Question

Evaluating the integral $\int_{0}^{+\infty}\sin x\sin(x^2)dx$

score 254 · Answer 1 · 2016-12-23 11:22:06

254

Views

Evaluating the integral $\int_{0}^{+\infty}\sin x\sin(x^2)dx$

Published on 23 Dec 2016 - 11:22

score 152 · Answer 2 · 2016-12-23 20:42:27

152

Views

Is $\int_0^\infty \vert \sin x \vert^{x^2} \ dx$ convergent?

Published on 23 Dec 2016 - 20:42

score 166 · Answer 3 · 2026-04-11 13:05:32

166

Views

What's about the Frullani extension for infinite series?

Published on 11 Apr 2026 - 13:05

score 1.8k · Answer 4 · 2016-12-25 14:13:42

1.8k

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Show that $\int_0^\infty{x^2e^{-x}dx}$ converges without calculating the integral.

Published on 25 Dec 2016 - 14:13

score 45 · Answer 5 · 2016-12-26 15:03:46

45

Views

How do I study the convergence of $\int_{0}^{1}\frac{e^{\frac{i}{t(1-t)}}}{1+t}dt$

Published on 26 Dec 2016 - 15:03

score 275 · Answer 6 · 2026-04-08 20:35:52

275

Views

Interchanging limits and integration

Published on 08 Apr 2026 - 20:35

score 130 · Answer 7 · 2016-12-27 14:13:39

130

Views

Studying the improper integral $\int^{1}_{0}\frac{\ln(x)}{\sqrt{1-x}}dx$

Published on 27 Dec 2016 - 14:13

score 30 · Answer 8 · 2016-12-28 10:35:10

30

Views

How to study the convergence of $\int_{0}^{1}\frac{\cos(\frac{1}{t^{17}(1-t)^{13}})}{1+t}$

Published on 28 Dec 2016 - 10:35

score 237 · Answer 9 · 2026-04-01 15:40:43

237

Views

On a simple integral involving Gompertz constant

Published on 01 Apr 2026 - 15:40

score 35 · Answer 10 · 2026-04-11 13:19:22

35

Views

A small issue with the comparison of a series and its integrals.

Published on 11 Apr 2026 - 13:19

score 111 · Answer 11 · 2016-12-29 01:30:19

111

Views

Calculations for $\int_0^\infty \frac{2\sinh^2\left(\frac{x}{e}\right)}{e^x+1}dx$, or $\sum_{n=1}^\infty\frac{(4^n-1)\zeta(2n+1)}{e^{2n}}$

Published on 29 Dec 2016 - 1:30

score 63 · Answer 12 · 2016-12-29 18:39:19

63

Views

How to study the convergence of $\int^{\infty}_{0}\frac{2\cos(t)\sin(t)}{t}dt$?

Published on 29 Dec 2016 - 18:39

score 45 · Answer 13 · 2016-12-29 19:25:05

45

Views

Showing that $\frac{2^{\alpha-3}}{(n+1)^{\alpha}\pi^{\alpha-1}}\leq u_n \leq \frac{1}{n^{\alpha}\pi^{\alpha-1}} $?

Published on 29 Dec 2016 - 19:25

score 54 · Answer 14 · 2026-04-09 09:54:44

54

Views

About the convergence of an integral

Published on 09 Apr 2026 - 9:54

score 186 · Answer 15 · 2016-12-30 12:43:59

186

Views

Improper integral $\int _3^{\infty }\:\frac{\sqrt{x^3+2}}{\left(x^2-3x\right)^\phi}$

Published on 30 Dec 2016 - 12:43

List Question

Evaluating the integral $\int_{0}^{+\infty}\sin x\sin(x^2)dx$

Is $\int_0^\infty \vert \sin x \vert^{x^2} \ dx$ convergent?

What's about the Frullani extension for infinite series?

Show that $\int_0^\infty{x^2e^{-x}dx}$ converges without calculating the integral.

How do I study the convergence of $\int_{0}^{1}\frac{e^{\frac{i}{t(1-t)}}}{1+t}dt$

Interchanging limits and integration

Studying the improper integral $\int^{1}_{0}\frac{\ln(x)}{\sqrt{1-x}}dx$

How to study the convergence of $\int_{0}^{1}\frac{\cos(\frac{1}{t^{17}(1-t)^{13}})}{1+t}$

On a simple integral involving Gompertz constant

A small issue with the comparison of a series and its integrals.

Calculations for $\int_0^\infty \frac{2\sinh^2\left(\frac{x}{e}\right)}{e^x+1}dx$, or $\sum_{n=1}^\infty\frac{(4^n-1)\zeta(2n+1)}{e^{2n}}$

How to study the convergence of $\int^{\infty}_{0}\frac{2\cos(t)\sin(t)}{t}dt$?

Showing that $\frac{2^{\alpha-3}}{(n+1)^{\alpha}\pi^{\alpha-1}}\leq u_n \leq \frac{1}{n^{\alpha}\pi^{\alpha-1}} $?

About the convergence of an integral

Improper integral $\int _3^{\infty }\:\frac{\sqrt{x^3+2}}{\left(x^2-3x\right)^\phi}$

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