Question

Closed form of an improper integral to solve the period of a dynamical system

score 259 · Answer 1 · 2026-03-25 01:18:24

259

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Closed form of an improper integral to solve the period of a dynamical system

Published on 25 Mar 2026 - 1:18

score 646 · Answer 2 · 2018-12-14 02:24:46

646

Views

$\int_0^\infty e^{-x}x^{n-1}dx$ is convergent for $n>0$

Published on 14 Dec 2018 - 2:24

score 112 · Answer 3 · 2018-12-14 04:06:17

112

Views

Convergence of $\int_0^\infty \sin(x^m)/x^n dx$

Published on 14 Dec 2018 - 4:06

score 261 · Answer 4 · 2018-12-14 14:29:43

261

Views

Is this a correct proof for convergence of Gamma Function

Published on 14 Dec 2018 - 14:29

score 191 · Answer 5 · 2026-03-25 10:56:53

191

Views

How to prove $\int_{-\infty}^{+\infty} \frac{x^2}{\cosh(x)^2} dx = \frac{\pi^2}{6}$?

Published on 25 Mar 2026 - 10:56

score 582 · Answer 6 · 2026-03-26 13:51:32

582

Views

$\int_{-\infty}^{\infty}\frac{\mathrm{d}x}{ax^2+bx+c}=\pi$ similar identities

Published on 26 Mar 2026 - 13:51

score 57 · Answer 7 · 2026-03-25 23:42:45

Does this integral converge? $\int \frac{d^2x}{(2\pi)^2} \frac{d^2y}{(2\pi)^2} [\dots] \exp [- \frac{1}{4\pi i}(x_1^2 - y_1^2)+(x_2^2- y_2^2)] $

score 290 · Answer 8 · 2026-03-26 16:09:48

290

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On $\int_0^\infty \frac{\exp(-x^2)}{1+x^2}dx=\frac{\pi e}2\text{erfc}(1)$

Published on 26 Mar 2026 - 16:09

score 162 · Answer 9 · 2018-12-17 21:49:55

162

Views

when does $\int_{0}^{\infty}\frac{\sin(t)}{(t+1)^\alpha}dt$ converge?

Published on 17 Dec 2018 - 21:49

score 63 · Answer 10 · 2018-12-17 22:53:03

63

Views

Evaluating $I(s)=\int_0^{\frac{\pi}{2}}\ln(1+s\tan(\theta))\cot(\theta)d\theta$

Published on 17 Dec 2018 - 22:53

score 273 · Answer 11 · 2026-03-28 06:22:48

273

Views

Calculate $\int_{-\infty}^\infty \frac{e^{-x^2}}{x^2+a^2}\ dx$.

Published on 28 Mar 2026 - 6:22

score 138 · Answer 12 · 2018-12-18 12:09:38

138

Views

My math prof does not have a proof for this: Existence of improper integrals for $\lim_{k\to \infty} \int_{a_k}^{b_k} f(x)\,\mathrm{d}x=\alpha$

Published on 18 Dec 2018 - 12:09

score 628 · Answer 13 · 2018-12-18 13:25:21

628

Views

Improper Integral of $\log(x)$

Published on 18 Dec 2018 - 13:25

score 1.4k · Answer 14 · 2026-03-26 01:35:03

1.4k

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Solving $\int\limits_{-\infty}^\infty \frac{1}{x^8+1}dx$ through Glasser's Master Theorem

Published on 26 Mar 2026 - 1:35

score 86 · Answer 15 · 2026-03-25 04:41:20

86

Views

Methods on finding closed form of $\int_0^\infty x^{s-1}e^{-a(x+\frac{1}{x})}dx$

Published on 25 Mar 2026 - 4:41

List Question

Closed form of an improper integral to solve the period of a dynamical system

$\int_0^\infty e^{-x}x^{n-1}dx$ is convergent for $n>0$

Convergence of $\int_0^\infty \sin(x^m)/x^n dx$

Is this a correct proof for convergence of Gamma Function

How to prove $\int_{-\infty}^{+\infty} \frac{x^2}{\cosh(x)^2} dx = \frac{\pi^2}{6}$?

$\int_{-\infty}^{\infty}\frac{\mathrm{d}x}{ax^2+bx+c}=\pi$ similar identities

Does this integral converge? $\int \frac{d^2x}{(2\pi)^2} \frac{d^2y}{(2\pi)^2} [\dots] \exp [- \frac{1}{4\pi i}(x_1^2 - y_1^2)+(x_2^2- y_2^2)] $

On $\int_0^\infty \frac{\exp(-x^2)}{1+x^2}dx=\frac{\pi e}2\text{erfc}(1)$

when does $\int_{0}^{\infty}\frac{\sin(t)}{(t+1)^\alpha}dt$ converge?

Evaluating $I(s)=\int_0^{\frac{\pi}{2}}\ln(1+s\tan(\theta))\cot(\theta)d\theta$

Calculate $\int_{-\infty}^\infty \frac{e^{-x^2}}{x^2+a^2}\ dx$.

My math prof does not have a proof for this: Existence of improper integrals for $\lim_{k\to \infty} \int_{a_k}^{b_k} f(x)\,\mathrm{d}x=\alpha$

Improper Integral of $\log(x)$

Solving $\int\limits_{-\infty}^\infty \frac{1}{x^8+1}dx$ through Glasser's Master Theorem

Methods on finding closed form of $\int_0^\infty x^{s-1}e^{-a(x+\frac{1}{x})}dx$

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