List questions from improper-integrals

317

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Two limits involving integrals: $\lim_{\varepsilon\to 0^+}\left(\int_0^{1-\varepsilon}\frac{\ln (1-x)}{x\ln^p x}dx-f_p(\varepsilon)\right)$, $p=1,2$.

Published on 17 Aug 2016 - 13:59

413

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How to solve integral with rational function of exponential functions using Residue Theorem?

Published on 09 Apr 2026 - 1:40

90

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Integral proof involving periodic functions

Published on 30 Mar 2026 - 22:44

738

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Two integrals involving $\sqrt{\cosh x}$

Published on 19 Aug 2016 - 9:13

539

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Prove this integral $\int_0^\infty \frac{dx}{\sqrt{x^4+a^4}+\sqrt{x^4+b^4}}=\frac{\Gamma(1/4)^2 }{6 \sqrt{\pi}} \frac{a^3-b^3}{a^4-b^4}$

Published on 26 Mar 2026 - 16:10

141

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When does $\int_1^\infty \frac{x^a}{1+x^a} dx$ converge?

Published on 21 Aug 2016 - 2:20

80

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How to procced in following integration

Published on 09 Apr 2026 - 3:32

603

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What's about the Laplace transform of the Gudermannian function?

Published on 02 Apr 2026 - 11:26

56

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Expressing an lntegral in Standard, Nonstandard Functions

Published on 31 Mar 2026 - 7:13

122

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Problem in integrations

Published on 05 Apr 2026 - 0:16

82

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Integration with trigonometry

Published on 06 Apr 2026 - 4:52

214

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Differentiate solution to Laplace's equation

Published on 26 Mar 2026 - 13:01

613

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Integration with multidimensional delta function.

Published on 07 Apr 2026 - 20:16

474

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integral $\int_0^{\pi} \left( \frac{\pi}{2} - x \right) \frac{\tan x}{x} \, {\rm d}x$

Published on 23 Aug 2016 - 17:15

705

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Evaluate an improper integral involving log

Published on 06 Apr 2026 - 19:29

List Question

Two limits involving integrals: $\lim_{\varepsilon\to 0^+}\left(\int_0^{1-\varepsilon}\frac{\ln (1-x)}{x\ln^p x}dx-f_p(\varepsilon)\right)$, $p=1,2$.

How to solve integral with rational function of exponential functions using Residue Theorem?

Integral proof involving periodic functions

Two integrals involving $\sqrt{\cosh x}$

Prove this integral $\int_0^\infty \frac{dx}{\sqrt{x^4+a^4}+\sqrt{x^4+b^4}}=\frac{\Gamma(1/4)^2 }{6 \sqrt{\pi}} \frac{a^3-b^3}{a^4-b^4}$

When does $\int_1^\infty \frac{x^a}{1+x^a} dx$ converge?

How to procced in following integration

What's about the Laplace transform of the Gudermannian function?

Expressing an lntegral in Standard, Nonstandard Functions

Problem in integrations

Integration with trigonometry

Differentiate solution to Laplace's equation

Integration with multidimensional delta function.

integral $\int_0^{\pi} \left( \frac{\pi}{2} - x \right) \frac{\tan x}{x} \, {\rm d}x$

Evaluate an improper integral involving log

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