Question

Finding a closed form for $\int_0^{\infty} \frac{\sin(x/\epsilon)}{1+x^2}dx$ in terms of $\epsilon$?

score 158 · Answer 1 · 2026-04-15 00:45:52

158

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Finding a closed form for $\int_0^{\infty} \frac{\sin(x/\epsilon)}{1+x^2}dx$ in terms of $\epsilon$?

Published on 15 Apr 2026 - 0:45

score 6.2k · Answer 2 · 2026-04-12 21:40:25

6.2k

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When determining a CDF from a continuous PDF, why are the limits of the integral written from negative infinity to x?

Published on 12 Apr 2026 - 21:40

score 354 · Answer 3 · 2026-04-12 15:11:22

354

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Real integral: $\cos(ax)/\sqrt{1+x^2}$

Published on 12 Apr 2026 - 15:11

score 3.3k · Answer 4 · 2026-04-15 03:07:36

3.3k

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Improper integral $\int_0^\infty \frac{e^{ix}}{x^{\alpha}} \, dx $ convergence(?) for $0< \alpha<1$.

Published on 15 Apr 2026 - 3:07

score 151 · Answer 5 · 2026-04-13 04:14:48

151

Views

values of convergence for an improper integral

Published on 13 Apr 2026 - 4:14

score 229 · Answer 6 · 2026-04-09 16:05:53

229

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Limits of Gaussian error function

Published on 09 Apr 2026 - 16:05

score 125 · Answer 7 · 2026-04-16 07:07:18

125

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Does the integral $\int\limits_0^{\infty}\frac{\sin^{2}x}{x^{2}\ln(1+\sqrt x)} dx$ converge?

Published on 16 Apr 2026 - 7:07

score 146 · Answer 8 · 2026-04-16 11:01:49

146

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Fourier transform of $\exp( ic_1x^3 -c_2x^2 )$ [when $c_2=0$ it is the Airy function]

Published on 16 Apr 2026 - 11:01

score 2.1k · Answer 9 · 2026-04-15 02:35:42

2.1k

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Inverse Fourier transform of $\frac{1}{k^2+a^2}$

Published on 15 Apr 2026 - 2:35

score 369 · Answer 10 · 2026-04-29 08:41:59

369

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The uniform convergence of $\int_0^\infty e^{-\alpha x}\sin x\,dx$ for $\alpha$

Published on 29 Apr 2026 - 8:41

score 92 · Answer 11 · 2026-04-17 08:42:41

92

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Integral convergence test $\int_{0}^5 \frac{1}{(x^p-1)^{1/3}}dx$

Published on 17 Apr 2026 - 8:42

score 72 · Answer 12 · 2026-04-15 03:43:57

72

Views

3d integral similar to Poisson's integral.

Published on 15 Apr 2026 - 3:43

score 287 · Answer 13 · 2026-04-14 06:54:29

287

Views

Limit of $t^{p - 1}$ as $t$ approaches infinity

Published on 14 Apr 2026 - 6:54

score 65 · Answer 14 · 2026-04-09 05:08:33

65

Views

An integral equality involving BesselJ and Hankel function

Published on 09 Apr 2026 - 5:08

score 4k · Answer 15 · 2026-05-15 13:58:44

4k

Views

Proof of connection between improper Riemann Integral and Lebesgue integral

Published on 15 May 2026 - 13:58

List Question

Finding a closed form for $\int_0^{\infty} \frac{\sin(x/\epsilon)}{1+x^2}dx$ in terms of $\epsilon$?

When determining a CDF from a continuous PDF, why are the limits of the integral written from negative infinity to x?

Real integral: $\cos(ax)/\sqrt{1+x^2}$

Improper integral $\int_0^\infty \frac{e^{ix}}{x^{\alpha}} \, dx $ convergence(?) for $0< \alpha<1$.

values of convergence for an improper integral

Limits of Gaussian error function

Does the integral $\int\limits_0^{\infty}\frac{\sin^{2}x}{x^{2}\ln(1+\sqrt x)} dx$ converge?

Fourier transform of $\exp( ic_1x^3 -c_2x^2 )$ [when $c_2=0$ it is the Airy function]

Inverse Fourier transform of $\frac{1}{k^2+a^2}$

The uniform convergence of $\int_0^\infty e^{-\alpha x}\sin x\,dx$ for $\alpha$

Integral convergence test $\int_{0}^5 \frac{1}{(x^p-1)^{1/3}}dx$

3d integral similar to Poisson's integral.

Limit of $t^{p - 1}$ as $t$ approaches infinity

An integral equality involving BesselJ and Hankel function

Proof of connection between improper Riemann Integral and Lebesgue integral

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