Question

How to prove: $\lim_{y\to\infty}\int_{1}^{\infty}\frac{f(x)}{x^2+y^2}dx=0 $

score 413 · Answer 1 · 2026-04-13 20:44:32

413

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How to prove: $\lim_{y\to\infty}\int_{1}^{\infty}\frac{f(x)}{x^2+y^2}dx=0 $

Published on 13 Apr 2026 - 20:44

score 601 · Answer 2 · 2026-04-16 20:53:59

601

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Evaluate the improper integral $\int_{-\infty}^{+\infty} \frac{\ln(1+x^{4})}{1+x^{2}} dx$

Published on 16 Apr 2026 - 20:53

score 66 · Answer 3 · 2026-04-16 14:45:13

66

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Compute the integral $ \int_0^\infty e^{-u^\ell} u^m du $

Published on 16 Apr 2026 - 14:45

score 219 · Answer 4 · 2026-04-15 03:03:13

219

Views

How to compute $\int_0^\infty \frac1{(x+a)(\ln^2x+4\pi^2)}dx$

Published on 15 Apr 2026 - 3:03

score 72 · Answer 5 · 2026-04-15 16:39:57

72

Views

Compute the integral $\int_0^\infty t^{3/\xi-1} e^{-t} \Gamma(\frac{2}{\xi},t) \ dt$

Published on 15 Apr 2026 - 16:39

score 145 · Answer 6 · 2026-04-16 08:56:51

145

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Definite integral $\int_{0}^{+\infty} \exp(-\sqrt{x^2+bx+c}) dx$

Published on 16 Apr 2026 - 8:56

score 389 · Answer 7 · 2026-04-11 08:33:56

389

Views

About a sequence of (improper) integrals.

Published on 11 Apr 2026 - 8:33

score 113 · Answer 8 · 2026-03-25 17:40:39

113

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How to calculate $\int_{-\infty}^{\infty}\frac{\cos^{3}x}{x^2+1}\mathrm{d}x$ with the help of complex function?

Published on 25 Mar 2026 - 17:40

score 487 · Answer 9 · 2026-04-16 01:57:57

487

Views

Evaluate : $\int_0^{\frac{\pi}{2}} \frac{\ln(\sec ^2 x)\sec^2x }{(\sec ^2 x+1)\tan x}\mathrm dx$

Published on 16 Apr 2026 - 1:57

score 211 · Answer 10 · 2026-04-16 12:02:25

211

Views

Calculate $\int_0^\infty \frac{\ln(t)}{1+t^3}dt$

Published on 16 Apr 2026 - 12:02

score 53 · Answer 11 · 2026-04-13 20:52:31

53

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Does $\int_{0}\limits^{\infty}\prod\limits_{k=1}^{x}\frac{\prod\limits_{n=1}^{k}\frac{\lceil k+n\rceil}{\lfloor k+n\rfloor}}{2}dx=\frac{3}{2}$?

Published on 13 Apr 2026 - 20:52

score 1.1k · Answer 12 · 2026-04-16 10:28:22

1.1k

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Evaluate series: $\sum_{k=1}^\infty (-1)^k\left[ k\ln\left(\frac{k^4+2k^3+k^2}{k^4+2k^3+3k^2+2k+2}\right)+\ln\frac{k^2+2k+1}{k^2+1} \right]$

Published on 16 Apr 2026 - 10:28

score 64 · Answer 13 · 2026-04-13 18:55:33

64

Views

Divergent improper integral

Published on 13 Apr 2026 - 18:55

score 542 · Answer 14 · 2026-04-09 13:06:53

542

Views

A way to justify interchanging a summation and integration

Published on 09 Apr 2026 - 13:06

score 114 · Answer 15 · 2026-04-15 21:19:05

114

Views

For which $\alpha$, integral $\int_0^{\infty}\frac{\arctan{x}-x}{x^\alpha}dx$ converges

Published on 15 Apr 2026 - 21:19

List Question

How to prove: $\lim_{y\to\infty}\int_{1}^{\infty}\frac{f(x)}{x^2+y^2}dx=0 $

Evaluate the improper integral $\int_{-\infty}^{+\infty} \frac{\ln(1+x^{4})}{1+x^{2}} dx$

Compute the integral $ \int_0^\infty e^{-u^\ell} u^m du $

How to compute $\int_0^\infty \frac1{(x+a)(\ln^2x+4\pi^2)}dx$

Compute the integral $\int_0^\infty t^{3/\xi-1} e^{-t} \Gamma(\frac{2}{\xi},t) \ dt$

Definite integral $\int_{0}^{+\infty} \exp(-\sqrt{x^2+bx+c}) dx$

About a sequence of (improper) integrals.

How to calculate $\int_{-\infty}^{\infty}\frac{\cos^{3}x}{x^2+1}\mathrm{d}x$ with the help of complex function?

Evaluate : $\int_0^{\frac{\pi}{2}} \frac{\ln(\sec ^2 x)\sec^2x }{(\sec ^2 x+1)\tan x}\mathrm dx$

Calculate $\int_0^\infty \frac{\ln(t)}{1+t^3}dt$

Does $\int_{0}\limits^{\infty}\prod\limits_{k=1}^{x}\frac{\prod\limits_{n=1}^{k}\frac{\lceil k+n\rceil}{\lfloor k+n\rfloor}}{2}dx=\frac{3}{2}$?

Evaluate series: $\sum_{k=1}^\infty (-1)^k\left[ k\ln\left(\frac{k^4+2k^3+k^2}{k^4+2k^3+3k^2+2k+2}\right)+\ln\frac{k^2+2k+1}{k^2+1} \right]$

Divergent improper integral

A way to justify interchanging a summation and integration

For which $\alpha$, integral $\int_0^{\infty}\frac{\arctan{x}-x}{x^\alpha}dx$ converges

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