Question

Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$

score 506 · Answer 1 · 2026-03-28 02:04:53

506

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Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$

Published on 28 Mar 2026 - 2:04

score 133 · Answer 2 · 2026-03-27 04:23:35

133

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Expectation of $\cos(\|X\|)$ where $X \sim \mathcal{N}(\mu,\Sigma)$

Published on 27 Mar 2026 - 4:23

score 1.3k · Answer 3 · 2026-03-30 05:25:32

1.3k

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A definite integral in terms of Meijer G-function

Published on 30 Mar 2026 - 5:25

score 512 · Answer 4 · 2014-05-16 05:27:21

512

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The Fourier sine transform of $f(x)/\sin x$

Published on 16 May 2014 - 5:27

score 749 · Answer 5 · 2014-05-16 13:58:19

749

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Evaluate $\int_0^\infty\!\!\int_0^\infty\!\!\int_0^\infty\!\frac{(xyz)^{-1/7}(yz)^{-1/7}z^{-1/7}}{(x+1)(y+1)(z+1)}dx\,dy\,dz$

Published on 16 May 2014 - 13:58

score 1.1k · Answer 6 · 2014-05-17 10:14:57

1.1k

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How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$

Published on 17 May 2014 - 10:14

score 165 · Answer 7 · 2026-03-28 13:41:38

165

Views

Solve $\mathscr{F}^{-1} [ \cot{a \omega} \times \mathscr{F} \{ U(t) \sin{\omega_0 t} \} ] $ using contour integration

Published on 28 Mar 2026 - 13:41

score 231 · Answer 8 · 2014-05-18 11:57:09

231

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If $\int _1^{\infty }f\left(x\right)dx$ converges absolutely then $\int _1^{\infty }\sin \left(x\right)f\left(x\right)dx$ exists

Published on 18 May 2014 - 11:57

score 1.1k · Answer 9 · 2014-05-18 15:21:21

1.1k

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Evaluating $\int_0^\infty \frac {\cos {\pi x}} {e^{2\pi \sqrt x} - 1} \mathrm d x$

Published on 18 May 2014 - 15:21

score 177 · Answer 10 · 2014-05-18 18:10:07

177

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How to calculate the improper integral $\int_0^\infty\left(\frac{1}{\sqrt{x^2+4}}-\frac{P}{x+2}\right)dx$

Published on 18 May 2014 - 18:10

score 366 · Answer 11 · 2014-05-19 12:46:12

366

Views

Integral $\int_{0}^{\infty}e^{-u}e^{-u^{\alpha}x}\mathrm{d}u$

Published on 19 May 2014 - 12:46

score 93 · Answer 12 · 2026-03-26 14:16:09

93

Views

Improper integral calculation and nature

Published on 26 Mar 2026 - 14:16

score 143 · Answer 13 · 2026-03-30 07:09:08

143

Views

integral involving hypergeometric function $\int^1_0\frac{_2F_1(p,p;p+1;-\frac{1}{y})}{y}\,dy$

Published on 30 Mar 2026 - 7:09

score 112 · Answer 14 · 2026-03-25 00:02:19

112

Views

exact or numerical value of an improper integral

Published on 25 Mar 2026 - 0:02

score 253 · Answer 15 · 2014-05-21 05:41:55

253

Views

Double integral involving zeta function: $\int_0^\infty \frac{1-12y^2}{(1+4y^2)^3}\int_{1/2}^{\infty}\log|\zeta(x+iy)|~dx ~dy.$

Published on 21 May 2014 - 5:41

List Question

Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$

Expectation of $\cos(\|X\|)$ where $X \sim \mathcal{N}(\mu,\Sigma)$

A definite integral in terms of Meijer G-function

The Fourier sine transform of $f(x)/\sin x$

Evaluate $\int_0^\infty\!\!\int_0^\infty\!\!\int_0^\infty\!\frac{(xyz)^{-1/7}(yz)^{-1/7}z^{-1/7}}{(x+1)(y+1)(z+1)}dx\,dy\,dz$

How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$

Solve $\mathscr{F}^{-1} [ \cot{a \omega} \times \mathscr{F} \{ U(t) \sin{\omega_0 t} \} ] $ using contour integration

If $\int _1^{\infty }f\left(x\right)dx$ converges absolutely then $\int _1^{\infty }\sin \left(x\right)f\left(x\right)dx$ exists

Evaluating $\int_0^\infty \frac {\cos {\pi x}} {e^{2\pi \sqrt x} - 1} \mathrm d x$

How to calculate the improper integral $\int_0^\infty\left(\frac{1}{\sqrt{x^2+4}}-\frac{P}{x+2}\right)dx$

Integral $\int_{0}^{\infty}e^{-u}e^{-u^{\alpha}x}\mathrm{d}u$

Improper integral calculation and nature

integral involving hypergeometric function $\int^1_0\frac{_2F_1(p,p;p+1;-\frac{1}{y})}{y}\,dy$

exact or numerical value of an improper integral

Double integral involving zeta function: $\int_0^\infty \frac{1-12y^2}{(1+4y^2)^3}\int_{1/2}^{\infty}\log|\zeta(x+iy)|~dx ~dy.$

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