Question

Compute $ I(n) = \int^{+\infty}_{-\infty} \frac{e^{n x}}{1+e^x}\, dx$

score 225 · Answer 1 · 2026-04-16 19:49:37

225

Views

Compute $ I(n) = \int^{+\infty}_{-\infty} \frac{e^{n x}}{1+e^x}\, dx$

Published on 16 Apr 2026 - 19:49

score 4.1k · Answer 2 · 2026-04-16 16:52:38

4.1k

Views

Integral $\int_0^\infty\frac{\operatorname{arccot}\left(\sqrt{x}-2\,\sqrt{x+1}\right)}{x+1}\mathrm dx$

Published on 16 Apr 2026 - 16:52

score 23 · Answer 3 · 2026-04-12 06:56:32

23

Views

question about the convergence of a function

Published on 12 Apr 2026 - 6:56

score 815 · Answer 4 · 2026-04-14 00:34:58

815

Views

Can we simplify $\int_{0}^{\infty}\frac{{\sin}^px}{x^q}dx$?

Published on 14 Apr 2026 - 0:34

score 215 · Answer 5 · 2026-04-17 03:22:42

215

Views

Integral from $0$ to $\infty$ of $\frac{1}{3}\ln\left(\frac{x+1}{\sqrt{x^2-x+1}}\right)+\frac{1}{\sqrt 3}\arctan \left(\frac{2x-1}{\sqrt 3} \right)$

Published on 17 Apr 2026 - 3:22

score 119 · Answer 6 · 2026-04-15 09:35:14

119

Views

Prove that the improper integrals are equal

Published on 15 Apr 2026 - 9:35

score 1.7k · Answer 7 · 2026-04-16 18:03:27

1.7k

Views

Calculate $\int_{0}^{\infty}\frac{\arctan(x)}{(1+x^2)^{3/2}}dx$ or show that it diverges

Published on 16 Apr 2026 - 18:03

score 1.5k · Answer 8 · 2026-04-14 03:35:01

1.5k

Views

How to tell if an integral can be integrated (has an elementary anti-derivative)?

Published on 14 Apr 2026 - 3:35

score 2k · Answer 9 · 2026-04-15 20:22:31

2k

Views

Prove that if $\int f^2$ and $\int( f'')^2$ converge, so does $\int (f')^2$

Published on 15 Apr 2026 - 20:22

score 1.6k · Answer 10 · 2026-04-13 08:52:14

1.6k

Views

How to prove this integration is finite

Published on 13 Apr 2026 - 8:52

score 2.9k · Answer 11 · 2026-04-16 11:10:01

2.9k

Views

For monotonic $f$: if the improper integral $\int_0^\infty f(x)dx$ converges, then $\lim_{x\to \infty}xf(x)=0$

Published on 16 Apr 2026 - 11:10

score 343 · Answer 12 · 2026-04-16 22:04:43

343

Views

Evaluate $\int_{-\infty}^\infty x\exp(-x^2/2)\sin(\xi x)\ \mathrm dx$

Published on 16 Apr 2026 - 22:04

score 44 · Answer 13 · 2026-04-16 14:03:26

44

Views

Anti-derivative of a function involving exponentially distributed variable

Published on 16 Apr 2026 - 14:03

score 222 · Answer 14 · 2026-04-16 10:21:22

222

Views

Does the integral $\int _0^\infty \frac 1{1+(x \cos x)^2}\,dx$ converge?

Published on 16 Apr 2026 - 10:21

score 70 · Answer 15 · 2026-04-11 19:52:57

70

Views

Numerical instable integrals

Published on 11 Apr 2026 - 19:52

List Question

Compute $ I(n) = \int^{+\infty}_{-\infty} \frac{e^{n x}}{1+e^x}\, dx$

Integral $\int_0^\infty\frac{\operatorname{arccot}\left(\sqrt{x}-2\,\sqrt{x+1}\right)}{x+1}\mathrm dx$

question about the convergence of a function

Can we simplify $\int_{0}^{\infty}\frac{{\sin}^px}{x^q}dx$?

Integral from $0$ to $\infty$ of $\frac{1}{3}\ln\left(\frac{x+1}{\sqrt{x^2-x+1}}\right)+\frac{1}{\sqrt 3}\arctan \left(\frac{2x-1}{\sqrt 3} \right)$

Prove that the improper integrals are equal

Calculate $\int_{0}^{\infty}\frac{\arctan(x)}{(1+x^2)^{3/2}}dx$ or show that it diverges

How to tell if an integral can be integrated (has an elementary anti-derivative)?

Prove that if $\int f^2$ and $\int( f'')^2$ converge, so does $\int (f')^2$

How to prove this integration is finite

For monotonic $f$: if the improper integral $\int_0^\infty f(x)dx$ converges, then $\lim_{x\to \infty}xf(x)=0$

Evaluate $\int_{-\infty}^\infty x\exp(-x^2/2)\sin(\xi x)\ \mathrm dx$

Anti-derivative of a function involving exponentially distributed variable

Does the integral $\int _0^\infty \frac 1{1+(x \cos x)^2}\,dx$ converge?

Numerical instable integrals

Trending Questions

Popular # Hahtags

Popular Questions