Question

Derivation of parametric integral function

score 123 · Answer 1 · 2026-04-12 13:58:57

123

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Derivation of parametric integral function

Published on 12 Apr 2026 - 13:58

score 62 · Answer 2 · 2026-04-15 17:34:37

62

Views

Determine $ \int_0^\infty \frac{\sin x - e^{-x}-1}{x^{\frac{5}{2}}(x+1)}dx $ converge or not, using only Limit comparison test

Published on 15 Apr 2026 - 17:34

score 68 · Answer 3 · 2026-04-13 21:17:50

68

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Error estimate of discretization of inproper integral

Published on 13 Apr 2026 - 21:17

score 105 · Answer 4 · 2026-04-16 17:17:16

105

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Evaluate $\int_0^{\infty} \frac{ \operatorname{erf}^2(x)}{x^2}dx$, where, $\operatorname{erf}(x)=\frac{2}{\sqrt\pi}\int_0^x e^{-t^2}dt$

Published on 16 Apr 2026 - 17:17

score 33 · Answer 5 · 2026-04-14 22:53:37

33

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Convergence of $\int_{1}^{\infty}\frac{a^x}{\sqrt{x}}dx$ for $a>0$

Published on 14 Apr 2026 - 22:53

score 818 · Answer 6 · 2026-04-16 21:40:27

818

Views

$\int_0^\infty \frac{u^5 \, J_0\left( u\right)}{\left( u^2+x^2 \right)^{1/2}}\,e^{- u-\left( u^2+x^2 \right)^{1/2} }\,\mathrm{d}u $

Published on 16 Apr 2026 - 21:40

score 76 · Answer 7 · 2026-04-14 04:16:53

76

Views

How to prove, that integral is divergent $\int_{1}^{\infty} \frac{e^{1/x}-1}{2^{1/x}} \mathrm{d}x$

Published on 14 Apr 2026 - 4:16

score 73 · Answer 8 · 2026-04-12 03:36:59

73

Views

Generalisation of a definite integral $I(a)$ with value independent of its parameter $a$.

Published on 12 Apr 2026 - 3:36

score 165 · Answer 9 · 2026-04-17 03:48:47

165

Views

Evaluating $\displaystyle\int_{0}^{\infty} \frac{{x}^{2/3}-{x}^{1/4}}{(1+{x}^{2})\ln(x)} dx$ using the gamma and beta functions

Published on 17 Apr 2026 - 3:48

score 56 · Answer 10 · 2026-04-17 01:15:31

56

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Convergence of $\int _0^{\infty }\:\left(-1\right)^{\left[x^2\right]}$ It's clear to me it doesn't converge absolutely as $\int_0^\infty\:1$ doesn't

Published on 17 Apr 2026 - 1:15

score 58 · Answer 11 · 2026-04-17 12:08:47

58

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Computing $\int_{1}^{\infty}\left(\frac{1}{t}-\text{arcsin}\left(\frac{1}{t}\right)\right)\text{d}t$

Published on 17 Apr 2026 - 12:08

score 126 · Answer 12 · 2026-04-15 22:41:48

126

Views

Check for uniform convergence of the integral $\int\limits_{0}^{1}\frac{\arctan ax}{(1-x^2)^a}dx$

Published on 15 Apr 2026 - 22:41

score 42 · Answer 13 · 2026-04-13 05:58:15

if $f(x)$ is a real rational function with denominator of degree at least two units higher than degree of the numerator Then improper integral exist

score 191 · Answer 14 · 2026-04-16 04:26:05

191

Views

Abel-Plana formula for $\int_0^\infty \frac{f(x)}{e^{2\pi x}-1}dx$ and $\int_0^\infty \frac{f(x)}{\sinh(\pi x)}dx$

Published on 16 Apr 2026 - 4:26

score 92 · Answer 15 · 2026-04-15 05:03:47

92

Views

How to evaluate $\int_{-\infty}^{\infty} e^{-k^{2} t^{2}-\frac{z^2}{4t^{2}}} dt$

Published on 15 Apr 2026 - 5:03

List Question

Derivation of parametric integral function

Determine $ \int_0^\infty \frac{\sin x - e^{-x}-1}{x^{\frac{5}{2}}(x+1)}dx $ converge or not, using only Limit comparison test

Error estimate of discretization of inproper integral

Evaluate $\int_0^{\infty} \frac{ \operatorname{erf}^2(x)}{x^2}dx$, where, $\operatorname{erf}(x)=\frac{2}{\sqrt\pi}\int_0^x e^{-t^2}dt$

Convergence of $\int_{1}^{\infty}\frac{a^x}{\sqrt{x}}dx$ for $a>0$

$\int_0^\infty \frac{u^5 \, J_0\left( u\right)}{\left( u^2+x^2 \right)^{1/2}}\,e^{- u-\left( u^2+x^2 \right)^{1/2} }\,\mathrm{d}u $

How to prove, that integral is divergent $\int_{1}^{\infty} \frac{e^{1/x}-1}{2^{1/x}} \mathrm{d}x$

Generalisation of a definite integral $I(a)$ with value independent of its parameter $a$.

Evaluating $\displaystyle\int_{0}^{\infty} \frac{{x}^{2/3}-{x}^{1/4}}{(1+{x}^{2})\ln(x)} dx$ using the gamma and beta functions

Convergence of $\int _0^{\infty }\:\left(-1\right)^{\left[x^2\right]}$ It's clear to me it doesn't converge absolutely as $\int_0^\infty\:1$ doesn't

Computing $\int_{1}^{\infty}\left(\frac{1}{t}-\text{arcsin}\left(\frac{1}{t}\right)\right)\text{d}t$

Check for uniform convergence of the integral $\int\limits_{0}^{1}\frac{\arctan ax}{(1-x^2)^a}dx$

if $f(x)$ is a real rational function with denominator of degree at least two units higher than degree of the numerator Then improper integral exist

Abel-Plana formula for $\int_0^\infty \frac{f(x)}{e^{2\pi x}-1}dx$ and $\int_0^\infty \frac{f(x)}{\sinh(\pi x)}dx$

How to evaluate $\int_{-\infty}^{\infty} e^{-k^{2} t^{2}-\frac{z^2}{4t^{2}}} dt$

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