List questions from improper-integrals

Published on 06 Nov 2019 - 17:08

95

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An intriguing relationship between pairs of integrals

Published on 06 Nov 2019 - 21:24

867

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Integral $\int_{-\infty}^\infty \frac{\exp{(-x^2)}}{1+x^4}dx$

Published on 07 Nov 2019 - 11:26

104

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Convergence test for series $\sum_{k\geq 0}\int_{k\pi}^{(k+1)\pi}\frac{\sin{x}}{x}dx=\frac{\pi}{2}$

Published on 02 Apr 2026 - 5:35

58

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The Closed-Form of $\displaystyle \int_{0}^{1}\mathrm{li}(x)\ln\Big(\ln\Big(\frac{1}{x}\Big)\Big) \mathrm{d}x$

Published on 30 Mar 2026 - 8:36

60

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Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}\left(x\right)}{x}dx$

Published on 10 Nov 2019 - 9:31

558

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Using L'Hopital Rule on a limit that does not exist

Published on 11 Nov 2019 - 2:26

180

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Is this integral evaluation legitimate?

Published on 25 Mar 2026 - 10:59

65

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Compute $\mathbb{E}[\Phi^n(\mu-\sigma X)]$, where $\Phi$ is the standard normal CDF and $X\sim\Phi$

Published on 02 Apr 2026 - 23:38

128

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The Convergence of the improper integral

Published on 12 Nov 2019 - 8:18

31

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Well-definedness of improper integral that converges.

Published on 12 Nov 2019 - 11:07

37

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Is it possible to solve/approximate this relation?

Published on 29 Mar 2026 - 22:13

242

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Exponential Integrals: What is the derivative of the exponential integral $E_n(x)$?

Published on 12 Nov 2019 - 20:37

265

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An improper integral of an exponential with rational fraction argument

Published on 29 Mar 2026 - 8:18

79

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an improper integral or establish its divergence by definition

Published on 14 Nov 2019 - 20:54

List Question

Evaluate the integral from $0$ to $\infty$

An intriguing relationship between pairs of integrals

Integral $\int_{-\infty}^\infty \frac{\exp{(-x^2)}}{1+x^4}dx$

Convergence test for series $\sum_{k\geq 0}\int_{k\pi}^{(k+1)\pi}\frac{\sin{x}}{x}dx=\frac{\pi}{2}$

The Closed-Form of $\displaystyle \int_{0}^{1}\mathrm{li}(x)\ln\Big(\ln\Big(\frac{1}{x}\Big)\Big) \mathrm{d}x$

Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}\left(x\right)}{x}dx$

Using L'Hopital Rule on a limit that does not exist

Is this integral evaluation legitimate?

Compute $\mathbb{E}[\Phi^n(\mu-\sigma X)]$, where $\Phi$ is the standard normal CDF and $X\sim\Phi$

The Convergence of the improper integral

Well-definedness of improper integral that converges.

Is it possible to solve/approximate this relation?

Exponential Integrals: What is the derivative of the exponential integral $E_n(x)$?

An improper integral of an exponential with rational fraction argument

an improper integral or establish its divergence by definition

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