Question

Improper Integral: $\int_{-\infty}^{\infty}\frac{\log(1+x^4)}{x^4}dx$

score 317 · Answer 1 · 2026-04-16 23:57:37

317

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Improper Integral: $\int_{-\infty}^{\infty}\frac{\log(1+x^4)}{x^4}dx$

Published on 16 Apr 2026 - 23:57

score 184 · Answer 2 · 2026-04-15 03:07:34

184

Views

Improper integral $\int_0^{\infty}\frac{x^{k-1}}{1+x^n}dx$

Published on 15 Apr 2026 - 3:07

score 81 · Answer 3 · 2026-04-09 10:17:48

81

Views

How to integrate this integral,

Published on 09 Apr 2026 - 10:17

score 436 · Answer 4 · 2026-04-13 01:07:23

436

Views

Integral from zero to infinity of $\int_0^{\infty}\frac{(1-e^{-\lambda z})}{\lambda^{a+1}} d \lambda$

Published on 13 Apr 2026 - 1:07

score 1.4k · Answer 5 · 2026-04-15 03:03:31

1.4k

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How to compute the integral $\int_{-\infty}^\infty e^{-x^2}\,dx$?

Published on 15 Apr 2026 - 3:03

score 2.6k · Answer 6 · 2026-04-15 06:46:12

2.6k

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Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$

Published on 15 Apr 2026 - 6:46

score 272 · Answer 7 · 2026-04-14 22:52:28

272

Views

For which values $a$ does the improper integral $\int_0^{\infty}\frac{\ln(1+x^2)}{x^a}dx$ converge

Published on 14 Apr 2026 - 22:52

score 217 · Answer 8 · 2026-04-15 03:15:44

Prove $\frac{\sqrt\pi z^v}{2^v~\Gamma\left(v+\frac{1}{2}\right)}\int_0^\infty e^{-z\cosh t}\sinh^{2v}t~dt=\int_0^\infty e^{-z\cosh t}\cosh vt~dt$?

score 3k · Answer 9 · 2026-04-17 06:54:21

3k

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Integral $\int_0^\infty\frac{1}{x\,\sqrt{2}+\sqrt{2\,x^2+1}}\cdot\frac{\log x}{\sqrt{x^2+1}}\mathrm dx$

Published on 17 Apr 2026 - 6:54

score 55 · Answer 10 · 2026-04-11 00:51:39

55

Views

Convergence of a integral

Published on 11 Apr 2026 - 0:51

score 600 · Answer 11 · 2026-04-15 07:14:46

600

Views

Evaluate an Integral involving Gaussian divided by square root of a quartic polynomial

Published on 15 Apr 2026 - 7:14

score 294 · Answer 12 · 2026-04-15 16:40:30

294

Views

Proving $\int_a^b \frac {x dx}{\sqrt{(x^2-a^2)(b^2-x^2)}} = \frac {\pi}{2} $

Published on 15 Apr 2026 - 16:40

score 60 · Answer 13 · 2026-04-14 23:40:03

60

Views

proving converge of an improper integral via riemann

Published on 14 Apr 2026 - 23:40

score 612 · Answer 14 · 2026-04-16 23:15:10

612

Views

Convergence or divergence of integral $\int_1^\infty \frac{x \sin x}{\sqrt{1+x^5}}dx$

Published on 16 Apr 2026 - 23:15

score 815 · Answer 15 · 2026-04-14 19:55:54

815

Views

A closed form for $\int_0^\infty\ln x\cdot\ln\left(1+\frac1{2\cosh x}\right)dx$

Published on 14 Apr 2026 - 19:55

List Question

Improper Integral: $\int_{-\infty}^{\infty}\frac{\log(1+x^4)}{x^4}dx$

Improper integral $\int_0^{\infty}\frac{x^{k-1}}{1+x^n}dx$

How to integrate this integral,

Integral from zero to infinity of $\int_0^{\infty}\frac{(1-e^{-\lambda z})}{\lambda^{a+1}} d \lambda$

How to compute the integral $\int_{-\infty}^\infty e^{-x^2}\,dx$?

Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$

For which values $a$ does the improper integral $\int_0^{\infty}\frac{\ln(1+x^2)}{x^a}dx$ converge

Prove $\frac{\sqrt\pi z^v}{2^v~\Gamma\left(v+\frac{1}{2}\right)}\int_0^\infty e^{-z\cosh t}\sinh^{2v}t~dt=\int_0^\infty e^{-z\cosh t}\cosh vt~dt$?

Integral $\int_0^\infty\frac{1}{x\,\sqrt{2}+\sqrt{2\,x^2+1}}\cdot\frac{\log x}{\sqrt{x^2+1}}\mathrm dx$

Convergence of a integral

Evaluate an Integral involving Gaussian divided by square root of a quartic polynomial

Proving $\int_a^b \frac {x dx}{\sqrt{(x^2-a^2)(b^2-x^2)}} = \frac {\pi}{2} $

proving converge of an improper integral via riemann

Convergence or divergence of integral $\int_1^\infty \frac{x \sin x}{\sqrt{1+x^5}}dx$

A closed form for $\int_0^\infty\ln x\cdot\ln\left(1+\frac1{2\cosh x}\right)dx$

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