Question

How resolve $\int_{-\infty}^{\infty}\frac{\sin x}{x+i}dx$

score 114 · Answer 1 · 2021-12-08 19:59:41

114

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How resolve $\int_{-\infty}^{\infty}\frac{\sin x}{x+i}dx$

Published on 08 Dec 2021 - 19:59

score 18 · Answer 2 · 2021-12-10 11:00:30

18

Views

Solving a curvilinear integral based on an equation

Published on 10 Dec 2021 - 11:00

score 87 · Answer 3 · 2026-04-09 11:13:02

87

Views

Computing convolution using only the definition.

Published on 09 Apr 2026 - 11:13

score 71 · Answer 4 · 2021-12-20 17:45:13

71

Views

Evaluate the integral $\int_0^{2\pi} e^{2\sin(\theta)}d\theta$

Published on 20 Dec 2021 - 17:45

score 216 · Answer 5 · 2021-12-24 22:19:00

216

Views

Evaluating $\int_{0}^{\infty} \frac{4\pi}{16\pi^2 + x^2} \left(\frac{1}{x}+\frac{1}{e^{-x}-1}\right) \, dx$

Published on 24 Dec 2021 - 22:19

score 874 · Answer 6 · 2021-12-25 13:46:29

874

Views

Solve $\int _{x=0}^{\infty }\int _{t=-\infty }^{\infty }\exp \left(\frac{-a t^2+i b t}{3 t^2+1}+i t x\right)\frac{x}{3 t^2+1}\mathrm{d}t\mathrm{d}x$

Published on 25 Dec 2021 - 13:46

score 164 · Answer 7 · 2021-12-26 01:17:56

164

Views

Contour integral $\oint_{|z|=1}\frac{z^2\sin(1/z)}{z-2}dz$

Published on 26 Dec 2021 - 1:17

score 395 · Answer 8 · 2021-12-27 08:32:58

395

Views

Calculating the contour integral: $\int_{|z-z_0|=r}\frac{1}{\bar{z}}dz$

Published on 27 Dec 2021 - 8:32

score 70 · Answer 9 · 2026-03-28 15:26:07

70

Views

Explicit computation of Mellin transformation and its inverse

Published on 28 Mar 2026 - 15:26

score 63 · Answer 10 · 2021-12-31 06:41:06

63

Views

showing $\frac{1}{(A+B)^{a}}=\frac{1}{\Gamma(a)} \frac{1}{2\pi i} \int_{-i\infty}^{+i \infty} dz \frac{B^z}{A^{a+z}} \Gamma(-z) \Gamma(a+z)$

Published on 31 Dec 2021 - 6:41

score 67 · Answer 11 · 2026-04-09 08:02:26

67

Views

Finding a complex function satisfying a relation

Published on 09 Apr 2026 - 8:02

score 515 · Answer 12 · 2026-03-30 01:52:04

515

Views

Integrating f(z)=$z/(16-z^2)(z+i)$ over a circle $|z|=5$

Published on 30 Mar 2026 - 1:52

score 232 · Answer 13 · 2022-01-05 21:13:41

232

Views

$\int_0^{2 \pi} e^{e^{it} + ikt} dt = 0$ using Cauchy's integral theorem

Published on 05 Jan 2022 - 21:13

score 167 · Answer 14 · 2026-04-09 01:34:32

167

Views

How to evaluate $\int_C e^z\cot(4z)dz$ where $|z|=1$

Published on 09 Apr 2026 - 1:34

score 49 · Answer 15 · 2022-01-09 08:33:12

49

Views

Using complex integration to compute a convergent integral $\int_0^\infty x^\alpha R (x)dx $ with a rational function $R (x) $ and $0< \alpha< 1$

Published on 09 Jan 2022 - 8:33

List Question

How resolve $\int_{-\infty}^{\infty}\frac{\sin x}{x+i}dx$

Solving a curvilinear integral based on an equation

Computing convolution using only the definition.

Evaluate the integral $\int_0^{2\pi} e^{2\sin(\theta)}d\theta$

Evaluating $\int_{0}^{\infty} \frac{4\pi}{16\pi^2 + x^2} \left(\frac{1}{x}+\frac{1}{e^{-x}-1}\right) \, dx$

Solve $\int _{x=0}^{\infty }\int _{t=-\infty }^{\infty }\exp \left(\frac{-a t^2+i b t}{3 t^2+1}+i t x\right)\frac{x}{3 t^2+1}\mathrm{d}t\mathrm{d}x$

Contour integral $\oint_{|z|=1}\frac{z^2\sin(1/z)}{z-2}dz$

Calculating the contour integral: $\int_{|z-z_0|=r}\frac{1}{\bar{z}}dz$

Explicit computation of Mellin transformation and its inverse

showing $\frac{1}{(A+B)^{a}}=\frac{1}{\Gamma(a)} \frac{1}{2\pi i} \int_{-i\infty}^{+i \infty} dz \frac{B^z}{A^{a+z}} \Gamma(-z) \Gamma(a+z)$

Finding a complex function satisfying a relation

Integrating f(z)=$z/(16-z^2)(z+i)$ over a circle $|z|=5$

$\int_0^{2 \pi} e^{e^{it} + ikt} dt = 0$ using Cauchy's integral theorem

How to evaluate $\int_C e^z\cot(4z)dz$ where $|z|=1$

Using complex integration to compute a convergent integral $\int_0^\infty x^\alpha R (x)dx $ with a rational function $R (x) $ and $0< \alpha< 1$

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