Question

Evaluating $\int_0^{\infty} {y^2 \cos^2(\frac{\pi y}{2}) \over (y^2-1)^2} dy$

score 173 · Answer 1 · 2026-04-16 08:16:10

173

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Evaluating $\int_0^{\infty} {y^2 \cos^2(\frac{\pi y}{2}) \over (y^2-1)^2} dy$

Published on 16 Apr 2026 - 8:16

score 643 · Answer 2 · 2026-04-14 08:54:15

643

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Integral form for the euler-mascheroni gamma constant using floor function

Published on 14 Apr 2026 - 8:54

score 1.6k · Answer 3 · 2026-04-14 04:25:55

1.6k

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if f is continuous and absolutely integrable $\lim\limits_{x\to\infty}f(x)=0$

Published on 14 Apr 2026 - 4:25

score 449 · Answer 4 · 2026-04-17 05:28:31

449

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Proving $\int_0^1\frac{\log (1-x)}{x}\mathrm dx=-\frac{\pi^2}6$

Published on 17 Apr 2026 - 5:28

score 752 · Answer 5 · 2026-03-27 23:48:15

752

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Dilogarithm integral $\int^x_0 \frac{\operatorname{Li}_2(1-t)\log(1-t)}{t}\, dt$

Published on 27 Mar 2026 - 23:48

score 623 · Answer 6 · 2026-04-17 20:51:21

623

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Evaluating $\int_0^\infty \frac{\cos(ax)-e^{-ax}}{x \left(x^4+b^4 \right)}dx$

Published on 17 Apr 2026 - 20:51

score 229 · Answer 7 · 2026-04-13 21:43:49

229

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Commuting an $\int$ improper at its both ends and $\lim$

Published on 13 Apr 2026 - 21:43

score 271 · Answer 8 · 2026-04-14 04:58:34

271

Views

Limit of an improper integral

Published on 14 Apr 2026 - 4:58

score 4.2k · Answer 9 · 2026-04-13 16:54:10

4.2k

Views

Integrating $\cos z/(z^2+1)$

Published on 13 Apr 2026 - 16:54

score 78 · Answer 10 · 2026-04-15 01:15:06

78

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$|f(x)|<|g(x)|$ and $\int g(x)<\infty\Rightarrow\ \int f(x)<\infty$

Published on 15 Apr 2026 - 1:15

score 202 · Answer 11 · 2026-04-17 20:49:15

202

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Evaluating $\int_{0}^{\infty} \frac{1}{1+x^{3/2}}\,\textrm{d}x$

Published on 17 Apr 2026 - 20:49

score 103 · Answer 12 · 2026-04-15 21:29:31

103

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derailed in solving the convergence of $\int_{x=2}^\infty \frac{1}{xe^x} dx$ with a Taylor expansion

Published on 15 Apr 2026 - 21:29

score 747 · Answer 13 · 2026-04-17 04:51:45

747

Views

The integral of $\frac{\cos(x)}{x}$ from $0$ to $1$

Published on 17 Apr 2026 - 4:51

score 430 · Answer 14 · 2026-04-10 13:48:00

430

Views

Improper integral properties

Published on 10 Apr 2026 - 13:48

score 1.5k · Answer 15 · 2026-04-15 22:57:58

1.5k

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Determine if the following integral is convergent or divergent. If it is convergent find its value.

Published on 15 Apr 2026 - 22:57

List Question

Evaluating $\int_0^{\infty} {y^2 \cos^2(\frac{\pi y}{2}) \over (y^2-1)^2} dy$

Integral form for the euler-mascheroni gamma constant using floor function

if f is continuous and absolutely integrable $\lim\limits_{x\to\infty}f(x)=0$

Proving $\int_0^1\frac{\log (1-x)}{x}\mathrm dx=-\frac{\pi^2}6$

Dilogarithm integral $\int^x_0 \frac{\operatorname{Li}_2(1-t)\log(1-t)}{t}\, dt$

Evaluating $\int_0^\infty \frac{\cos(ax)-e^{-ax}}{x \left(x^4+b^4 \right)}dx$

Commuting an $\int$ improper at its both ends and $\lim$

Limit of an improper integral

Integrating $\cos z/(z^2+1)$

$|f(x)|<|g(x)|$ and $\int g(x)<\infty\Rightarrow\ \int f(x)<\infty$

Evaluating $\int_{0}^{\infty} \frac{1}{1+x^{3/2}}\,\textrm{d}x$

derailed in solving the convergence of $\int_{x=2}^\infty \frac{1}{xe^x} dx$ with a Taylor expansion

The integral of $\frac{\cos(x)}{x}$ from $0$ to $1$

Improper integral properties

Determine if the following integral is convergent or divergent. If it is convergent find its value.

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