Question

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

score 80 · Answer 1 · 2026-04-29 12:42:41

80

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

Published on 29 Apr 2026 - 12:42

score 206 · Answer 2 · 2026-05-07 10:08:11

206

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

Published on 07 May 2026 - 10:08

score 91 · Answer 3 · 2026-04-29 12:42:46

91

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

Published on 29 Apr 2026 - 12:42

score 138 · Answer 4 · 2026-05-07 09:21:48

138

Views

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 07 May 2026 - 9:21

score 247 · Answer 5 · 2026-04-29 12:42:43

247

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

Published on 29 Apr 2026 - 12:42

score 79 · Answer 6 · 2026-04-29 12:42:45

79

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

Published on 29 Apr 2026 - 12:42

score 208 · Answer 7 · 2026-05-02 23:53:52

208

Views

Solve the improper integral with techniques of complex analysis

Published on 02 May 2026 - 23:53

score 617 · Answer 8 · 2026-05-05 10:56:51

617

Views

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

Published on 05 May 2026 - 10:56

score 131 · Answer 9 · 2026-05-02 18:29:13

131

Views

Compute the integral with use of complex analysis techniques

Published on 02 May 2026 - 18:29

score 183 · Answer 10 · 2026-04-29 12:42:39

183

Views

Leibniz rule for improper integrals

Published on 29 Apr 2026 - 12:42

score 79 · Answer 11 · 2026-04-29 12:42:40

79

Views

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 29 Apr 2026 - 12:42

score 299 · Answer 12 · 2026-04-29 12:23:50

299

Views

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

Published on 29 Apr 2026 - 12:23

score 921 · Answer 13 · 2026-04-29 12:42:32

921

Views

Proving integral diverges limits

Published on 29 Apr 2026 - 12:42

score 111 · Answer 14 · 2026-04-29 12:42:34

111

Views

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

Published on 29 Apr 2026 - 12:42

score 205 · Answer 15 · 2026-04-29 12:42:42

205

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

Published on 29 Apr 2026 - 12:42

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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