List questions from contour-integration

Published on 01 Apr 2026 - 9:36

80

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Integral of $\int_0^{2\pi} \frac{e^{-it }dt}{e^{it}-z}$

Published on 18 Oct 2014 - 3:46

275

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Use contour integration to calculate real integrals:$\int_0^{\pi/2}e^{-x\cos\theta}\ \cos(x\sin\theta)\ d\theta=\frac \pi 2-\int_0^x\frac{\sin u}u du$

Published on 18 Oct 2014 - 11:14

114

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$\int_{-\infty}^{+\infty}dx\frac{x\cos(xt)}{e^{ax}-e^{-ax}}$

Published on 20 Oct 2014 - 2:19

501

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inverse laplace transform by using complex integral

Published on 30 Mar 2026 - 23:19

65

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contour intrgration, what's the right answer?

Published on 22 Oct 2014 - 1:53

793

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Find $\int_{ - \infty }^{ + \infty } {\frac{1} {1 + {x^4}}} \;{\mathrm{d}}x$

Published on 22 Oct 2014 - 13:35

4.7k

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$\int_{0}^\pi \frac{\sin(nx)}{\sin x} dx$

Published on 22 Oct 2014 - 19:43

2.5k

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Prove using contour integration that $\int_0^\infty \frac{\log x}{x^3-1}\operatorname d\!x=\frac{4\pi^2}{27}$

Published on 23 Oct 2014 - 4:10

51

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How to relate two integration contour?

Published on 26 Mar 2026 - 3:18

1.5k

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Closed form of $I=\int_{0}^{\pi/2} \tan^{-1} \bigg( \frac{\cos(x)}{\sin(x) - 1 - \sqrt{2}} \bigg) \tan(x)\;dx$

Published on 29 Mar 2026 - 15:16

994

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Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

Published on 29 Mar 2026 - 15:16

472

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Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

Published on 28 Mar 2026 - 22:13

88

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Inequality complex integral with $|f|\le 1$.

Published on 27 Oct 2014 - 6:07

143

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using complex or real analysis solve $\int_{0}^{\pi/2}\frac{x^m}{\sin x}dx$

Published on 29 Mar 2026 - 16:47

List Question

Contour Integral About A Circle

Integral of $\int_0^{2\pi} \frac{e^{-it }dt}{e^{it}-z}$

Use contour integration to calculate real integrals:$\int_0^{\pi/2}e^{-x\cos\theta}\ \cos(x\sin\theta)\ d\theta=\frac \pi 2-\int_0^x\frac{\sin u}u du$

$\int_{-\infty}^{+\infty}dx\frac{x\cos(xt)}{e^{ax}-e^{-ax}}$

inverse laplace transform by using complex integral

contour intrgration, what's the right answer?

Find $\int_{ - \infty }^{ + \infty } {\frac{1} {1 + {x^4}}} \;{\mathrm{d}}x$

$\int_{0}^\pi \frac{\sin(nx)}{\sin x} dx$

Prove using contour integration that $\int_0^\infty \frac{\log x}{x^3-1}\operatorname d\!x=\frac{4\pi^2}{27}$

How to relate two integration contour?

Closed form of $I=\int_{0}^{\pi/2} \tan^{-1} \bigg( \frac{\cos(x)}{\sin(x) - 1 - \sqrt{2}} \bigg) \tan(x)\;dx$

Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

Closed form for $I=\int_{0}^{\infty}\frac{x^n}{x^2+u^2}\tanh(x) \, dx$

Inequality complex integral with $|f|\le 1$.

using complex or real analysis solve $\int_{0}^{\pi/2}\frac{x^m}{\sin x}dx$

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