New posts in definite-integrals

Is there a non-trivial definite integral that values to $\frac{e}{\pi}$?

integration definite-integrals constants

Bound on integral

definite-integrals

Using the residue theorem, calculate $\int_{0}^{2\pi}\frac{1}{1-2a\cos{\theta}+a^2}d\theta$

complex-analysis definite-integrals

Integral $\int_{\sqrt{33}}^\infty\frac{dx}{\sqrt{x^3-11x^2+11x+121}}$

integration definite-integrals elliptic-integrals

Proof of Cauchy's Beta Integral $\int_{-\infty}^\infty \frac{dt}{(1+it)^x(1-it)^y}$

calculus complex-analysis integration definite-integrals improper-integrals

The Laplace transform of $\frac{\ln(1+at)}{1+t}$

integration definite-integrals special-functions laplace-transform

Definite Integral of $e^{ax+bx^c}$

definite-integrals improper-integrals

How do I prove $\int_{-\infty}^{\infty}{\cos(x+a)\over (x+b)^2+1}dx={\pi\over e}{\cos(a-b)}$?

integration definite-integrals contour-integration

$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$

integration definite-integrals

Compute this following integral without Fourier series : $\int_0^{\pi/4}x\ln(\tan x)dx$

integration definite-integrals closed-form polylogarithm catalans-constant

How can we prove that $8\int_{0}^{\infty}{\ln x\over x}\left(e^{-x}-{1\over \sqrt[4]{1+8x}}\right)\mathrm dx=-32C+4\gamma^2-5\pi^2?$

calculus integration definite-integrals

Derivative of a constant is not zero

integration derivatives definite-integrals

Sum=Integral? Find $m$ so that $\sum _{n=1}^{\infty } \frac{n^m}{e^{2 \pi n}-1}=\int_0^{\infty } \frac{x^m}{e^{2 \pi x}-1} \, dx$

sequences-and-series definite-integrals special-functions

Log integrals IV

integration definite-integrals logarithms

Closed-forms of the integrals $\int_0^1 K(\sqrt{k})^2 \, dk$, $\int_0^1 E(\sqrt{k})^2 \, dk$ and $\int_0^1 K(\sqrt{k}) E(\sqrt{k}) \, dk$

calculus integration definite-integrals closed-form elliptic-integrals

How to evaluate $\int_0^1\frac{\ln(1-2t+2t^2)}{t}dt$?

calculus integration definite-integrals

How do you Evaluate $\int_{-\infty}^\infty \frac{\cos(x)}{x^2+1}dx$ Without Using Residue Calculus

calculus integration definite-integrals improper-integrals

Evaluate $\int_{-1}^1 \frac{x^2e^{\arctan x}}{\sqrt{{1+x^2}}}\ \mathrm{d}x$

calculus definite-integrals indefinite-integrals

$ \int_1^2\int_1^2 \int_1^2 \int_1^2 \frac{x_1+x_2+x_3-x_4}{x_1+x_2+x_3+x_4}dx_1dx_2dx_3dx_4 $

calculus integration multivariable-calculus definite-integrals

Compute $\int_0^\infty \frac{dx}{1+x^3}$

calculus integration definite-integrals