Question

How to show $e^t$ is the unique solution to the integral equation $\int_0^1 e^{ts} x(s) ds = \frac{e^{t+1}-1}{t+1}$?

score 71 · Answer 1 · 2026-04-14 16:04:02

71

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How to show $e^t$ is the unique solution to the integral equation $\int_0^1 e^{ts} x(s) ds = \frac{e^{t+1}-1}{t+1}$?

Published on 14 Apr 2026 - 16:04

score 57 · Answer 2 · 2026-04-16 15:05:06

57

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Find the primitive function of $\sum_{n=1}^{\infty}\frac{(-1)^n(2n+2)}{n!}(x-1)^{2n+1}$

Published on 16 Apr 2026 - 15:05

score 1.5k · Answer 3 · 2026-05-11 02:39:29

1.5k

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Integral with singularity on the real axis with complex integration

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score 47 · Answer 4 · 2026-04-14 22:47:50

47

Views

computing Fourier transform of $\frac{1}{x^2+a^2},\, a > 0$

Published on 14 Apr 2026 - 22:47

score 168 · Answer 5 · 2026-04-12 19:52:50

168

Views

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score 3.2k · Answer 6 · 2026-04-09 12:56:52

3.2k

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Published on 09 Apr 2026 - 12:56

score 370 · Answer 7 · 2026-04-07 19:10:33

370

Views

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score 60 · Answer 8 · 2026-04-15 22:46:03

60

Views

for which values of $x,\,$ $I_x = \int_{0}^{+\infty} \frac{(u\cos u - sin u)\cos ux}{u^3} \, du = 0$?

Published on 15 Apr 2026 - 22:46

score 125 · Answer 9 · 2026-05-10 19:11:41

125

Views

Double / Surface Integral over a circular area

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score 100 · Answer 10 · 2026-05-11 05:17:58

100

Views

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Published on 11 May 2026 - 5:17

score 126 · Answer 11 · 2026-05-10 12:31:14

126

Views

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Published on 10 May 2026 - 12:31

score 62 · Answer 12 · 2026-05-10 21:00:24

62

Views

Limit of a function tending to Dirac delta

Published on 10 May 2026 - 21:00

score 65 · Answer 13 · 2026-04-11 14:09:51

65

Views

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Published on 11 Apr 2026 - 14:09

score 92 · Answer 14 · 2026-04-17 11:58:42

92

Views

Evaluate integral for $\int \sin^2 (x+\frac{\pi}{6}) dx$

Published on 17 Apr 2026 - 11:58

score 62 · Answer 15 · 2026-04-14 14:50:14

62

Views

Fourier transform of $x \mapsto e^{x}e^{-e^x}$

Published on 14 Apr 2026 - 14:50

List Question

How to show $e^t$ is the unique solution to the integral equation $\int_0^1 e^{ts} x(s) ds = \frac{e^{t+1}-1}{t+1}$?

Find the primitive function of $\sum_{n=1}^{\infty}\frac{(-1)^n(2n+2)}{n!}(x-1)^{2n+1}$

Integral with singularity on the real axis with complex integration

computing Fourier transform of $\frac{1}{x^2+a^2},\, a > 0$

Showing $\frac{e^{-ax} - e^{(a-1)x}}{1-e^{-x}}$ is integrable on $\mathbb{R}$

Intuition for why a integral with jump discontinuity is continuous but not differentiable?

Integration of a divergent integral using the Cauchy Principal Value

for which values of $x,\,$ $I_x = \int_{0}^{+\infty} \frac{(u\cos u - sin u)\cos ux}{u^3} \, du = 0$?

Double / Surface Integral over a circular area

Finding the volume of an object (another)

Why are these two functions different for negative numbers?

Limit of a function tending to Dirac delta

Computing a definite integral and computing integration constant. ( A practice problem from textbook )

Evaluate integral for $\int \sin^2 (x+\frac{\pi}{6}) dx$

Fourier transform of $x \mapsto e^{x}e^{-e^x}$

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