Question

$\int_0^\infty \frac{\ln x}{(1+e^{x})^2}dx$ by contour integration

score 125 · Answer 1 · 2026-04-17 06:03:47

125

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$\int_0^\infty \frac{\ln x}{(1+e^{x})^2}dx$ by contour integration

Published on 17 Apr 2026 - 6:03

score 90 · Answer 2 · 2026-04-11 15:54:10

90

Views

Closed form for an improper integral

Published on 11 Apr 2026 - 15:54

score 113 · Answer 3 · 2026-04-13 13:11:39

113

Views

The reason that conditionally convergent integral produce different results

Published on 13 Apr 2026 - 13:11

score 264 · Answer 4 · 2026-03-25 04:00:28

264

Views

$I = \int_0^{\pi/2} \left( \int_0^{\pi/2} \frac{\log(\cos(x/2)) - \log(\cos(y/2))}{\cos(x) - \cos(y)} dx\right) \ dy $

Published on 25 Mar 2026 - 4:00

score 77 · Answer 5 · 2026-04-11 07:25:58

77

Views

An improper integral relates to Gamma function

Published on 11 Apr 2026 - 7:25

score 49 · Answer 6 · 2026-04-11 03:48:03

49

Views

How to solve this integral with two pole point and imaginary unit i?

Published on 11 Apr 2026 - 3:48

score 177 · Answer 7 · 2026-04-14 02:22:53

177

Views

Infinite series over recursive digit-counts

Published on 14 Apr 2026 - 2:22

score 23 · Answer 8 · 2026-04-14 09:36:29

23

Views

What does a Convergent Sequence of Improper Integrals Tell You About the Convergence of the Integrands?

Published on 14 Apr 2026 - 9:36

score 105 · Answer 9 · 2026-04-16 10:47:57

105

Views

Improper integral $\int_0^{+\infty} (\sqrt{x+\cos(x)}-\sqrt{x})\mathrm dx$

Published on 16 Apr 2026 - 10:47

score 56 · Answer 10 · 2026-04-10 16:09:46

56

Views

Improper integral with residue theorem and interpretation

Published on 10 Apr 2026 - 16:09

score 132 · Answer 11 · 2026-04-16 11:36:34

132

Views

How to evaluate $\int \frac{\text{sinc}\left(\sqrt{e^x}\right)}{4a^2} + x^{\phi(p)} \, dx$

Published on 16 Apr 2026 - 11:36

score 785 · Answer 12 · 2026-04-16 02:11:55

785

Views

Show that $\int_{-\pi/2}^{\pi/2}\sin(\tan(\tan(x)))\tan(x)dx=\frac{\pi}{e^{(e^2-1)/(e^2+1)}}-\frac{\pi}{e}$

Published on 16 Apr 2026 - 2:11

score 40 · Answer 13 · 2026-04-14 18:48:10

40

Views

Why not use real Gaussian formulas to evaluate complex ones?

Published on 14 Apr 2026 - 18:48

score 26 · Answer 14 · 2026-03-25 15:10:44

26

Views

Cauchy conversion Criteria Integral

Published on 25 Mar 2026 - 15:10

score 131 · Answer 15 · 2026-04-15 20:56:51

131

Views

How to evaluate $I = \int_{0}^{1}\frac{\arctan^2(x)\log(1-x)}{1+x^2}\,dx$

Published on 15 Apr 2026 - 20:56

List Question

$\int_0^\infty \frac{\ln x}{(1+e^{x})^2}dx$ by contour integration

Closed form for an improper integral

The reason that conditionally convergent integral produce different results

$I = \int_0^{\pi/2} \left( \int_0^{\pi/2} \frac{\log(\cos(x/2)) - \log(\cos(y/2))}{\cos(x) - \cos(y)} dx\right) \ dy $

An improper integral relates to Gamma function

How to solve this integral with two pole point and imaginary unit i?

Infinite series over recursive digit-counts

What does a Convergent Sequence of Improper Integrals Tell You About the Convergence of the Integrands?

Improper integral $\int_0^{+\infty} (\sqrt{x+\cos(x)}-\sqrt{x})\mathrm dx$

Improper integral with residue theorem and interpretation

How to evaluate $\int \frac{\text{sinc}\left(\sqrt{e^x}\right)}{4a^2} + x^{\phi(p)} \, dx$

Show that $\int_{-\pi/2}^{\pi/2}\sin(\tan(\tan(x)))\tan(x)dx=\frac{\pi}{e^{(e^2-1)/(e^2+1)}}-\frac{\pi}{e}$

Why not use real Gaussian formulas to evaluate complex ones?

Cauchy conversion Criteria Integral

How to evaluate $I = \int_{0}^{1}\frac{\arctan^2(x)\log(1-x)}{1+x^2}\,dx$

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