Question

Improper definite integral $\int_0^\infty e^{-x^2}(x + k)^\alpha dx$

score 91 · Answer 1 · 2026-04-16 20:26:38

91

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Improper definite integral $\int_0^\infty e^{-x^2}(x + k)^\alpha dx$

Published on 16 Apr 2026 - 20:26

score 258 · Answer 2 · 2026-04-15 17:19:57

258

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Is there a simple proof for $\int_1^{\infty}\frac{2x^2\log^2 x}{(x^2-1)^2}dx=\frac{1}{4}(7\zeta(3)+\pi^2)$?

Published on 15 Apr 2026 - 17:19

score 192 · Answer 3 · 2026-04-16 05:45:35

192

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Closed form of $\int_{x = 0}^{C} \exp\left(-\frac{x}{A}-\frac{B}{x}\right)\,dx$

Published on 16 Apr 2026 - 5:45

score 145 · Answer 4 · 2026-03-27 00:07:59

145

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Elliptical Integral that diverges at one point

Published on 27 Mar 2026 - 0:07

score 123 · Answer 5 · 2026-04-15 22:37:04

123

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Prove that $\int_{2}^{\infty} \frac{dx}{x^{1-\epsilon}\cdot \ln(x)^{\beta}}$ diverges for every $\beta$.

Published on 15 Apr 2026 - 22:37

score 66 · Answer 6 · 2026-04-15 07:34:26

66

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Improper integral of $\frac{1}{x} \sin \frac{1}{x}$

Published on 15 Apr 2026 - 7:34

score 129 · Answer 7 · 2026-04-09 11:44:30

129

Views

Uniformly boundedness of an oscillatory integral

Published on 09 Apr 2026 - 11:44

score 100 · Answer 8 · 2026-04-14 10:32:14

100

Views

How to prove that: $\int_{0}^{\infty} \frac {1}{\frac 1 2(e^x-e^{-x} )\cdot x} dx$ Diverges.

Published on 14 Apr 2026 - 10:32

score 1.4k · Answer 9 · 2026-04-05 22:20:13

1.4k

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Proof that $ \int_0^\infty x^{d-4}\sin x\, dx = \cos \frac{\pi d}{2} \Gamma(d-3)$, for $2<\Re(d)<4 $?

Published on 05 Apr 2026 - 22:20

score 567 · Answer 10 · 2026-04-15 07:48:42

567

Views

Is the integral $\int e^{2 \pi i z^2} dz$ uniformly bounded for any interval of $\mathbb{R}$?

Published on 15 Apr 2026 - 7:48

score 1k · Answer 11 · 2026-04-14 21:45:33

1k

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Comparing the Indefinite Integrals Convergence for $1/x$ and $1/x^{2}$ between 1 and $\infty$.

Published on 14 Apr 2026 - 21:45

score 1.3k · Answer 12 · 2026-04-13 11:44:54

1.3k

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Integral of Lorentzian type with trigonometric function

Published on 13 Apr 2026 - 11:44

score 84 · Answer 13 · 2026-04-11 20:04:24

84

Views

Value of integral

Published on 11 Apr 2026 - 20:04

score 109 · Answer 14 · 2026-03-31 09:41:41

109

Views

Contour integral to real integral: find suitable change of variables

Published on 31 Mar 2026 - 9:41

score 89 · Answer 15 · 2026-04-14 09:40:06

89

Views

For which $a>0$ does $\int_a^\infty \frac{\mathrm{d}x}{(x^2-a)^{4a}}$ converge?

Published on 14 Apr 2026 - 9:40

List Question

Improper definite integral $\int_0^\infty e^{-x^2}(x + k)^\alpha dx$

Is there a simple proof for $\int_1^{\infty}\frac{2x^2\log^2 x}{(x^2-1)^2}dx=\frac{1}{4}(7\zeta(3)+\pi^2)$?

Closed form of $\int_{x = 0}^{C} \exp\left(-\frac{x}{A}-\frac{B}{x}\right)\,dx$

Elliptical Integral that diverges at one point

Prove that $\int_{2}^{\infty} \frac{dx}{x^{1-\epsilon}\cdot \ln(x)^{\beta}}$ diverges for every $\beta$.

Improper integral of $\frac{1}{x} \sin \frac{1}{x}$

Uniformly boundedness of an oscillatory integral

How to prove that: $\int_{0}^{\infty} \frac {1}{\frac 1 2(e^x-e^{-x} )\cdot x} dx$ Diverges.

Proof that $ \int_0^\infty x^{d-4}\sin x\, dx = \cos \frac{\pi d}{2} \Gamma(d-3)$, for $2<\Re(d)<4 $?

Is the integral $\int e^{2 \pi i z^2} dz$ uniformly bounded for any interval of $\mathbb{R}$?

Comparing the Indefinite Integrals Convergence for $1/x$ and $1/x^{2}$ between 1 and $\infty$.

Integral of Lorentzian type with trigonometric function

Value of integral

Contour integral to real integral: find suitable change of variables

For which $a>0$ does $\int_a^\infty \frac{\mathrm{d}x}{(x^2-a)^{4a}}$ converge?

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