Question

Value of $I$ where $I=\frac{1}{2\pi i} \oint_{\gamma}z^7\cos(\frac{1}{z^2})dz$

score 180 · Answer 1 · 2026-03-30 00:04:16

180

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Value of $I$ where $I=\frac{1}{2\pi i} \oint_{\gamma}z^7\cos(\frac{1}{z^2})dz$

Published on 30 Mar 2026 - 0:04

score 221 · Answer 2 · 2026-03-26 16:08:44

221

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Using the Residue Theorem to Evaluate Contour Integrals

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score 109 · Answer 3 · 2026-03-30 01:45:12

109

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score 57 · Answer 4 · 2020-02-03 18:07:57

57

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Integral on real line computed expressly via contour integration

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score 104 · Answer 5 · 2026-03-28 00:06:18

104

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Compute$\int_0^{2\pi}\frac{\cos^2\theta }{ |re^{i\theta} -z|^2}d\theta$

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score 344 · Answer 6 · 2026-02-23 11:24:33

344

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Does the inverse Laplace transform of $F(s)=\frac{\sin(\xi\sqrt{s})}{\sqrt{s}}$ exist for some $\xi\in\mathbb{C}$?

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score 159 · Answer 7 · 2020-02-04 22:40:05

159

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Trouble with contour integration bounds: $\int_0^{\infty}dx \dfrac{(\log x)^2}{1+x^2}$

Published on 04 Feb 2020 - 22:40

score 125 · Answer 8 · 2020-02-05 19:09:24

125

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How to unify the working out of $\int_{|z|=1} dz/((z-a)(z-b))$ for $a \neq b$ and $a = b$?

Published on 05 Feb 2020 - 19:09

score 89 · Answer 9 · 2020-02-05 20:56:53

89

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Compute $\int_{-\infty}^{+\infty}\frac{x^2}{(x^2-\sqrt{2}x+1)(x^2+1)^{\alpha}}dx$

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score 83 · Answer 10 · 2026-03-30 01:45:13

83

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Complex Integral and Residue theorem

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score 42 · Answer 11 · 2020-02-07 00:32:22

42

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Contour integration on either side of a branch cut

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score 31 · Answer 12 · 2026-03-29 20:46:21

31

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score 107 · Answer 13 · 2020-02-07 22:47:41

107

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Integration of $\exp(-z^2)/(z-z_0)$

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score 1.3k · Answer 14 · 2026-03-30 06:49:25

1.3k

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score 126 · Answer 15 · 2020-02-09 17:48:18

126

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contour integral for $\int_0^\infty\frac{\ln x}{x^2+a^2}dx$

Published on 09 Feb 2020 - 17:48

List Question

Value of $I$ where $I=\frac{1}{2\pi i} \oint_{\gamma}z^7\cos(\frac{1}{z^2})dz$

Using the Residue Theorem to Evaluate Contour Integrals

Issue when applying the residue theorem

Integral on real line computed expressly via contour integration

Compute$\int_0^{2\pi}\frac{\cos^2\theta }{ |re^{i\theta} -z|^2}d\theta$

Does the inverse Laplace transform of $F(s)=\frac{\sin(\xi\sqrt{s})}{\sqrt{s}}$ exist for some $\xi\in\mathbb{C}$?

Trouble with contour integration bounds: $\int_0^{\infty}dx \dfrac{(\log x)^2}{1+x^2}$

How to unify the working out of $\int_{|z|=1} dz/((z-a)(z-b))$ for $a \neq b$ and $a = b$?

Compute $\int_{-\infty}^{+\infty}\frac{x^2}{(x^2-\sqrt{2}x+1)(x^2+1)^{\alpha}}dx$

Complex Integral and Residue theorem

Contour integration on either side of a branch cut

Clarification question about a common integral evaluated using residue theorem

Integration of $\exp(-z^2)/(z-z_0)$

The Hankel Integral Representation for $\Gamma(z)$

contour integral for $\int_0^\infty\frac{\ln x}{x^2+a^2}dx$

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