Question

Cauchy Principal Value of $\int_0^\infty \frac{x}{(x^2 + a^2) \, \sin(\mu x)} dx$

score 512 · Answer 1 · 2026-03-09 12:23:32

512

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Cauchy Principal Value of $\int_0^\infty \frac{x}{(x^2 + a^2) \, \sin(\mu x)} dx$

Published on 09 Mar 2026 - 12:23

score 46 · Answer 2 · 2016-02-27 12:09:33

46

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Contour integral $\int_{\gamma}e^{-t\mu}(-\mu)^{-m}\log\sqrt{-\mu}d\mu$

Published on 27 Feb 2016 - 12:09

score 210 · Answer 3 · 2026-04-04 02:49:18

210

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Compute $\int_{|r|=2}\frac{1}{z^2+1}dz$

Published on 04 Apr 2026 - 2:49

score 90 · Answer 4 · 2026-04-04 02:53:44

90

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Compute, for all integers $m,n$, $\int_{|z|=2}z^n(1-z^m)dz$

Published on 04 Apr 2026 - 2:53

score 230 · Answer 5 · 2026-04-04 04:18:16

230

Views

Evaluation of an improper integral with complex exponential

Published on 04 Apr 2026 - 4:18

score 1.9k · Answer 6 · 2016-02-29 14:29:24

1.9k

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evaluate $\int _0 ^\infty \frac{1-\cos(ax)}{x^2}dx$

Published on 29 Feb 2016 - 14:29

score 893 · Answer 7 · 2026-04-08 14:10:09

893

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How to evaluate integral $\int_0^{\infty} e^{-x^2} \frac{\sin(a x)}{\sin(b x)} dx$?

Published on 08 Apr 2026 - 14:10

score 216 · Answer 8 · 2016-03-01 17:57:43

216

Views

How to solve a contour integral?

Published on 01 Mar 2016 - 17:57

score 434 · Answer 9 · 2026-03-26 07:43:11

434

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Integrate $\int_{-\infty}^\infty\frac{e^{-ik\sqrt{x^2+a^2}}}{\sqrt{x^2+a^2}}dx$

Published on 26 Mar 2026 - 7:43

score 94 · Answer 10 · 2026-04-04 04:18:16

94

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Prove that the following function has a branch cut

Published on 04 Apr 2026 - 4:18

score 85 · Answer 11 · 2016-03-06 16:49:47

85

Views

Complex: evaluating integral with residues

Published on 06 Mar 2016 - 16:49

score 370 · Answer 12 · 2016-03-06 22:40:29

370

Views

A definite integral that surely needs contour integration: $\int_0^{\infty} \frac{1}{x^2 + a^2}\cos\left(\frac{x(x^2 - b^2)}{x^2 - c^2}\right)\, dx$

Published on 06 Mar 2016 - 22:40

score 141 · Answer 13 · 2016-03-07 20:47:45

141

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How to evaluate the integral $\int_0^{2\pi}\mathrm{d}\theta e^{ia\cos(\theta-\theta_1)}\cos^2(\theta-\theta_2)$

Published on 07 Mar 2016 - 20:47

score 142 · Answer 14 · 2016-03-08 13:22:44

142

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Improper integral $\int _{0+0}^{1-0}\frac{dx}{\left(4-3x\right)\sqrt{x-x^2}}\:dx$

Published on 08 Mar 2016 - 13:22

score 33 · Answer 15 · 2016-03-09 06:57:58

33

Views

Is this dual behavior allowed in integration in Complex Analysis?

Published on 09 Mar 2016 - 6:57

List Question

Cauchy Principal Value of $\int_0^\infty \frac{x}{(x^2 + a^2) \, \sin(\mu x)} dx$

Contour integral $\int_{\gamma}e^{-t\mu}(-\mu)^{-m}\log\sqrt{-\mu}d\mu$

Compute $\int_{|r|=2}\frac{1}{z^2+1}dz$

Compute, for all integers $m,n$, $\int_{|z|=2}z^n(1-z^m)dz$

Evaluation of an improper integral with complex exponential

evaluate $\int _0 ^\infty \frac{1-\cos(ax)}{x^2}dx$

How to evaluate integral $\int_0^{\infty} e^{-x^2} \frac{\sin(a x)}{\sin(b x)} dx$?

How to solve a contour integral?

Integrate $\int_{-\infty}^\infty\frac{e^{-ik\sqrt{x^2+a^2}}}{\sqrt{x^2+a^2}}dx$

Prove that the following function has a branch cut

Complex: evaluating integral with residues

A definite integral that surely needs contour integration: $\int_0^{\infty} \frac{1}{x^2 + a^2}\cos\left(\frac{x(x^2 - b^2)}{x^2 - c^2}\right)\, dx$

How to evaluate the integral $\int_0^{2\pi}\mathrm{d}\theta e^{ia\cos(\theta-\theta_1)}\cos^2(\theta-\theta_2)$

Improper integral $\int _{0+0}^{1-0}\frac{dx}{\left(4-3x\right)\sqrt{x-x^2}}\:dx$

Is this dual behavior allowed in integration in Complex Analysis?

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