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Sine transform of $f(x) = \dfrac{1}{e^{\sqrt{2 \pi} x}-1} - \dfrac{1}{\sqrt{2 \pi} x}$

score 66 · Answer 1 · 2026-04-16 11:41:02

66

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Sine transform of $f(x) = \dfrac{1}{e^{\sqrt{2 \pi} x}-1} - \dfrac{1}{\sqrt{2 \pi} x}$

Published on 16 Apr 2026 - 11:41

score 94 · Answer 2 · 2026-04-11 21:23:47

94

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A challenging Integral Involving Logarithmic and Trigonometric Functions

Published on 11 Apr 2026 - 21:23

score 73 · Answer 3 · 2026-04-11 11:26:03

73

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Compute improper Integral using a previous result.

Published on 11 Apr 2026 - 11:26

score 90 · Answer 4 · 2026-04-12 11:48:15

90

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Interchange of two improper integrals in Section 2.7. Titchmarsh's book of Riemann Zeta Function

Published on 12 Apr 2026 - 11:48

score 132 · Answer 5 · 2026-04-12 07:30:35

132

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Convergent Improper Integral

Published on 12 Apr 2026 - 7:30

score 293 · Answer 6 · 2026-04-17 08:15:20

293

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Show that $\dfrac{1}{e^x-1} = \dfrac{1}{x} - \dfrac{1}{2} + 2x \sum_{n=1}^{\infty} \dfrac{1}{(4n^2 \pi^2 +x^2)}$.

Published on 17 Apr 2026 - 8:15

score 71 · Answer 7 · 2026-04-13 19:52:06

71

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Does the integral $\int \frac{1}{1+x^{a+2}} \ dx$ converge?

Published on 13 Apr 2026 - 19:52

score 64 · Answer 8 · 2026-04-14 04:01:33

64

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Is there an easy way to calculate the subfactorial of a number?

Published on 14 Apr 2026 - 4:01

score 95 · Answer 9 · 2026-04-09 16:56:26

95

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Determining a specific Lagrange error for an integral

Published on 09 Apr 2026 - 16:56

score 456 · Answer 10 · 2026-04-16 13:24:04

456

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What is $\int\limits_{0}^{\infty}\frac{\sin(x^n)}{x^2+1}dx$?

Published on 16 Apr 2026 - 13:24

score 44 · Answer 11 · 2026-04-11 11:42:34

44

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How to perform the $p$ test for integral convergence

Published on 11 Apr 2026 - 11:42

score 483 · Answer 12 · 2026-04-17 02:47:08

483

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Evaluate $\int_{0}^{1} \frac{\operatorname{arsinh}x}{x\sqrt{1-x^4}} \,\mathrm{d}x$

Published on 17 Apr 2026 - 2:47

score 147 · Answer 13 · 2026-04-12 17:40:06

147

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Product of Laplace transforms with disjoint Region Of Convergence (ROC)

Published on 12 Apr 2026 - 17:40

score 175 · Answer 14 · 2026-03-25 20:12:45

175

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Show that $\dfrac{1}{2 \pi i} \int_{c- i \infty}^{c+ i \infty} F(s) G(w-s) ds = \int_0^{\infty} f(x) g(x) x^{w-1} dx.$

Published on 25 Mar 2026 - 20:12

score 174 · Answer 15 · 2026-04-16 14:56:53

174

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Deriving $\operatorname{arccot}(x)=\int\limits_{x}^ {\infty} \frac{1}{1+t^2} ~dt$

Published on 16 Apr 2026 - 14:56

List Question

Sine transform of $f(x) = \dfrac{1}{e^{\sqrt{2 \pi} x}-1} - \dfrac{1}{\sqrt{2 \pi} x}$

A challenging Integral Involving Logarithmic and Trigonometric Functions

Compute improper Integral using a previous result.

Interchange of two improper integrals in Section 2.7. Titchmarsh's book of Riemann Zeta Function

Convergent Improper Integral

Show that $\dfrac{1}{e^x-1} = \dfrac{1}{x} - \dfrac{1}{2} + 2x \sum_{n=1}^{\infty} \dfrac{1}{(4n^2 \pi^2 +x^2)}$.

Does the integral $\int \frac{1}{1+x^{a+2}} \ dx$ converge?

Is there an easy way to calculate the subfactorial of a number?

Determining a specific Lagrange error for an integral

What is $\int\limits_{0}^{\infty}\frac{\sin(x^n)}{x^2+1}dx$?

How to perform the $p$ test for integral convergence

Evaluate $\int_{0}^{1} \frac{\operatorname{arsinh}x}{x\sqrt{1-x^4}} \,\mathrm{d}x$

Product of Laplace transforms with disjoint Region Of Convergence (ROC)

Show that $\dfrac{1}{2 \pi i} \int_{c- i \infty}^{c+ i \infty} F(s) G(w-s) ds = \int_0^{\infty} f(x) g(x) x^{w-1} dx.$

Deriving $\operatorname{arccot}(x)=\int\limits_{x}^ {\infty} \frac{1}{1+t^2} ~dt$

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