Question

Cauchy Principal Value Integral of $P V \int\limits _{-\infty} ^{\infty} \frac {1}{x(x^4-1)} dx .$

score 3.9k · Answer 1 · 2026-04-14 00:36:19

3.9k

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Cauchy Principal Value Integral of $P V \int\limits _{-\infty} ^{\infty} \frac {1}{x(x^4-1)} dx .$

Published on 14 Apr 2026 - 0:36

score 182 · Answer 2 · 2026-04-13 20:10:08

182

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Use the residue theorem to evaluate

Published on 13 Apr 2026 - 20:10

score 11.7k · Answer 3 · 2026-03-26 09:17:57

11.7k

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Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$

Published on 26 Mar 2026 - 9:17

score 731 · Answer 4 · 2026-04-08 17:45:47

731

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Help with understanding the evaluation of a real integral using complex analysis

Published on 08 Apr 2026 - 17:45

score 230 · Answer 5 · 2026-04-13 17:51:01

230

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How do you integrate $\int_0^\infty \exp(it^k)\,\mathrm dt$ for $k \in \Bbb N$?

Published on 13 Apr 2026 - 17:51

score 213 · Answer 6 · 2026-04-09 06:38:56

213

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Contour integral with power of sine

Published on 09 Apr 2026 - 6:38

score 177 · Answer 7 · 2013-06-18 19:42:20

177

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Real integral $ \int_{-\infty}^{\infty} \frac{dx}{1+x^2} $ with the help of complex friends

Published on 18 Jun 2013 - 19:42

score 435 · Answer 8 · 2026-04-13 22:28:13

435

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Using residue theory, show that $\oint_C\frac{e^{z/2}}{1+e^z}dz = 2\pi$

Published on 13 Apr 2026 - 22:28

score 1.3k · Answer 9 · 2026-04-12 04:10:43

1.3k

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Contour integration with branch cut

Published on 12 Apr 2026 - 4:10

score 69 · Answer 10 · 2026-04-13 14:59:11

69

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Complex integral, correct?

Published on 13 Apr 2026 - 14:59

score 121 · Answer 11 · 2026-04-12 08:38:19

121

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Inequality contour integral

Published on 12 Apr 2026 - 8:38

score 2.5k · Answer 12 · 2013-06-24 16:35:39

2.5k

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Evaluating the integral $\int_{-1}^{1} \frac{\sqrt{1-x^{2}}}{1+x^{2}} \, dx$ using a dumbbell-shaped contour

Published on 24 Jun 2013 - 16:35

score 425 · Answer 13 · 2026-04-11 04:03:43

425

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Is it true that a complex function has a global antiderivative if and only if it integrates to zero over every closed curve?

Published on 11 Apr 2026 - 4:03

score 2.8k · Answer 14 · 2026-04-13 00:11:18

2.8k

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Dogbone contour integral/branch cuts/residue at infinity

Published on 13 Apr 2026 - 0:11

score 703 · Answer 15 · 2013-06-27 12:02:46

703

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Contour integration: $\int_0^{\infty} x^p /(x^4+1) dx$ where $-1 < p < 3$

Published on 27 Jun 2013 - 12:02

List Question

Cauchy Principal Value Integral of $P V \int\limits _{-\infty} ^{\infty} \frac {1}{x(x^4-1)} dx .$

Use the residue theorem to evaluate

Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$

Help with understanding the evaluation of a real integral using complex analysis

How do you integrate $\int_0^\infty \exp(it^k)\,\mathrm dt$ for $k \in \Bbb N$?

Contour integral with power of sine

Real integral $ \int_{-\infty}^{\infty} \frac{dx}{1+x^2} $ with the help of complex friends

Using residue theory, show that $\oint_C\frac{e^{z/2}}{1+e^z}dz = 2\pi$

Contour integration with branch cut

Complex integral, correct?

Inequality contour integral

Evaluating the integral $\int_{-1}^{1} \frac{\sqrt{1-x^{2}}}{1+x^{2}} \, dx$ using a dumbbell-shaped contour

Is it true that a complex function has a global antiderivative if and only if it integrates to zero over every closed curve?

Dogbone contour integral/branch cuts/residue at infinity

Contour integration: $\int_0^{\infty} x^p /(x^4+1) dx$ where $-1 < p < 3$

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