Question

Integral $\int_0^{\infty}\cos(a_0+a_1x+a_2x^2)\frac{1}{x^2+\frac{1}{4}}dx$

score 69 · Answer 1 · 2026-04-15 01:28:58

69

Views

Integral $\int_0^{\infty}\cos(a_0+a_1x+a_2x^2)\frac{1}{x^2+\frac{1}{4}}dx$

Published on 15 Apr 2026 - 1:28

score 517 · Answer 2 · 2026-04-16 16:03:48

517

Views

$\int^\infty_0 \frac{\cos(x)}{\sqrt{x}}\,dx$ Evaluate using Fresnel Integrals

Published on 16 Apr 2026 - 16:03

score 113 · Answer 3 · 2026-04-16 02:14:02

113

Views

Need help with continuing an idea concerning showing that $4\sum\limits_{n \ge 1} a_n^2 \ge \sum\limits_{n \ge 1} \frac1{n^2}(a_1+...+a_n)^2 $

Published on 16 Apr 2026 - 2:14

score 584 · Answer 4 · 2026-04-15 09:56:28

584

Views

How to show $\int_0^{\infty} \frac{1}{\sqrt{x}}\sin({\frac{1}{x}})dx$ converges

Published on 15 Apr 2026 - 9:56

score 358 · Answer 5 · 2026-04-16 04:53:52

358

Views

Convergence testing of the improper integral $\int_{0}^{\infty}\frac{\ln x}{\sqrt{x}(x^2-1)}\ \text dx$

Published on 16 Apr 2026 - 4:53

score 271 · Answer 6 · 2026-04-15 21:43:39

271

Views

How to compute $\int_{0}^{\infty}dx\:\frac{\exp(-ax^2+bx)}{x+1}\:\text{ for }\: a>0, b\in \mathbb{C}$?

Published on 15 Apr 2026 - 21:43

score 313 · Answer 7 · 2026-04-11 10:26:11

313

Views

How to find the compound of poisson and normal distribution?

Published on 11 Apr 2026 - 10:26

score 113 · Answer 8 · 2026-04-16 06:06:21

113

Views

Prove $\int^\infty_0 \frac{\frac{1}{1+(bx)^2}-\frac{1}{1+(ax)^2}}{x}dx = \ln(\frac{a}{b})$ with Frullani Integrals

Published on 16 Apr 2026 - 6:06

score 200 · Answer 9 · 2026-04-15 23:22:40

200

Views

Prove $\int^\infty_0 b\sin(\frac{1}{bx})-a\sin(\frac{1}{ax}) \mathrm d x= -\ln(\frac{b}{a})$ using Frullani integrals

Published on 15 Apr 2026 - 23:22

score 282 · Answer 10 · 2026-04-13 21:26:18

282

Views

Integral of a Bessel function involving rational functions

Published on 13 Apr 2026 - 21:26

score 172 · Answer 11 · 2026-04-15 12:08:54

172

Views

Bounded bessel functions in an s-set projection proof

Published on 15 Apr 2026 - 12:08

score 65 · Answer 12 · 2026-04-15 13:53:15

65

Views

Justify the change of order of integration in $\int^\infty_0 (\int^1_0 e^{-ay} \sin(2bxy)dx)dy$ using a Tonelli condition

Published on 15 Apr 2026 - 13:53

score 132 · Answer 13 · 2026-04-16 08:48:17

132

Views

Computing a double integral $\int_{-\infty}^\infty\int_{-\infty}^\infty\frac{f(t)}{1+{(x+g(t))}^2}dt\ dx$

Published on 16 Apr 2026 - 8:48

score 270 · Answer 14 · 2026-04-12 05:24:59

270

Views

Integral of a Dirichlet Series

Published on 12 Apr 2026 - 5:24

score 613 · Answer 15 · 2026-04-10 04:38:29

613

Views

Which methods can be used to evaluate the following integral?

Published on 10 Apr 2026 - 4:38

List Question

Integral $\int_0^{\infty}\cos(a_0+a_1x+a_2x^2)\frac{1}{x^2+\frac{1}{4}}dx$

$\int^\infty_0 \frac{\cos(x)}{\sqrt{x}}\,dx$ Evaluate using Fresnel Integrals

Need help with continuing an idea concerning showing that $4\sum\limits_{n \ge 1} a_n^2 \ge \sum\limits_{n \ge 1} \frac1{n^2}(a_1+...+a_n)^2 $

How to show $\int_0^{\infty} \frac{1}{\sqrt{x}}\sin({\frac{1}{x}})dx$ converges

Convergence testing of the improper integral $\int_{0}^{\infty}\frac{\ln x}{\sqrt{x}(x^2-1)}\ \text dx$

How to compute $\int_{0}^{\infty}dx\:\frac{\exp(-ax^2+bx)}{x+1}\:\text{ for }\: a>0, b\in \mathbb{C}$?

How to find the compound of poisson and normal distribution?

Prove $\int^\infty_0 \frac{\frac{1}{1+(bx)^2}-\frac{1}{1+(ax)^2}}{x}dx = \ln(\frac{a}{b})$ with Frullani Integrals

Prove $\int^\infty_0 b\sin(\frac{1}{bx})-a\sin(\frac{1}{ax}) \mathrm d x= -\ln(\frac{b}{a})$ using Frullani integrals

Integral of a Bessel function involving rational functions

Bounded bessel functions in an s-set projection proof

Justify the change of order of integration in $\int^\infty_0 (\int^1_0 e^{-ay} \sin(2bxy)dx)dy$ using a Tonelli condition

Computing a double integral $\int_{-\infty}^\infty\int_{-\infty}^\infty\frac{f(t)}{1+{(x+g(t))}^2}dt\ dx$

Integral of a Dirichlet Series

Which methods can be used to evaluate the following integral?

Trending Questions

Popular # Hahtags

Popular Questions