Question

Closed form for $\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx$

score 3.3k · Answer 1 · 2026-04-15 19:05:26

3.3k

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Closed form for $\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx$

Published on 15 Apr 2026 - 19:05

score 61 · Answer 2 · 2026-04-15 18:16:14

61

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Proving that length of a curve is $\infty$

Published on 15 Apr 2026 - 18:16

score 4.6k · Answer 3 · 2026-04-16 20:01:46

4.6k

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Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$

Published on 16 Apr 2026 - 20:01

score 259 · Answer 4 · 2026-04-12 15:18:02

259

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For which values of $\alpha \in \mathbb R$ two improper integrals converge

Published on 12 Apr 2026 - 15:18

score 84 · Answer 5 · 2026-04-15 18:28:42

84

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Help evaluating $\int_0^\infty \frac{1}{x^{1/2}(x+1)}dx$

Published on 15 Apr 2026 - 18:28

score 96 · Answer 6 · 2026-04-16 13:49:57

96

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Evaluating $\int_0^{\infty}\frac{2}{x^2-8x+15}dx$

Published on 16 Apr 2026 - 13:49

score 453 · Answer 7 · 2026-04-13 14:39:10

453

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expectation of logarithm under generalised inverse gaussian

Published on 13 Apr 2026 - 14:39

score 212 · Answer 8 · 2026-04-15 03:34:04

212

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uniformly continuous and $\int_0^\infty f(t)\,\mathrm dt$ exists $\implies \lim_{x\to\infty}f(x) = 0 $

Published on 15 Apr 2026 - 3:34

score 293 · Answer 9 · 2026-04-14 06:34:43

293

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Inverse Laplace Transform. Computing the integral.

Published on 14 Apr 2026 - 6:34

score 677 · Answer 10 · 2026-04-14 01:06:31

677

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How to solve $\int_0^\infty J_0(x)\ \text{sinc}(\pi\,x)\ e^{-x}\,\mathrm dx$?

Published on 14 Apr 2026 - 1:06

score 204 · Answer 11 · 2026-04-17 11:34:34

204

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$\int^{\pi/2}_{0}\log|\sin x| \,dx = \int^{\pi/2}_{0}\log|\cos x| \,dx $

Published on 17 Apr 2026 - 11:34

score 886 · Answer 12 · 2026-04-16 12:02:56

886

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Prove that $\int_{-\infty}^{\infty} \sin x \, dx = 0 $

Published on 16 Apr 2026 - 12:02

score 650 · Answer 13 · 2026-03-27 01:47:43

650

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Closed form for $\int_1^\infty\int_0^1\frac{\mathrm dy\,\mathrm dx}{\sqrt{x^2-1}\sqrt{1-y^2}\sqrt{1-y^2+4\,x^2y^2}}$

Published on 27 Mar 2026 - 1:47

score 281 · Answer 14 · 2026-04-16 06:26:31

281

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Convergence of $\int_{-\infty}^\infty \frac{1}{1+x^6}dx$

Published on 16 Apr 2026 - 6:26

score 74 · Answer 15 · 2026-04-16 18:45:42

74

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Convergence of $\int_{0}^{1} \frac{\ln^{2} x}{x^{2}+x-2} \ dx $

Published on 16 Apr 2026 - 18:45

List Question

Closed form for $\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx$

Proving that length of a curve is $\infty$

Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$

For which values of $\alpha \in \mathbb R$ two improper integrals converge

Help evaluating $\int_0^\infty \frac{1}{x^{1/2}(x+1)}dx$

Evaluating $\int_0^{\infty}\frac{2}{x^2-8x+15}dx$

expectation of logarithm under generalised inverse gaussian

uniformly continuous and $\int_0^\infty f(t)\,\mathrm dt$ exists $\implies \lim_{x\to\infty}f(x) = 0 $

Inverse Laplace Transform. Computing the integral.

How to solve $\int_0^\infty J_0(x)\ \text{sinc}(\pi\,x)\ e^{-x}\,\mathrm dx$?

$\int^{\pi/2}_{0}\log|\sin x| \,dx = \int^{\pi/2}_{0}\log|\cos x| \,dx $

Prove that $\int_{-\infty}^{\infty} \sin x \, dx = 0 $

Closed form for $\int_1^\infty\int_0^1\frac{\mathrm dy\,\mathrm dx}{\sqrt{x^2-1}\sqrt{1-y^2}\sqrt{1-y^2+4\,x^2y^2}}$

Convergence of $\int_{-\infty}^\infty \frac{1}{1+x^6}dx$

Convergence of $\int_{0}^{1} \frac{\ln^{2} x}{x^{2}+x-2} \ dx $

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