Question

Prove $\int_{-\infty}^{\infty} \frac{du}{(1+u^{2})^{\frac{7-p}{2}}} =\frac{\sqrt{\pi}\Gamma[\frac{1}{2}(6-p)]}{\Gamma[\frac{1}{2}(7-p)]}$

score 90 · Answer 1 · 2014-07-16 15:01:55

Prove $\int_{-\infty}^{\infty} \frac{du}{(1+u^{2})^{\frac{7-p}{2}}} =\frac{\sqrt{\pi}\Gamma[\frac{1}{2}(6-p)]}{\Gamma[\frac{1}{2}(7-p)]}$

score 113 · Answer 2 · 2026-03-28 05:20:55

113

Views

Improper parametric arc length

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score 210 · Answer 3 · 2026-03-30 13:59:12

210

Views

Trying to solve $\int{-2\exp{\left(z\cos^2 \theta \frac{\left(a^2 - 1\right)}{2a^2}\right)}}d\theta$

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score 807 · Answer 4 · 2014-07-16 23:26:08

807

Views

An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$

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score 252 · Answer 5 · 2014-07-18 06:58:14

252

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score 148 · Answer 6 · 2026-03-22 17:34:27

148

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Fresnel Integral multiplied with cosine term.

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score 273 · Answer 7 · 2014-07-19 10:28:10

273

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Improper integral $\int_{0}^{\pi} \frac{x}{\sin x} dx$

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score 1.4k · Answer 8 · 2014-07-19 18:41:34

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score 178 · Answer 9 · 2014-07-21 20:54:50

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score 1.8k · Answer 10 · 2026-03-28 06:59:51

1.8k

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A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$

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score 77 · Answer 11 · 2014-07-23 00:35:14

77

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Existence of a function with certain integral properties

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score 126 · Answer 12 · 2014-07-23 12:35:07

126

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Existence of improper integral

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score 835 · Answer 13 · 2014-07-24 10:31:01

835

Views

Evaluate $\int_{0}^{\large\frac{\pi}{4}} \ln {(\sin x)}\cdot\ln {(\cos x)} \left(\frac{\ln{(\sin x)}}{\cot x}+\frac{\ln {(\cos x)}}{\tan x}\right)dx$

Published on 24 Jul 2014 - 10:31

score 1.6k · Answer 14 · 2026-03-28 08:50:13

1.6k

Views

Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ \mathrm dx$

Published on 28 Mar 2026 - 8:50

score 2.3k · Answer 15 · 2026-03-27 21:44:37

2.3k

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Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$

Published on 27 Mar 2026 - 21:44

List Question

Prove $\int_{-\infty}^{\infty} \frac{du}{(1+u^{2})^{\frac{7-p}{2}}} =\frac{\sqrt{\pi}\Gamma[\frac{1}{2}(6-p)]}{\Gamma[\frac{1}{2}(7-p)]}$

Improper parametric arc length

Trying to solve $\int{-2\exp{\left(z\cos^2 \theta \frac{\left(a^2 - 1\right)}{2a^2}\right)}}d\theta$

An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$

How to $\int_{0}^\infty {\sin^3(x)\over x}dx$

Fresnel Integral multiplied with cosine term.

Improper integral $\int_{0}^{\pi} \frac{x}{\sin x} dx$

Improper double integral evaluation by changing the order of integration

Convergence of improper integral of $\ln f(x)$

A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$

Existence of a function with certain integral properties

Existence of improper integral

Evaluate $\int_{0}^{\large\frac{\pi}{4}} \ln {(\sin x)}\cdot\ln {(\cos x)} \left(\frac{\ln{(\sin x)}}{\cot x}+\frac{\ln {(\cos x)}}{\tan x}\right)dx$

Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ \mathrm dx$

Prove ${\large\int}_0^\infty\frac{\ln x}{\sqrt{x}\ \sqrt{x+1}\ \sqrt{2x+1}}dx\stackrel?=\frac{\pi^{3/2}\,\ln2}{2^{3/2}\Gamma^2\left(\tfrac34\right)}$

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