Question

Better approach for evaluating $\int_{0}^{\infty} \frac{x\sin(\pi x)}{(x^2+4)^3} dx$

score 184 · Answer 1 · 2026-04-07 09:54:40

184

Views

Better approach for evaluating $\int_{0}^{\infty} \frac{x\sin(\pi x)}{(x^2+4)^3} dx$

Published on 07 Apr 2026 - 9:54

score 266 · Answer 2 · 2017-01-27 20:46:47

266

Views

Calculate an approximation of $\int_0^1\int_0^1\frac{\log(xy)xy}{-1+\log(xy)}dxdy$

Published on 27 Jan 2017 - 20:46

score 400 · Answer 3 · 2026-04-09 17:55:00

400

Views

Contour integration with semicircular arcs.

Published on 09 Apr 2026 - 17:55

score 298 · Answer 4 · 2017-01-28 17:24:51

298

Views

Domain of Integral $F(X)=\int_{0}^{x}\frac{1}{\ln(2-t^2)}dt$

Published on 28 Jan 2017 - 17:24

score 215 · Answer 5 · 2017-01-28 18:24:40

215

Views

$\int_{U}f(x)dx$ converge iff $\int_{U}|f(x)|dx$ converge

Published on 28 Jan 2017 - 18:24

score 28 · Answer 6 · 2017-01-30 15:37:34

28

Views

Integrating when the boundaries converge to each other

Published on 30 Jan 2017 - 15:37

score 65 · Answer 7 · 2026-04-12 07:08:58

65

Views

Is there some close form solution available for following integral?

Published on 12 Apr 2026 - 7:08

score 289 · Answer 8 · 2017-01-31 08:32:51

289

Views

How to show that $\int_{0}^{\infty}{(2x)^4\over (1-x^2+x^4)^4}\mathrm dx=\int_{0}^{\infty}{(2x)^4\over (1-x^2+x^4)^3}\mathrm dx=3\pi$

Published on 31 Jan 2017 - 8:32

score 122 · Answer 9 · 2017-01-31 13:18:18

122

Views

Computing $\int_{0}^{\infty}\frac{1}{x^{p}}\,dx$

Published on 31 Jan 2017 - 13:18

score 71 · Answer 10 · 2017-01-31 19:25:30

71

Views

convergence of $\int_{\mathbb{R}^3}\frac{dx\,dy\,dz}{1+x^4+y^4+z^4}$

Published on 31 Jan 2017 - 19:25

score 91 · Answer 11 · 2017-02-01 04:26:57

91

Views

Proving $\text {limsup}_{x\to \infty}x\int_{x}^{x+1}\sin (t^2) \mathrm{d}t=1$

Published on 01 Feb 2017 - 4:26

score 101 · Answer 12 · 2017-02-01 10:54:08

101

Views

Show that $\int_0^\infty \frac{1}{x^\alpha(1+\log^2x)^\alpha}dx$ diverges for any $\alpha>0$

Published on 01 Feb 2017 - 10:54

score 189 · Answer 13 · 2017-02-01 11:22:47

189

Views

Power series as an integral of $\sum_{n=0}^\infty \frac{a_n}{n!}z^n$

Published on 01 Feb 2017 - 11:22

score 107 · Answer 14 · 2017-02-01 16:24:58

107

Views

Exact Values of the integal $\int_0^\infty \frac{r^{n-1}}{(1+r^2)^{\frac{s}{2}}}\,dr$

Published on 01 Feb 2017 - 16:24

score 20 · Answer 15 · 2026-04-08 06:49:44

Does $\int_{-\infty}^\infty \text da \ \int_{-\infty}^\infty \text db \ e^{i u (a^2-b^2) - v(a^2-b^2)^2}a^p b^q$ converge?

List Question

Better approach for evaluating $\int_{0}^{\infty} \frac{x\sin(\pi x)}{(x^2+4)^3} dx$

Calculate an approximation of $\int_0^1\int_0^1\frac{\log(xy)xy}{-1+\log(xy)}dxdy$

Contour integration with semicircular arcs.

Domain of Integral $F(X)=\int_{0}^{x}\frac{1}{\ln(2-t^2)}dt$

$\int_{U}f(x)dx$ converge iff $\int_{U}|f(x)|dx$ converge

Integrating when the boundaries converge to each other

Is there some close form solution available for following integral?

How to show that $\int_{0}^{\infty}{(2x)^4\over (1-x^2+x^4)^4}\mathrm dx=\int_{0}^{\infty}{(2x)^4\over (1-x^2+x^4)^3}\mathrm dx=3\pi$

Computing $\int_{0}^{\infty}\frac{1}{x^{p}}\,dx$

convergence of $\int_{\mathbb{R}^3}\frac{dx\,dy\,dz}{1+x^4+y^4+z^4}$

Proving $\text {limsup}_{x\to \infty}x\int_{x}^{x+1}\sin (t^2) \mathrm{d}t=1$

Show that $\int_0^\infty \frac{1}{x^\alpha(1+\log^2x)^\alpha}dx$ diverges for any $\alpha>0$

Power series as an integral of $\sum_{n=0}^\infty \frac{a_n}{n!}z^n$

Exact Values of the integal $\int_0^\infty \frac{r^{n-1}}{(1+r^2)^{\frac{s}{2}}}\,dr$

Does $\int_{-\infty}^\infty \text da \ \int_{-\infty}^\infty \text db \ e^{i u (a^2-b^2) - v(a^2-b^2)^2}a^p b^q$ converge?

Trending Questions

Popular # Hahtags

Popular Questions