List questions from improper-integrals

Published on 29 Mar 2026 - 20:23

57

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Convergence, continuity, differentiability of an improper integral

Published on 04 Apr 2026 - 10:21

76

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Compute $\int_{0}^{+\infty} \frac{\sin(nx^n)}{nx^{n + 1/2}} \textrm{d}x$

Published on 03 Apr 2026 - 22:06

49

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Can the definite integral be written as the difference of two integrals with lower limits of $-\infty$

Published on 13 Dec 2019 - 17:43

237

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Square integrable smooth functions on punctured disk

Published on 13 Dec 2019 - 19:32

53

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Proving a limit with Dominated convergence theorem

Published on 24 Feb 2026 - 0:46

191

Views

Convergence or divergence for $\int_1^\infty \frac{1}{x\sqrt{x}-1} dx$

Published on 14 Dec 2019 - 20:46

145

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Integral $\int_0^{\infty}\frac{\ln(x)}{x^2+nx+n^2}dx=\frac{2\pi}{3\sqrt{3}}\frac{\ln(n)}{n}$

Published on 15 Dec 2019 - 18:42

216

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Convergence or divergence for $\int _0 ^\infty e^{\sin x} \frac{\sin 2x}{x^\lambda } dx,\lambda>0$

Published on 15 Dec 2019 - 19:27

62

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investigate conditional and absolute convergence of improper integral

Published on 26 Mar 2026 - 4:32

68

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$\int_{0}^{\infty}\frac{x^{s}}{ax^{3}+bx^{2}+cx+d}dx$

Published on 30 Mar 2026 - 11:58

54

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Show $\lim_{x\to +\infty} \int_1^x \frac 1{x^\alpha+t^\beta}\;\mathrm{d} t = 0$.

Published on 16 Dec 2019 - 11:40

61

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Problem with improper integral with parameter

Published on 16 Dec 2019 - 20:23

108

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Evaluate integral $\int_1^\infty\frac{x^2-2}{x^4+3}dx$

Published on 17 Dec 2019 - 3:04

40

Views

Dominated convergence theorem with function $\frac{1}{x^{\frac12+\frac1n}}\left(\sin\frac{\pi}{x}\right)^n$

Published on 17 Dec 2019 - 13:27

List Question

$\int _0 ^\infty \frac{1}{(x+1)(1-x) \sqrt{x}} dx$

Convergence, continuity, differentiability of an improper integral

Compute $\int_{0}^{+\infty} \frac{\sin(nx^n)}{nx^{n + 1/2}} \textrm{d}x$

Can the definite integral be written as the difference of two integrals with lower limits of $-\infty$

Square integrable smooth functions on punctured disk

Proving a limit with Dominated convergence theorem

Convergence or divergence for $\int_1^\infty \frac{1}{x\sqrt{x}-1} dx$

Integral $\int_0^{\infty}\frac{\ln(x)}{x^2+nx+n^2}dx=\frac{2\pi}{3\sqrt{3}}\frac{\ln(n)}{n}$

Convergence or divergence for $\int _0 ^\infty e^{\sin x} \frac{\sin 2x}{x^\lambda } dx,\lambda>0$

investigate conditional and absolute convergence of improper integral

$\int_{0}^{\infty}\frac{x^{s}}{ax^{3}+bx^{2}+cx+d}dx$

Show $\lim_{x\to +\infty} \int_1^x \frac 1{x^\alpha+t^\beta}\;\mathrm{d} t = 0$.

Problem with improper integral with parameter

Evaluate integral $\int_1^\infty\frac{x^2-2}{x^4+3}dx$

Dominated convergence theorem with function $\frac{1}{x^{\frac12+\frac1n}}\left(\sin\frac{\pi}{x}\right)^n$

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