluate$J(k) = \int_{0}^{1} \frac{\ln^2x\ln\left ( \frac{1-x}{1+x} \right ) }{(x-1)^2-k^2(x+1)^2}\text{d}x$

integration definite-integrals logarithms contour-integration polylogarithm

When a change of variable results in equal limits of integration

calculus integration definite-integrals

How do you evaluate $\int_{0}^{\frac{\pi}{2}} \frac{(\sec x)^{\frac{1}{3}}}{(\sec x)^{\frac{1}{3}}+(\tan x)^{\frac{1}{3}}} \, dx ?$

calculus integration definite-integrals contest-math

Integral of Hermite polynomial multiplied by $\exp(-x^2/2)$

integration special-functions definite-integrals orthogonal-polynomials

Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$

calculus real-analysis integration analysis definite-integrals

Closed forms of Nielsen polylogarithms $\int_0^1\frac{(\ln t)^{n-1}(\ln(1-z\,t))^p}{t}dt$?

integration definite-integrals closed-form big-list polylogarithm

Proving $\int _{-\pi }^{\pi }\int _{-\pi }^{\pi }\int _{-\pi }^{\pi }\log \left| 1+e^{i x}+e^{i y}+e^{i z}\right| dxdydz=28 \pi \zeta (3)$

integration definite-integrals

Is there an integral for $\frac{\pi}{\mathrm{G}}$?

integration definite-integrals pi constants catalans-constant

$\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$

definite-integrals

Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

integration definite-integrals contour-integration closed-form complex-integration