Question

Solving the integral $\int \ln\left ( \frac{1+\sqrt{1-x^2}}{1-\sqrt{1-x^2}} \right ) \frac{dx}{1-x^2}$

score 218 · Answer 1 · 2026-03-27 18:09:26

218

Views

Solving the integral $\int \ln\left ( \frac{1+\sqrt{1-x^2}}{1-\sqrt{1-x^2}} \right ) \frac{dx}{1-x^2}$

Published on 27 Mar 2026 - 18:09

score 44 · Answer 2 · 2019-11-14 02:06:58

44

Views

Is it true that $| \int_\gamma f|= \int_\gamma|f|$, for any closed path $\gamma$

Published on 14 Nov 2019 - 2:06

score 92 · Answer 3 · 2019-11-15 16:14:32

92

Views

Complex contour integration, Cauchy's theorem

Published on 15 Nov 2019 - 16:14

score 49 · Answer 4 · 2019-11-16 07:33:40

49

Views

$f(z) = \frac{1}{\pi} \int_E \frac{f(w)}{(1-z \bar{w})^2} dudv $ , where $w = u + iv$

Published on 16 Nov 2019 - 7:33

score 55 · Answer 5 · 2019-11-16 20:26:08

55

Views

why Residue of 1/Z^2 at Z=0 different by Laurent series and Residue theorem?

Published on 16 Nov 2019 - 20:26

score 138 · Answer 6 · 2026-03-26 14:17:43

138

Views

Confused on evaluating line integral with parameterization

Published on 26 Mar 2026 - 14:17

score 50 · Answer 7 · 2019-11-17 06:10:05

50

Views

Semi-continuity of the value of contour integral in the Argument principle

Published on 17 Nov 2019 - 6:10

score 134 · Answer 8 · 2019-11-21 02:33:25

134

Views

integrating real functions using residue Theorem.

Published on 21 Nov 2019 - 2:33

score 110 · Answer 9 · 2019-11-21 12:38:39

110

Views

Find the value of $\int_{-\infty}^{\infty} \frac{e^{-x^2}}{1+x^2} dx$ .

Published on 21 Nov 2019 - 12:38

score 60 · Answer 10 · 2019-11-21 15:56:04

60

Views

Calculation of $\int _ { \gamma } z ^ { i} d z$, where $\gamma$ is any path (contour) from $- 1$ to $1$ lying above the $x$-axis.

Published on 21 Nov 2019 - 15:56

score 83 · Answer 11 · 2019-11-22 13:38:00

83

Views

Countour integration + partial fraction decompositon + poles

Published on 22 Nov 2019 - 13:38

score 118 · Answer 12 · 2019-11-23 00:30:21

118

Views

$\int_C\frac{z}{z^2+1}\,dz$ where $C:\ \{z:\ |z-0|=2\}$

Published on 23 Nov 2019 - 0:30

score 40 · Answer 13 · 2026-03-23 00:01:44

40

Views

$\int_{\varphi } {f}'/f = 0$ if $f(z)$ has no non positiv real values

Published on 23 Mar 2026 - 0:01

score 84 · Answer 14 · 2026-03-25 23:10:43

84

Views

Does "entire" mean the same thing as "antiderivative exists"?

Published on 25 Mar 2026 - 23:10

score 1.5k · Answer 15 · 2026-03-28 19:35:58

1.5k

Views

How to show the complex line integral is independent?

Published on 28 Mar 2026 - 19:35

List Question

Solving the integral $\int \ln\left ( \frac{1+\sqrt{1-x^2}}{1-\sqrt{1-x^2}} \right ) \frac{dx}{1-x^2}$

Is it true that $| \int_\gamma f|= \int_\gamma|f|$, for any closed path $\gamma$

Complex contour integration, Cauchy's theorem

$f(z) = \frac{1}{\pi} \int_E \frac{f(w)}{(1-z \bar{w})^2} dudv $ , where $w = u + iv$

why Residue of 1/Z^2 at Z=0 different by Laurent series and Residue theorem?

Confused on evaluating line integral with parameterization

Semi-continuity of the value of contour integral in the Argument principle

integrating real functions using residue Theorem.

Find the value of $\int_{-\infty}^{\infty} \frac{e^{-x^2}}{1+x^2} dx$ .

Calculation of $\int _ { \gamma } z ^ { i} d z$, where $\gamma$ is any path (contour) from $- 1$ to $1$ lying above the $x$-axis.

Countour integration + partial fraction decompositon + poles

$\int_C\frac{z}{z^2+1}\,dz$ where $C:\ \{z:\ |z-0|=2\}$

$\int_{\varphi } {f}'/f = 0$ if $f(z)$ has no non positiv real values

Does "entire" mean the same thing as "antiderivative exists"?

How to show the complex line integral is independent?

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