Question

Improper integral of $\exp[-(a+bi)x]\log x$

score 72 · Answer 1 · 2026-03-17 12:04:29

72

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Improper integral of $\exp[-(a+bi)x]\log x$

Published on 17 Mar 2026 - 12:04

score 195 · Answer 2 · 2026-03-20 00:10:00

195

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Self-convolution of $f(\vec{r}) = e^{-x^2-y^2}/r^2$

Published on 20 Mar 2026 - 0:10

score 84 · Answer 3 · 2018-01-21 12:16:07

84

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How to calculate $\int_0^\infty e^{-x} \prod_{n=1}^\infty (1-e^{-24nx} ) dx$

Published on 21 Jan 2018 - 12:16

score 128 · Answer 4 · 2026-03-22 22:57:09

128

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How can one show that $\int_{0}^{1}{x\ln{x}\ln(1-x^2)\over \sqrt{1-x^2}}\mathrm dx=4-{\pi^2\over 4}-\ln{4}?$

Published on 22 Mar 2026 - 22:57

score 238 · Answer 5 · 2018-01-22 04:34:27

238

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Evaluate the improper integral: $\int_{0}^{\infty}\frac{\ln(x)}{1+x^{2}}dx$

Published on 22 Jan 2018 - 4:34

score 71 · Answer 6 · 2018-01-22 17:25:15

71

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Integral $\int_{1}^{\sqrt{x}} \frac{1}{t^2 \sqrt{\log{t}}}dt.$

Published on 22 Jan 2018 - 17:25

score 201 · Answer 7 · 2026-03-23 00:24:08

201

Views

Solve the improper integral with techniques of complex analysis

Published on 23 Mar 2026 - 0:24

score 608 · Answer 8 · 2026-03-23 06:39:02

608

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Prove $\int_0^{\infty} \frac{\cos xt}{1+t^2} dt = \frac{\pi}{2}e^{-x}$ by using Laplace Transform

Published on 23 Mar 2026 - 6:39

score 122 · Answer 9 · 2026-03-23 09:13:49

122

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Compute the integral with use of complex analysis techniques

Published on 23 Mar 2026 - 9:13

score 176 · Answer 10 · 2026-03-17 11:25:48

176

Views

Leibniz rule for improper integrals

Published on 17 Mar 2026 - 11:25

score 72 · Answer 11 · 2018-01-24 19:37:05

72

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Finding a limit including an improper integral: $\lim_{n\to\infty}⁡ \int_0^{\sqrt n} \left({1-\frac{x^2}{n}}\right)^n\,dx$

Published on 24 Jan 2018 - 19:37

score 292 · Answer 12 · 2026-03-22 07:02:45

292

Views

$\int\limits_{-\infty}^\infty \frac{1}{e^{x^{2}}+1}dx$

Published on 22 Mar 2026 - 7:02

score 912 · Answer 13 · 2026-03-17 03:50:54

912

Views

Proving integral diverges limits

Published on 17 Mar 2026 - 3:50

score 105 · Answer 14 · 2026-03-22 13:37:43

105

Views

convergence of $\int_{\Bbb R^2} \frac{\sin(x^2+y^2)}{(1+x^2+y^2)^\alpha}dxdy$

Published on 22 Mar 2026 - 13:37

score 197 · Answer 15 · 2026-03-17 23:25:21

197

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Convergence of $ \int_0^{\infty} \frac{e^{-x^2}-e^{-3x^2}}{x^a}$.

Published on 17 Mar 2026 - 23:25

List Question

Improper integral of $\exp[-(a+bi)x]\log x$

Self-convolution of $f(\vec{r}) = e^{-x^2-y^2}/r^2$

How to calculate $\int_0^\infty e^{-x} \prod_{n=1}^\infty (1-e^{-24nx} ) dx$

How can one show that $\int_{0}^{1}{x\ln{x}\ln(1-x^2)\over \sqrt{1-x^2}}\mathrm dx=4-{\pi^2\over 4}-\ln{4}?$

Evaluate the improper integral: $\int_{0}^{\infty}\frac{\ln(x)}{1+x^{2}}dx$

Integral $\int_{1}^{\sqrt{x}} \frac{1}{t^2 \sqrt{\log{t}}}dt.$

Solve the improper integral with techniques of complex analysis

Prove $\int_0^{\infty} \frac{\cos xt}{1+t^2} dt = \frac{\pi}{2}e^{-x}$ by using Laplace Transform

Compute the integral with use of complex analysis techniques

Leibniz rule for improper integrals

Finding a limit including an improper integral: $\lim_{n\to\infty}⁡ \int_0^{\sqrt n} \left({1-\frac{x^2}{n}}\right)^n\,dx$

$\int\limits_{-\infty}^\infty \frac{1}{e^{x^{2}}+1}dx$

Proving integral diverges limits

convergence of $\int_{\Bbb R^2} \frac{\sin(x^2+y^2)}{(1+x^2+y^2)^\alpha}dxdy$

Convergence of $ \int_0^{\infty} \frac{e^{-x^2}-e^{-3x^2}}{x^a}$.

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