Question

Convergence of $\int_0^2\frac{1}{x^\alpha |\ln^\beta(x)|}$

score 34 · Answer 1 · 2019-01-29 23:09:37

34

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Convergence of $\int_0^2\frac{1}{x^\alpha |\ln^\beta(x)|}$

Published on 29 Jan 2019 - 23:09

score 231 · Answer 2 · 2026-03-27 16:09:16

231

Views

$\int_{1}^{\infty}\frac{\ln x}{x^2-1}dx=\frac{\pi^2}{8}$

Published on 27 Mar 2026 - 16:09

score 254 · Answer 3 · 2026-03-27 00:58:06

254

Views

General formula for $\int_0^{\pi/2} \tan^{\alpha}(x) dx$?

Published on 27 Mar 2026 - 0:58

score 201 · Answer 4 · 2026-03-27 00:57:16

201

Views

Where does $\Gamma \left( \frac{3}{2} \right) = \int _0 ^{+\infty}\! \mathrm e ^{-x^2} \, \mathrm d x$ come from?

Published on 27 Mar 2026 - 0:57

score 48 · Answer 5 · 2019-02-03 11:14:01

48

Views

Study convergence of integral $\alpha$ according to parameter $\alpha$

Published on 03 Feb 2019 - 11:14

score 75 · Answer 6 · 2019-02-03 11:20:18

75

Views

integral of exponential (Green) function with trigonometric variable

Published on 03 Feb 2019 - 11:20

score 133 · Answer 7 · 2019-02-03 22:45:25

133

Views

Show that Laplace transform exists

Published on 03 Feb 2019 - 22:45

score 441 · Answer 8 · 2026-03-28 06:48:14

441

Views

Find a function for which integral does not exist but converges as a limit of a sequence

Published on 28 Mar 2026 - 6:48

score 369 · Answer 9 · 2019-02-04 00:57:22

369

Views

The integral of a function multiplied with an unbounded function converges if the product is a bounded function

Published on 04 Feb 2019 - 0:57

score 57 · Answer 10 · 2019-02-04 21:31:40

57

Views

convergence of $\int_{0}^{\infty}{\frac{x^2-1}{x^2+1}\frac{\sin(2x)}{x} dx}$

Published on 04 Feb 2019 - 21:31

score 68 · Answer 11 · 2019-02-05 13:16:45

68

Views

State whether the following improper integral converges, and, if it does, find its value.

Published on 05 Feb 2019 - 13:16

score 53 · Answer 12 · 2019-02-05 15:48:23

53

Views

Proof that improper integral $\int_{0}^{\infty} e^{-x}(1+\sin(x^2)) dx$ exists

Published on 05 Feb 2019 - 15:48

score 203 · Answer 13 · 2026-03-25 19:01:17

203

Views

Integral involving a Gaussian and a rational function.

Published on 25 Mar 2026 - 19:01

score 227 · Answer 14 · 2026-03-27 07:18:45

227

Views

Infinite Integral of a Product of Bessel Functions

Published on 27 Mar 2026 - 7:18

score 1.3k · Answer 15 · 2019-02-06 02:00:43

1.3k

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Given $\int_0^{\infty} e^{-x^2}dx = \frac{\sqrt\pi}{2}$, find $\int_0^{\infty} e^{-\frac{x^2}{2}} dx$

Published on 06 Feb 2019 - 2:00

List Question

Convergence of $\int_0^2\frac{1}{x^\alpha |\ln^\beta(x)|}$

$\int_{1}^{\infty}\frac{\ln x}{x^2-1}dx=\frac{\pi^2}{8}$

General formula for $\int_0^{\pi/2} \tan^{\alpha}(x) dx$?

Where does $\Gamma \left( \frac{3}{2} \right) = \int _0 ^{+\infty}\! \mathrm e ^{-x^2} \, \mathrm d x$ come from?

Study convergence of integral $\alpha$ according to parameter $\alpha$

integral of exponential (Green) function with trigonometric variable

Show that Laplace transform exists

Find a function for which integral does not exist but converges as a limit of a sequence

The integral of a function multiplied with an unbounded function converges if the product is a bounded function

convergence of $\int_{0}^{\infty}{\frac{x^2-1}{x^2+1}\frac{\sin(2x)}{x} dx}$

State whether the following improper integral converges, and, if it does, find its value.

Proof that improper integral $\int_{0}^{\infty} e^{-x}(1+\sin(x^2)) dx$ exists

Integral involving a Gaussian and a rational function.

Infinite Integral of a Product of Bessel Functions

Given $\int_0^{\infty} e^{-x^2}dx = \frac{\sqrt\pi}{2}$, find $\int_0^{\infty} e^{-\frac{x^2}{2}} dx$

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