Question

Sovling an improper integral in $\mathbb R^2$

score 220 · Answer 1 · 2018-04-05 13:22:40

220

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Sovling an improper integral in $\mathbb R^2$

Published on 05 Apr 2018 - 13:22

score 272 · Answer 2 · 2018-04-05 13:28:52

272

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Improper integral of the form $I=\int_{0}^{\infty} \frac{\sin(ax)}{x^2+b^2}dx$

Published on 05 Apr 2018 - 13:28

score 43 · Answer 3 · 2018-04-05 21:43:01

43

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Let $f:[a,\infty) \rightarrow \mathbb{R}$ continuous and $f(t)\ge0$, prove $F(x)=\int_a^{x}f(t)dt$ is increasing

Published on 05 Apr 2018 - 21:43

score 304 · Answer 4 · 2026-03-25 11:33:00

304

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Solution of the integral $\int_{0}^{R} x^{\lambda} (1-x)^{\mu-1} K_{1}(a\sqrt{x}) \, dx$

Published on 25 Mar 2026 - 11:33

score 111 · Answer 5 · 2026-03-25 12:31:21

111

Views

Differentiability of an (improper) integral

Published on 25 Mar 2026 - 12:31

score 332 · Answer 6 · 2026-03-25 13:51:50

332

Views

How to integrate gamma function

Published on 25 Mar 2026 - 13:51

score 85 · Answer 7 · 2018-04-08 15:57:24

85

Views

Compute the following improper integral with parameters:

Published on 08 Apr 2018 - 15:57

score 1.5k · Answer 8 · 2018-04-08 21:45:38

1.5k

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Evaluate $\int_1^\infty \left(\frac{\log x}{x}\right)^{2011}dx$.

Published on 08 Apr 2018 - 21:45

score 436 · Answer 9 · 2026-03-25 04:36:31

436

Views

Ratio of integrals

Published on 25 Mar 2026 - 4:36

score 76 · Answer 10 · 2018-04-09 10:34:03

76

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find $I=\int_0^{\infty} \log{(x+1/x)}\,\frac{dx}{1+x^2} $

Published on 09 Apr 2018 - 10:34

score 133 · Answer 11 · 2026-03-22 19:24:53

133

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Integral - Combinations of logarithms, exponentials, and powers $\int_0^\infty x^{\nu-1}\ e^{-\mu x}\ \ln(x+a)\,dx$

Published on 22 Mar 2026 - 19:24

score 124 · Answer 12 · 2018-04-09 15:42:19

124

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Show that $\int_0^{\infty} \frac{dx}{(x+\sqrt{1+x^2})^n}$ converges and is equal to $\frac{n}{n^2-1}$

Published on 09 Apr 2018 - 15:42

score 55 · Answer 13 · 2018-04-09 18:24:22

55

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Show that $I=\int_0^{\infty}e^{-a^2x^2}x^m\sin{nx}\,dx$ is absolutely converges for $m>0$

Published on 09 Apr 2018 - 18:24

score 303 · Answer 14 · 2026-03-25 00:02:19

303

Views

Integrating the Gaussian function over (nearly) symmetric bounds

Published on 25 Mar 2026 - 0:02

score 296 · Answer 15 · 2018-04-10 10:21:55

296

Views

Integral $\int_0^{\infty} \frac{x\cos^2 x}{e^x-1}dx$

Published on 10 Apr 2018 - 10:21

List Question

Sovling an improper integral in $\mathbb R^2$

Improper integral of the form $I=\int_{0}^{\infty} \frac{\sin(ax)}{x^2+b^2}dx$

Let $f:[a,\infty) \rightarrow \mathbb{R}$ continuous and $f(t)\ge0$, prove $F(x)=\int_a^{x}f(t)dt$ is increasing

Solution of the integral $\int_{0}^{R} x^{\lambda} (1-x)^{\mu-1} K_{1}(a\sqrt{x}) \, dx$

Differentiability of an (improper) integral

How to integrate gamma function

Compute the following improper integral with parameters:

Evaluate $\int_1^\infty \left(\frac{\log x}{x}\right)^{2011}dx$.

Ratio of integrals

find $I=\int_0^{\infty} \log{(x+1/x)}\,\frac{dx}{1+x^2} $

Integral - Combinations of logarithms, exponentials, and powers $\int_0^\infty x^{\nu-1}\ e^{-\mu x}\ \ln(x+a)\,dx$

Show that $\int_0^{\infty} \frac{dx}{(x+\sqrt{1+x^2})^n}$ converges and is equal to $\frac{n}{n^2-1}$

Show that $I=\int_0^{\infty}e^{-a^2x^2}x^m\sin{nx}\,dx$ is absolutely converges for $m>0$

Integrating the Gaussian function over (nearly) symmetric bounds

Integral $\int_0^{\infty} \frac{x\cos^2 x}{e^x-1}dx$

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