Question

Find $\int_{0}^{\infty }\frac{\cos x-\cos x^2}{x}\mathrm dx$

score 577 · Answer 1 · 2017-01-16 03:59:37

577

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Find $\int_{0}^{\infty }\frac{\cos x-\cos x^2}{x}\mathrm dx$

Published on 16 Jan 2017 - 3:59

score 342 · Answer 2 · 2026-04-07 08:22:08

342

Views

Integrate $\int _0^{\infty }\frac{\sqrt[3]{x}}{x^2+1\:}\:dx$

Published on 07 Apr 2026 - 8:22

score 279 · Answer 3 · 2017-01-16 15:00:28

279

Views

Determine whether the improper integral $\int_0^{\infty} \sin(x) \sin(x^2) dx$ is convergent or divergent?

Published on 16 Jan 2017 - 15:00

score 208 · Answer 4 · 2026-04-11 22:55:49

208

Views

Conditions for absolute convergence of a series?

Published on 11 Apr 2026 - 22:55

score 956 · Answer 5 · 2026-03-26 10:53:47

956

Views

Real Analysis Methodologies to show $\gamma =2\int_0^\infty \frac{\cos(x^2)-\cos(x)}{x}\,dx$

Published on 26 Mar 2026 - 10:53

score 445 · Answer 6 · 2026-04-12 08:41:18

445

Views

Integral with residue theorem, zero or does not exist?

Published on 12 Apr 2026 - 8:41

score 480 · Answer 7 · 2026-03-25 22:05:07

480

Views

Mathematica gives: $\int_{0}^{\infty}{\cos(x^n)-\cos(x^{2n})\over x}\cdot{\ln{x}}\mathrm dx={12\gamma^2-\pi^2\over 2(4n)^2}$

Published on 25 Mar 2026 - 22:05

score 303 · Answer 8 · 2017-01-17 12:17:52

303

Views

Show us how to prove that $\int_{0}^{\infty}{\sin(e^{-\gamma}x)}\cdot{\ln{x}\over x}\mathrm dx=0$

Published on 17 Jan 2017 - 12:17

score 83 · Answer 9 · 2026-04-10 15:23:56

83

Views

Can the following improper integral be seen as a Lebesgue integral?

Published on 10 Apr 2026 - 15:23

score 36 · Answer 10 · 2026-04-12 02:43:14

36

Views

Doubt: It says here the integral exists only if the power to x is less than one, how so?

Published on 12 Apr 2026 - 2:43

score 931 · Answer 11 · 2026-04-02 09:12:50

931

Views

Computing the integral $\int_0 ^{\infty} t^{3/2}e^{-t}dt$

Published on 02 Apr 2026 - 9:12

score 232 · Answer 12 · 2026-03-26 21:12:47

232

Views

Closed form expression of $\int_{-\infty}^{+\infty}dx \exp[-\alpha(x^2-a^2)^2]$

Published on 26 Mar 2026 - 21:12

score 75 · Answer 13 · 2017-01-18 15:16:45

75

Views

Integral where limit of bounds both goes to infinity

Published on 18 Jan 2017 - 15:16

score 63 · Answer 14 · 2026-04-11 16:46:08

63

Views

How to construct a function of two variable non integrable on a stripe

Published on 11 Apr 2026 - 16:46

score 98 · Answer 15 · 2026-04-12 07:37:01

98

Views

This Improper integral triggers me

Published on 12 Apr 2026 - 7:37

List Question

Find $\int_{0}^{\infty }\frac{\cos x-\cos x^2}{x}\mathrm dx$

Integrate $\int _0^{\infty }\frac{\sqrt[3]{x}}{x^2+1\:}\:dx$

Determine whether the improper integral $\int_0^{\infty} \sin(x) \sin(x^2) dx$ is convergent or divergent?

Conditions for absolute convergence of a series?

Real Analysis Methodologies to show $\gamma =2\int_0^\infty \frac{\cos(x^2)-\cos(x)}{x}\,dx$

Integral with residue theorem, zero or does not exist?

Mathematica gives: $\int_{0}^{\infty}{\cos(x^n)-\cos(x^{2n})\over x}\cdot{\ln{x}}\mathrm dx={12\gamma^2-\pi^2\over 2(4n)^2}$

Show us how to prove that $\int_{0}^{\infty}{\sin(e^{-\gamma}x)}\cdot{\ln{x}\over x}\mathrm dx=0$

Can the following improper integral be seen as a Lebesgue integral?

Doubt: It says here the integral exists only if the power to x is less than one, how so?

Computing the integral $\int_0 ^{\infty} t^{3/2}e^{-t}dt$

Closed form expression of $\int_{-\infty}^{+\infty}dx \exp[-\alpha(x^2-a^2)^2]$

Integral where limit of bounds both goes to infinity

How to construct a function of two variable non integrable on a stripe

This Improper integral triggers me

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