Question

Do integrals $\int_0^\pi \frac{x}{\sin{x}}dx$ and $\int_0^\pi \frac{x}{\sqrt{\sin{x}}}dx$ converge?

score 219 · Answer 1 · 2016-08-24 11:59:56

219

Views

Do integrals $\int_0^\pi \frac{x}{\sin{x}}dx$ and $\int_0^\pi \frac{x}{\sqrt{\sin{x}}}dx$ converge?

Published on 24 Aug 2016 - 11:59

score 266 · Answer 2 · 2016-08-25 22:36:37

266

Views

How do I evaluate $\int_{-\infty}^{\infty}(1-x^{2})e^{-x^{2}}\mathrm{d}x$ using simple calculus?

Published on 25 Aug 2016 - 22:36

score 309 · Answer 3 · 2026-03-26 16:10:46

309

Views

Turning Incomplete Beta Integral to Complete Beta Integral

Published on 26 Mar 2026 - 16:10

score 225 · Answer 4 · 2016-08-27 17:29:49

225

Views

improper integral with logarithm $x \mapsto \infty$

Published on 27 Aug 2016 - 17:29

score 3.7k · Answer 5 · 2016-08-28 21:59:51

3.7k

Views

Limit comparison test for Improper Integrals

Published on 28 Aug 2016 - 21:59

score 665 · Answer 6 · 2016-08-31 00:42:18

665

Views

Tools for investigating the convergence of the improper integral $\int_0^1\cos(1/x)\mathrm dx$ and similar integrals

Published on 31 Aug 2016 - 0:42

score 103 · Answer 7 · 2026-03-27 00:55:02

103

Views

Euler-Langrange equation for improper action integral

Published on 27 Mar 2026 - 0:55

score 212 · Answer 8 · 2026-04-01 03:09:16

212

Views

Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.

Published on 01 Apr 2026 - 3:09

score 1.1k · Answer 9 · 2026-03-25 13:58:12

1.1k

Views

Provide us a detailed explanation to calculate the Mellin transform of a cosine function, and get the closed form of a related sum

Published on 25 Mar 2026 - 13:58

score 2.9k · Answer 10 · 2016-09-03 08:19:26

2.9k

Views

why doesn't wolfram alpha evaluate this integral?

Published on 03 Sep 2016 - 8:19

score 382 · Answer 11 · 2016-09-03 15:57:02

382

Views

Find integral $\int_0^1 \frac{\ln x}{1 - x^2} \mathrm{d}x$

Published on 03 Sep 2016 - 15:57

score 1.3k · Answer 12 · 2026-04-01 03:12:58

1.3k

Views

Improper Integral $\int_0^\infty\left(\frac{\tanh(x)}{x^3}-\frac1{x^2\cosh^2(x)}\right)dx = \frac{7\zeta(3)}{\pi^2} $

Published on 01 Apr 2026 - 3:12

score 412 · Answer 13 · 2026-04-01 03:07:29

412

Views

Improper Integral $\int_0^\infty\tan\left(\frac x{\sqrt{x^3+x^2}}\right)\frac{\ln(1+\sqrt x)}xdx$

Published on 01 Apr 2026 - 3:07

score 715 · Answer 14 · 2016-09-05 14:11:14

715

Views

Calculate area under curve $(y+1)^2 x=1$ in first quadrant

Published on 05 Sep 2016 - 14:11

score 69 · Answer 15 · 2026-04-09 04:13:27

69

Views

Improper integral with parameter help needed

Published on 09 Apr 2026 - 4:13

List Question

Do integrals $\int_0^\pi \frac{x}{\sin{x}}dx$ and $\int_0^\pi \frac{x}{\sqrt{\sin{x}}}dx$ converge?

How do I evaluate $\int_{-\infty}^{\infty}(1-x^{2})e^{-x^{2}}\mathrm{d}x$ using simple calculus?

Turning Incomplete Beta Integral to Complete Beta Integral

improper integral with logarithm $x \mapsto \infty$

Limit comparison test for Improper Integrals

Tools for investigating the convergence of the improper integral $\int_0^1\cos(1/x)\mathrm dx$ and similar integrals

Euler-Langrange equation for improper action integral

Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.

Provide us a detailed explanation to calculate the Mellin transform of a cosine function, and get the closed form of a related sum

why doesn't wolfram alpha evaluate this integral?

Find integral $\int_0^1 \frac{\ln x}{1 - x^2} \mathrm{d}x$

Improper Integral $\int_0^\infty\left(\frac{\tanh(x)}{x^3}-\frac1{x^2\cosh^2(x)}\right)dx = \frac{7\zeta(3)}{\pi^2} $

Improper Integral $\int_0^\infty\tan\left(\frac x{\sqrt{x^3+x^2}}\right)\frac{\ln(1+\sqrt x)}xdx$

Calculate area under curve $(y+1)^2 x=1$ in first quadrant

Improper integral with parameter help needed

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