Question

Integral $\int_0^1 x^n\, \text{li}(x) \, dx$

score 154 · Answer 1 · 2019-07-25 18:35:36

154

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Integral $\int_0^1 x^n\, \text{li}(x) \, dx$

Published on 25 Jul 2019 - 18:35

score 347 · Answer 2 · 2019-07-26 05:33:17

347

Views

Computing whether $\int_0^\infty \frac{\ln{x}}{x^2} dx$ converges or diverges using the comparison theorem

Published on 26 Jul 2019 - 5:33

score 1.5k · Answer 3 · 2026-03-31 12:16:34

1.5k

Views

Integral $ \int_0^\infty \frac{\ln x}{(x+c)(x-1)} dx$

Published on 31 Mar 2026 - 12:16

score 43 · Answer 4 · 2019-07-28 10:31:54

43

Views

Limit of a function times an improper integral

Published on 28 Jul 2019 - 10:31

score 97 · Answer 5 · 2019-07-28 22:40:23

97

Views

How to prove that $\int\limits_{-\infty}^\infty \frac{x^{1/3}}{\sqrt{1+x^2}}\,dx$ does not converge?

Published on 28 Jul 2019 - 22:40

score 293 · Answer 6 · 2019-07-28 22:52:14

293

Views

For which real $a$ and $b$ is $I=\int _1^{\infty }\frac{x^a}{1+x^b}dx$ convergent? divergent?

Published on 28 Jul 2019 - 22:52

score 3.7k · Answer 7 · 2019-07-28 23:51:40

3.7k

Views

A lucky proof for the Basel problem.

Published on 28 Jul 2019 - 23:51

score 58 · Answer 8 · 2019-07-29 13:21:37

58

Views

Is $\int_a^b \frac{f(x)}{g(x)}g(x)\,dx$ improper integral when $g(a)=0$?

Published on 29 Jul 2019 - 13:21

score 92 · Answer 9 · 2019-07-29 19:36:10

92

Views

What's my mistake in finding $\int_0^\infty dx e^{-ax^2} \sin(b/x^2)$?

Published on 29 Jul 2019 - 19:36

score 608 · Answer 10 · 2019-07-31 15:28:27

608

Views

Abel-Dirichlet improper integral test (without continuity required)

Published on 31 Jul 2019 - 15:28

score 126 · Answer 11 · 2026-03-30 10:13:12

126

Views

Integrate $ I(x) = \frac{1}{2 \pi}\int\limits_{-\infty}^{\infty} \frac{1}{(1-jt)^{N}} e^{\frac{jaNt}{1-jt}} e^{-jxt} dt$

Published on 30 Mar 2026 - 10:13

score 120 · Answer 12 · 2019-08-01 11:49:28

120

Views

Use $\int_1^\infty\frac{e^y}{y^y}dy$ to show $\sum_{i=2}^\infty\frac{1}{(\ln(n))^{\ln(n)}}$ converges

Published on 01 Aug 2019 - 11:49

score 106 · Answer 13 · 2026-03-29 11:06:59

106

Views

Integrate $I(x) = \frac{1}{ 2 \pi} \int_{-\infty}^{\infty} \frac{e^{-Na}}{jt(1+jt)} e^{\frac{Na}{1+jt}} e^{jxt}dt $

Published on 29 Mar 2026 - 11:06

score 405 · Answer 14 · 2026-03-25 09:32:03

405

Views

How can I prove $\frac{\gamma}{2}=\int_{0}^{\infty}\frac{e^{-x^{2}}-e^{-x}}{x}\text{d}x$?

Published on 25 Mar 2026 - 9:32

score 172 · Answer 15 · 2019-08-03 13:48:28

172

Views

Check convergence of improper integral

Published on 03 Aug 2019 - 13:48

List Question

Integral $\int_0^1 x^n\, \text{li}(x) \, dx$

Computing whether $\int_0^\infty \frac{\ln{x}}{x^2} dx$ converges or diverges using the comparison theorem

Integral $ \int_0^\infty \frac{\ln x}{(x+c)(x-1)} dx$

Limit of a function times an improper integral

How to prove that $\int\limits_{-\infty}^\infty \frac{x^{1/3}}{\sqrt{1+x^2}}\,dx$ does not converge?

For which real $a$ and $b$ is $I=\int _1^{\infty }\frac{x^a}{1+x^b}dx$ convergent? divergent?

A lucky proof for the Basel problem.

Is $\int_a^b \frac{f(x)}{g(x)}g(x)\,dx$ improper integral when $g(a)=0$?

What's my mistake in finding $\int_0^\infty dx e^{-ax^2} \sin(b/x^2)$?

Abel-Dirichlet improper integral test (without continuity required)

Integrate $ I(x) = \frac{1}{2 \pi}\int\limits_{-\infty}^{\infty} \frac{1}{(1-jt)^{N}} e^{\frac{jaNt}{1-jt}} e^{-jxt} dt$

Use $\int_1^\infty\frac{e^y}{y^y}dy$ to show $\sum_{i=2}^\infty\frac{1}{(\ln(n))^{\ln(n)}}$ converges

Integrate $I(x) = \frac{1}{ 2 \pi} \int_{-\infty}^{\infty} \frac{e^{-Na}}{jt(1+jt)} e^{\frac{Na}{1+jt}} e^{jxt}dt $

How can I prove $\frac{\gamma}{2}=\int_{0}^{\infty}\frac{e^{-x^{2}}-e^{-x}}{x}\text{d}x$?

Check convergence of improper integral

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