Question

Convergence/Divergence of $\int_0^{+\infty} {\frac {\sin x}{x\ln^2 (x^2+2)}} \mathrm{d}x$

score 79 · Answer 1 · 2019-01-13 14:25:42

79

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Convergence/Divergence of $\int_0^{+\infty} {\frac {\sin x}{x\ln^2 (x^2+2)}} \mathrm{d}x$

Published on 13 Jan 2019 - 14:25

score 75 · Answer 2 · 2019-01-14 12:41:54

75

Views

$ \int_0^{+\infty} \frac{1}{(1+x^2)(1+x^{\phi})}\, dx \, \, \, (\phi>0) $

Published on 14 Jan 2019 - 12:41

score 502 · Answer 3 · 2019-01-17 03:58:57

502

Views

Show the function is in $L^2(\mathbb{R})$

Published on 17 Jan 2019 - 3:58

score 58 · Answer 4 · 2026-03-27 06:08:17

58

Views

Logical mistake in a proof of Dirichlet's test

Published on 27 Mar 2026 - 6:08

score 65 · Answer 5 · 2019-01-17 13:57:55

65

Views

Proof that $\int_{0}^{1}\frac{1}{x-\ln(x)}\mathbb{d}x$ is convergent.

Published on 17 Jan 2019 - 13:57

score 2.4k · Answer 6 · 2019-01-18 03:38:28

2.4k

Views

Convergence for improper integral $\int_0^\infty x^re^{-x} \,dx$

Published on 18 Jan 2019 - 3:38

score 220 · Answer 7 · 2019-01-18 16:37:04

Does there exist the limit at infinity of a function $f:[1,+\infty)\to[0,+\infty)$ such that $\int_{1}^{+\infty}f(x)dx$ is convergent.

score 126 · Answer 8 · 2019-01-19 20:53:42

126

Views

Calculate $\int\limits_{-\infty}^{\infty}\frac{\sin^2(x)\cos(wx)}{x^2}dx$ using complex analysis technique

Published on 19 Jan 2019 - 20:53

score 70 · Answer 9 · 2019-01-19 23:29:32

70

Views

For which values of $\alpha$ the integral $\int_{R^2} \frac{\sin(x^2+y^2)}{(x^2+y^2+1)^{\alpha}}$ converges?

Published on 19 Jan 2019 - 23:29

score 51 · Answer 10 · 2026-03-27 21:51:28

51

Views

show $F(a)=\sideset{_{-\infty}}{^a}\int f(x)dx$ is a distribution function

Published on 27 Mar 2026 - 21:51

score 85 · Answer 11 · 2019-01-20 21:00:54

85

Views

Does $\int_{0}^{\infty}\frac{r^2}{1+\alpha r^4}dr$ converge?

Published on 20 Jan 2019 - 21:00

score 82 · Answer 12 · 2026-03-26 01:28:30

82

Views

Degree choice in improper integrals resulting in trigonometric functions

Published on 26 Mar 2026 - 1:28

score 956 · Answer 13 · 2019-01-21 01:24:50

956

Views

Need help understanding why $\int_0^\infty \int_0^\infty |x-y|e^{-x}e^{-y} \, dx \,dy = 2 \int_0^\infty \int_y^\infty (x-y)e^{-x}e^{-y} \, dx \,dy $

Published on 21 Jan 2019 - 1:24

score 40 · Answer 14 · 2019-01-21 12:49:49

40

Views

can knowing an improper integral dependence on first parameter help in studying dependence from second parameter?

Published on 21 Jan 2019 - 12:49

score 155 · Answer 15 · 2019-01-21 19:42:26

155

Views

Integral from -infinity to infinity as a pair of distinct integrals

Published on 21 Jan 2019 - 19:42

List Question

Convergence/Divergence of $\int_0^{+\infty} {\frac {\sin x}{x\ln^2 (x^2+2)}} \mathrm{d}x$

$ \int_0^{+\infty} \frac{1}{(1+x^2)(1+x^{\phi})}\, dx \, \, \, (\phi>0) $

Show the function is in $L^2(\mathbb{R})$

Logical mistake in a proof of Dirichlet's test

Proof that $\int_{0}^{1}\frac{1}{x-\ln(x)}\mathbb{d}x$ is convergent.

Convergence for improper integral $\int_0^\infty x^re^{-x} \,dx$

Does there exist the limit at infinity of a function $f:[1,+\infty)\to[0,+\infty)$ such that $\int_{1}^{+\infty}f(x)dx$ is convergent.

Calculate $\int\limits_{-\infty}^{\infty}\frac{\sin^2(x)\cos(wx)}{x^2}dx$ using complex analysis technique

For which values of $\alpha$ the integral $\int_{R^2} \frac{\sin(x^2+y^2)}{(x^2+y^2+1)^{\alpha}}$ converges?

show $F(a)=\sideset{_{-\infty}}{^a}\int f(x)dx$ is a distribution function

Does $\int_{0}^{\infty}\frac{r^2}{1+\alpha r^4}dr$ converge?

Degree choice in improper integrals resulting in trigonometric functions

Need help understanding why $\int_0^\infty \int_0^\infty |x-y|e^{-x}e^{-y} \, dx \,dy = 2 \int_0^\infty \int_y^\infty (x-y)e^{-x}e^{-y} \, dx \,dy $

can knowing an improper integral dependence on first parameter help in studying dependence from second parameter?

Integral from -infinity to infinity as a pair of distinct integrals

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