Question

Closed form of $\begin{align}\int_{0}^{\infty}x^{1-x^{2-x^{3-...}}}dx\end{align}$.

score 415 · Answer 1 · 2026-04-14 21:43:27

415

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Closed form of $\begin{align}\int_{0}^{\infty}x^{1-x^{2-x^{3-...}}}dx\end{align}$.

Published on 14 Apr 2026 - 21:43

score 98 · Answer 2 · 2026-04-09 17:11:36

98

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Integral problem involving derangements and improper integrals

Published on 09 Apr 2026 - 17:11

score 60 · Answer 3 · 2026-04-11 05:54:16

60

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Convergence of an integral involving Bessel functions

Published on 11 Apr 2026 - 5:54

score 74 · Answer 4 · 2026-04-14 18:48:18

74

Views

If $f$ and $g$ are integrable, is $fg$ integrable?

Published on 14 Apr 2026 - 18:48

score 47 · Answer 5 · 2026-04-11 00:00:42

47

Views

Proving that two integral are equal (changing variable of integration)

Published on 11 Apr 2026 - 0:00

score 192 · Answer 6 · 2026-04-09 06:26:01

192

Views

Applying Fundamental Theorem of Calculus to improper integral

Published on 09 Apr 2026 - 6:26

score 115 · Answer 7 · 2026-04-14 21:12:49

115

Views

Doubts in $\lim_{x \to +\infty} \frac{\int_{-x}^x \frac{1}{y^2}dy}{x}$

Published on 14 Apr 2026 - 21:12

score 55 · Answer 8 · 2026-04-13 04:04:02

55

Views

An improper integral and a related volume calculation

Published on 13 Apr 2026 - 4:04

score 887 · Answer 9 · 2026-04-11 17:52:46

887

Views

Is there any method other than Feynman’s trick which can deal further with powers higher than 2?

Published on 11 Apr 2026 - 17:52

score 40 · Answer 10 · 2026-04-15 05:23:22

Is it true that if $g$ is monotone on $(0,1]$ and $\int_0^1 x^k g$ exists for some $k>-1$, then $\displaystyle\lim_{x\to0} x^{k+1} g(x)=0$?

score 64 · Answer 11 · 2026-04-10 18:53:54

64

Views

How to establish existence of an optimal control with infinite horizon?

Published on 10 Apr 2026 - 18:53

score 72 · Answer 12 · 2026-04-15 05:20:35

72

Views

Finding a closed-form of ${\frac{\sum\limits_{n=1}^{x}\frac{1}{\int_{0}^{\infty}e^{-t^{n}}dt}}{x}-1}$ and its improper integral from $1$ to $\infty$.

Published on 15 Apr 2026 - 5:20

score 347 · Answer 13 · 2026-04-14 20:22:40

347

Views

Is there a simpler method to compute $\int_0^{\infty} \frac{1}{(1+x)\left(\pi+\ln ^{2n } x\right)} d x$

Published on 14 Apr 2026 - 20:22

score 44 · Answer 14 · 2026-04-14 22:02:38

44

Views

Determine the convergence of the following improper integrals of non-negative integrands:

Published on 14 Apr 2026 - 22:02

score 262 · Answer 15 · 2023-03-31 15:57:58

262

Views

$\int_0^\infty\frac{u}{2\nu^2}\left(u+\left(u^2+\nu^2\right)^\frac{1}{2}\right)\left(e^{-u}-e^{-\left(u^2+\nu^2\right)^\frac{1}{2}}\right)\sin(ut)du$

Published on 31 Mar 2023 - 15:57

List Question

Closed form of $\begin{align}\int_{0}^{\infty}x^{1-x^{2-x^{3-...}}}dx\end{align}$.

Integral problem involving derangements and improper integrals

Convergence of an integral involving Bessel functions

If $f$ and $g$ are integrable, is $fg$ integrable?

Proving that two integral are equal (changing variable of integration)

Applying Fundamental Theorem of Calculus to improper integral

Doubts in $\lim_{x \to +\infty} \frac{\int_{-x}^x \frac{1}{y^2}dy}{x}$

An improper integral and a related volume calculation

Is there any method other than Feynman’s trick which can deal further with powers higher than 2?

Is it true that if $g$ is monotone on $(0,1]$ and $\int_0^1 x^k g$ exists for some $k>-1$, then $\displaystyle\lim_{x\to0} x^{k+1} g(x)=0$?

How to establish existence of an optimal control with infinite horizon?

Finding a closed-form of ${\frac{\sum\limits_{n=1}^{x}\frac{1}{\int_{0}^{\infty}e^{-t^{n}}dt}}{x}-1}$ and its improper integral from $1$ to $\infty$.

Is there a simpler method to compute $\int_0^{\infty} \frac{1}{(1+x)\left(\pi+\ln ^{2n } x\right)} d x$

Determine the convergence of the following improper integrals of non-negative integrands:

$\int_0^\infty\frac{u}{2\nu^2}\left(u+\left(u^2+\nu^2\right)^\frac{1}{2}\right)\left(e^{-u}-e^{-\left(u^2+\nu^2\right)^\frac{1}{2}}\right)\sin(ut)du$

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