New posts in definite-integrals

Functional equation $ f(x) + f\left(1-\frac{1}{x}\right) = \tan^{-1}(x) $ and definite integral

calculus trigonometry definite-integrals functional-equations

integral involving invertible functions

integration definite-integrals

How to compute $\int_0^{\infty} \frac{\sqrt{x}}{x^2-1}\mathrm dx$

complex-analysis definite-integrals contour-integration

An integral of rational function with third power of cosine hyperbolic function

calculus integration definite-integrals contour-integration

Compute $ \int_{0}^{1}\frac{\ln(x) \ln^2 (1-x)}{x} dx $

calculus real-analysis integration definite-integrals

Evaluation of an integral involving the Lambert W function

integration special-functions definite-integrals lambert-w

How to find closed-form of $\int_{0}^{+\infty} \operatorname{sech}^2 (x^2)\,dx$

calculus integration definite-integrals improper-integrals closed-form

Prove the inequality of integral using Hölder

calculus integration inequality definite-integrals holder-inequality

Calculating half derivative of $x$ using Cauchy's repeated integral formula

integration derivatives definite-integrals gamma-function fractional-calculus

Solving $\int_0^{\infty} \ln^m(x)\sin\left(x^n\right)\:dx$

integration definite-integrals trigonometric-integrals

Integral involving hypergeometric function $\int_0^1[{}_2F_1(\frac13,\frac23;1;x^3)]^2dx$

integration definite-integrals special-functions hypergeometric-function modular-forms

Supposedly simple integral

integration definite-integrals

How can i evaluate this integral with or without using CAS $\int_0^{\infty}\frac{\mathrm dx}{(x^2+1)\cosh(\pi x)}$

calculus integration complex-analysis definite-integrals

How to evaluate the Fourier Series of $\frac{\sin(\alpha\sin(\omega t))}{\alpha\sin(\omega t)}\exp(-j\beta\sin(\omega t))$?

definite-integrals fourier-series bessel-functions

Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$ [closed]

integration complex-analysis definite-integrals

Why can $\int_{x=0}^{\infty} x\,\mathrm{e}^{-\alpha x^2}\mathrm {d}x$ not be evaluated by parts to obtain $\frac{1}{2\alpha}$?

calculus integration definite-integrals exponentiation gaussian-integral

If $ \int_0^{\pi}f(x)\cos(nx)\,dx=0$ for all $n$ then prove that $f\equiv 0$

real-analysis integration analysis definite-integrals

Compute the integral $\int_{-1}^1 \frac{|x-y|^{\alpha}}{(1 - x^2)^{\frac{1+\alpha}{2}}}dx = \frac{\pi}{\cos(\pi \alpha/2)}$

real-analysis integration definite-integrals

Complex Gaussian Integral by change of variable

integration complex-analysis definite-integrals gaussian-integral

$I_k=\int_0^1 \frac{1}{\mathbf{B}(\alpha , \beta )} \cos^k (\pi \theta) \theta^{\alpha -1} (1-\theta)^{\beta -1}d\theta $

integration sequences-and-series definite-integrals hypergeometric-function