Question

Integral of hyperbolic function combined with a polynomial over symmetric interval

score 75 · Answer 1 · 2026-04-11 17:39:39

75

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Integral of hyperbolic function combined with a polynomial over symmetric interval

Published on 11 Apr 2026 - 17:39

score 72 · Answer 2 · 2026-04-12 00:21:47

72

Views

How should $\int_0^\infty e^{-(x+ci)^2}dx$ be evaluated, where $c$ is a real constant.

Published on 12 Apr 2026 - 0:21

score 87 · Answer 3 · 2022-08-18 14:48:41

87

Views

Complex integration: $\int_{-\infty}^{\infty} \dfrac{\sin(x^2)}{1+x^4}dx$

Published on 18 Aug 2022 - 14:48

score 335 · Answer 4 · 2022-08-20 02:53:49

335

Views

A contour integration approach for $\int_{0}^{\infty} \frac{\ln \left(x^{4}+2 x^{2} \cos 2 a+1\right)}{1+x^{2}} \, d x$

Published on 20 Aug 2022 - 2:53

score 161 · Answer 5 · 2022-08-20 17:30:03

161

Views

Integral $\int \frac{1}{\sqrt{1 - ix^3}}$ dx using complex calculus.

Published on 20 Aug 2022 - 17:30

score 100 · Answer 6 · 2022-08-21 04:23:20

100

Views

Several questions on calculating $\int_0^{2\pi} \frac{\mathrm{d} \theta}{1+r\sin \theta}$ via contours

Published on 21 Aug 2022 - 4:23

score 73 · Answer 7 · 2022-08-21 23:57:14

73

Views

Why is $|z_1| < 1$ and $|z_2| > 1$?

Published on 21 Aug 2022 - 23:57

score 27 · Answer 8 · 2022-08-24 18:05:57

27

Views

Construction of the subrectangles in Palka's proof that $\int\limits_{\partial R}f(z)dz=0$ when $f$ is analytic and $R$ is a rectangle

Published on 24 Aug 2022 - 18:05

score 47 · Answer 9 · 2026-04-11 04:21:24

47

Views

a simple Inequality with an integral

Published on 11 Apr 2026 - 4:21

score 457 · Answer 10 · 2022-08-28 16:58:45

457

Views

Integration $\int_{0}^{\infty} \frac{2x-1}{x^{2/3}\sqrt{(x+1)((x+1)^3-x)}}\text{d}x=0.$

Published on 28 Aug 2022 - 16:58

score 140 · Answer 11 · 2026-04-08 23:09:39

140

Views

Understanding the proof of Cauchy's Estimate.

Published on 08 Apr 2026 - 23:09

score 48 · Answer 12 · 2022-08-30 15:08:03

48

Views

Limit of $\exp(i\log x)$ for $x \to 0$

Published on 30 Aug 2022 - 15:08

score 68 · Answer 13 · 2022-09-02 08:33:17

68

Views

Classification of singularities and residue at $z=0$ of $\frac{e^{1/z}\sin(z^2)}{\sin(e^{iz})}$

Published on 02 Sep 2022 - 8:33

score 89 · Answer 14 · 2026-04-09 12:09:25

89

Views

Confused by paragraph in Conway's book "Functions of one complex variable".

Published on 09 Apr 2026 - 12:09

score 276 · Answer 15 · 2026-04-11 10:07:14

276

Views

help evaluating tricky contour integral

Published on 11 Apr 2026 - 10:07

List Question

Integral of hyperbolic function combined with a polynomial over symmetric interval

How should $\int_0^\infty e^{-(x+ci)^2}dx$ be evaluated, where $c$ is a real constant.

Complex integration: $\int_{-\infty}^{\infty} \dfrac{\sin(x^2)}{1+x^4}dx$

A contour integration approach for $\int_{0}^{\infty} \frac{\ln \left(x^{4}+2 x^{2} \cos 2 a+1\right)}{1+x^{2}} \, d x$

Integral $\int \frac{1}{\sqrt{1 - ix^3}}$ dx using complex calculus.

Several questions on calculating $\int_0^{2\pi} \frac{\mathrm{d} \theta}{1+r\sin \theta}$ via contours

Why is $|z_1| < 1$ and $|z_2| > 1$?

Construction of the subrectangles in Palka's proof that $\int\limits_{\partial R}f(z)dz=0$ when $f$ is analytic and $R$ is a rectangle

a simple Inequality with an integral

Integration $\int_{0}^{\infty} \frac{2x-1}{x^{2/3}\sqrt{(x+1)((x+1)^3-x)}}\text{d}x=0.$

Understanding the proof of Cauchy's Estimate.

Limit of $\exp(i\log x)$ for $x \to 0$

Classification of singularities and residue at $z=0$ of $\frac{e^{1/z}\sin(z^2)}{\sin(e^{iz})}$

Confused by paragraph in Conway's book "Functions of one complex variable".

help evaluating tricky contour integral

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