Question

Why do we say that when a definite integral equals infinity it diverges?

score 101 · Answer 1 · 2019-12-21 20:09:45

101

Views

Why do we say that when a definite integral equals infinity it diverges?

Published on 21 Dec 2019 - 20:09

score 60 · Answer 2 · 2026-03-26 16:10:17

60

Views

Line integral along the curve $\gamma(l)=(l\cos(\frac{2\pi}{l}),l\sin(\frac{2\pi}{l})),\ l\in(0,1)$

Published on 26 Mar 2026 - 16:10

score 347 · Answer 3 · 2026-03-30 12:37:20

347

Views

Use Grönwall's proof to prove boundedness of ODE's solution

Published on 30 Mar 2026 - 12:37

score 72 · Answer 4 · 2026-04-03 13:28:05

72

Views

Regarding convergence of improper integral to be used in Analytic number theory

Published on 03 Apr 2026 - 13:28

score 138 · Answer 5 · 2019-12-26 21:28:20

138

Views

Evaluating the integral $\int_{0}^{\infty}\frac{1}{(1+x^a)(1+x^b)} dx$ for real $a, b \ge 0$

Published on 26 Dec 2019 - 21:28

score 1.5k · Answer 6 · 2019-12-27 15:30:27

1.5k

Views

Is the integral $\int^{\infty}_{0}\frac{\arctan x}{x}dx$ convergent?

Published on 27 Dec 2019 - 15:30

score 353 · Answer 7 · 2019-12-27 19:16:03

353

Views

Characterizing smooth, square-integrable functions on $(0,1]$

Published on 27 Dec 2019 - 19:16

score 337 · Answer 8 · 2026-03-25 07:45:23

337

Views

Evaluation of $\int\limits ^{\infty }_{0}\frac{x}{\left( x^{2} +1\right)^2\left( e^{tx} +1\right)} dx$

Published on 25 Mar 2026 - 7:45

score 87 · Answer 9 · 2026-03-29 06:33:48

87

Views

How to find $\int\log(\cos(a/x))dx$ in closed form or asymptotic estimation?

Published on 29 Mar 2026 - 6:33

score 247 · Answer 10 · 2019-12-30 06:54:30

247

Views

Solving $\int_1^2 e^{1-\frac{1}{(x-1)^2}} + 2 + \frac{1}{\sqrt{1-\log(x-1)}}\:dx$ with a clean trick

Published on 30 Dec 2019 - 6:54

score 100 · Answer 11 · 2026-03-26 08:14:23

100

Views

change of variable for radially symmetric function

Published on 26 Mar 2026 - 8:14

score 240 · Answer 12 · 2026-04-01 05:12:35

240

Views

The closed-form of $\int_0^\infty \frac{e^{-x}\cos(x)}{x^2+1}\mathrm{d}x$

Published on 01 Apr 2026 - 5:12

score 50 · Answer 13 · 2019-12-31 08:09:52

50

Views

How to test this improper integral is convergent?

Published on 31 Dec 2019 - 8:09

score 82 · Answer 14 · 2019-12-31 23:17:52

82

Views

Convergence of $\int_0^\infty \frac{\sin(x^2+ax)}{x}dx$

Published on 31 Dec 2019 - 23:17

score 47 · Answer 15 · 2020-01-01 14:34:26

47

Views

integrate $\int_{-\infty}^\infty e^{x-\frac{1}{2}\frac{(x+0.95)^2}{0.35^2}}dx $

Published on 01 Jan 2020 - 14:34

List Question

Why do we say that when a definite integral equals infinity it diverges?

Line integral along the curve $\gamma(l)=(l\cos(\frac{2\pi}{l}),l\sin(\frac{2\pi}{l})),\ l\in(0,1)$

Use Grönwall's proof to prove boundedness of ODE's solution

Regarding convergence of improper integral to be used in Analytic number theory

Evaluating the integral $\int_{0}^{\infty}\frac{1}{(1+x^a)(1+x^b)} dx$ for real $a, b \ge 0$

Is the integral $\int^{\infty}_{0}\frac{\arctan x}{x}dx$ convergent?

Characterizing smooth, square-integrable functions on $(0,1]$

Evaluation of $\int\limits ^{\infty }_{0}\frac{x}{\left( x^{2} +1\right)^2\left( e^{tx} +1\right)} dx$

How to find $\int\log(\cos(a/x))dx$ in closed form or asymptotic estimation?

Solving $\int_1^2 e^{1-\frac{1}{(x-1)^2}} + 2 + \frac{1}{\sqrt{1-\log(x-1)}}\:dx$ with a clean trick

change of variable for radially symmetric function

The closed-form of $\int_0^\infty \frac{e^{-x}\cos(x)}{x^2+1}\mathrm{d}x$

How to test this improper integral is convergent?

Convergence of $\int_0^\infty \frac{\sin(x^2+ax)}{x}dx$

integrate $\int_{-\infty}^\infty e^{x-\frac{1}{2}\frac{(x+0.95)^2}{0.35^2}}dx $

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