Question

Calculating $\int_{-\infty}^{+\infty}\mathrm{d}x\frac{\exp(-x^2)}{x^2+1}$ with the Cauchy formula

score 148 · Answer 1 · 2026-03-26 07:34:52

148

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Calculating $\int_{-\infty}^{+\infty}\mathrm{d}x\frac{\exp(-x^2)}{x^2+1}$ with the Cauchy formula

Published on 26 Mar 2026 - 7:34

score 310 · Answer 2 · 2026-03-30 01:53:06

310

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How to solve this Mellin–Barnes integral

Published on 30 Mar 2026 - 1:53

score 337 · Answer 3 · 2026-03-25 07:45:23

337

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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 31 · Answer 4 · 2019-12-29 10:59:22

31

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integrating $\frac{(2z-1)}{(z^2 - 1)}$ around the circle of radius $1$ centred at $1$, anticlockwise.

Published on 29 Dec 2019 - 10:59

score 102 · Answer 5 · 2019-12-31 15:44:43

102

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How to find the value of the integral?

Published on 31 Dec 2019 - 15:44

score 41 · Answer 6 · 2020-01-01 08:18:22

41

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How to evaluate the integral $\int_0^\infty \frac{1}{(1+x^2)(1+x^\alpha)} \mathbb dx$?

Published on 01 Jan 2020 - 8:18

score 115 · Answer 7 · 2020-01-02 16:16:41

115

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Contour integral of log over fractional power

Published on 02 Jan 2020 - 16:16

score 90 · Answer 8 · 2020-01-02 21:00:39

90

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Does $f(z) = \frac{1}{z-1} - \frac{1}{z+1}$ have an antiderivative in $|z|>2?$

Published on 02 Jan 2020 - 21:00

score 119 · Answer 9 · 2020-01-04 17:42:34

119

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Keyhole contour in complex analysis

Published on 04 Jan 2020 - 17:42

score 31 · Answer 10 · 2020-01-05 13:03:56

31

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How do i define $f(z_0)$ in an contour integral?

Published on 05 Jan 2020 - 13:03

score 2.8k · Answer 11 · 2026-03-29 22:13:27

2.8k

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Residue Theorem if Pole is on Contour

Published on 29 Mar 2026 - 22:13

score 121 · Answer 12 · 2020-01-07 04:28:27

121

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Cauchy’s integral theorem statement

Published on 07 Jan 2020 - 4:28

score 162 · Answer 13 · 2020-01-07 07:43:58

162

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A corollary of Cauchy integral theorem

Published on 07 Jan 2020 - 7:43

score 77 · Answer 14 · 2026-03-29 19:11:40

77

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Use the Cauchy Integral Formula to evaluate the following integral: $\int_C{\frac{z}{z^2+4z+3} dz}$

Published on 29 Mar 2026 - 19:11

score 73 · Answer 15 · 2026-03-29 17:27:36

73

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Use the Cauchy Integral Formula to evaluate the following integral:$\int_e{\frac{1}{z^2+4}}dz$

Published on 29 Mar 2026 - 17:27

List Question

Calculating $\int_{-\infty}^{+\infty}\mathrm{d}x\frac{\exp(-x^2)}{x^2+1}$ with the Cauchy formula

How to solve this Mellin–Barnes integral

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

integrating $\frac{(2z-1)}{(z^2 - 1)}$ around the circle of radius $1$ centred at $1$, anticlockwise.

How to find the value of the integral?

How to evaluate the integral $\int_0^\infty \frac{1}{(1+x^2)(1+x^\alpha)} \mathbb dx$?

Contour integral of log over fractional power

Does $f(z) = \frac{1}{z-1} - \frac{1}{z+1}$ have an antiderivative in $|z|>2?$

Keyhole contour in complex analysis

How do i define $f(z_0)$ in an contour integral?

Residue Theorem if Pole is on Contour

Cauchy’s integral theorem statement

A corollary of Cauchy integral theorem

Use the Cauchy Integral Formula to evaluate the following integral: $\int_C{\frac{z}{z^2+4z+3} dz}$

Use the Cauchy Integral Formula to evaluate the following integral:$\int_e{\frac{1}{z^2+4}}dz$

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