List questions from improper-integrals

Published on 16 Apr 2026 - 23:05

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$\int \frac{e^{-x}}{\sqrt{x}}\,\mathrm dx$

Published on 15 Apr 2026 - 20:21

173

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Integral $\int_0^{\infty} \log(x) e^{-x^2} \mathrm{d}x = -\frac{1}{4}\sqrt{\pi} (\gamma + \log(4)).$

Published on 26 Mar 2026 - 12:06

257

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A Mathematical Proof for an Improper Integral

Published on 12 Apr 2026 - 0:36

1.5k

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Integrating a special skew normal -- the CDF of a convolution of a normal with a truncated normal

Published on 14 Apr 2026 - 15:20

614

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Integral $\int_0^\infty\exp\left(-\sqrt2\,x^2\right)\,\operatorname{erfi}(x)\,\log(x)\,x^3\,dx$

Published on 17 Apr 2026 - 9:26

902

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Integral through Fourier Transform and Parseval's Identity

Published on 18 Apr 2026 - 19:56

82

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Nature of the improper integral $\int_{0}^{\infty}{\dfrac{1}{t}}dt$

Published on 15 Apr 2026 - 12:58

170

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Differentiation under integral sign help

Published on 12 Apr 2026 - 1:34

763

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Evaluate integral $\int_0^\frac{\pi}{2}x\ln(\sin x)~dx$

Published on 17 Apr 2026 - 11:58

59

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perturbative series expansion of integral via complex integration

Published on 12 Apr 2026 - 15:46

203

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How do I compute this improper integral?

Published on 09 Apr 2026 - 11:36

50

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mean of a probability density function

Published on 13 Apr 2026 - 3:44

120

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for any $k\in N$, p.v$\int_{a}^{b}\frac{\cos kx}{t-x}dx=?$

Published on 16 Apr 2026 - 9:13

108

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How does one prove this formula?

Published on 09 Apr 2026 - 23:37

List Question

$\lim_{\varepsilon \to 0}\int_{|x|>\varepsilon}\frac{e^{-(t-x)^2}}{x}dx=?$

$\int \frac{e^{-x}}{\sqrt{x}}\,\mathrm dx$

Integral $\int_0^{\infty} \log(x) e^{-x^2} \mathrm{d}x = -\frac{1}{4}\sqrt{\pi} (\gamma + \log(4)).$

A Mathematical Proof for an Improper Integral

Integrating a special skew normal -- the CDF of a convolution of a normal with a truncated normal

Integral $\int_0^\infty\exp\left(-\sqrt2\,x^2\right)\,\operatorname{erfi}(x)\,\log(x)\,x^3\,dx$

Integral through Fourier Transform and Parseval's Identity

Nature of the improper integral $\int_{0}^{\infty}{\dfrac{1}{t}}dt$

Differentiation under integral sign help

Evaluate integral $\int_0^\frac{\pi}{2}x\ln(\sin x)~dx$

perturbative series expansion of integral via complex integration

How do I compute this improper integral?

mean of a probability density function

for any $k\in N$, p.v$\int_{a}^{b}\frac{\cos kx}{t-x}dx=?$

How does one prove this formula?

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