Question

Evaluate $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}} \,\mathrm dx$

score 3.3k · Answer 1 · 2014-12-13 08:45:45

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Evaluate $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}} \,\mathrm dx$

Published on 13 Dec 2014 - 8:45

score 274 · Answer 2 · 2026-03-29 23:59:59

274

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Is it possible to evaluate $\int_0^1 \sin(\frac{1}{t})\,dt\,$?

Published on 29 Mar 2026 - 23:59

score 140 · Answer 3 · 2014-12-13 19:36:43

140

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Evaluation of an improper integral

Published on 13 Dec 2014 - 19:36

score 438 · Answer 4 · 2026-03-29 23:59:54

438

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How to evaluate $\int_{0}^{\infty}\frac{(x^2-1)\ln{x}}{1+x^4}dx$?

Published on 29 Mar 2026 - 23:59

score 2.9k · Answer 5 · 2026-04-02 23:20:23

2.9k

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The integral of $e^{-x^2}$

Published on 02 Apr 2026 - 23:20

score 157 · Answer 6 · 2014-12-15 03:53:57

157

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For what $p$ does the surface of revolution for $x^p$ have finite surface area?

Published on 15 Dec 2014 - 3:53

score 1.3k · Answer 7 · 2014-12-15 09:46:52

1.3k

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How to prove that $\int_{0}^{\infty}\sin{x}\arctan{\frac{1}{x}}\,\mathrm dx=\frac{\pi }{2} \big(\frac{e-1}e\big)$

Published on 15 Dec 2014 - 9:46

score 1.7k · Answer 8 · 2026-03-30 01:48:07

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Closed form of $\int_0^\infty \ln \left( \frac{x^2+2kx\cos b+k^2}{x^2+2kx\cos a+k^2}\right) \;\frac{\mathrm dx}{x}$

Published on 30 Mar 2026 - 1:48

score 111 · Answer 9 · 2014-12-15 23:42:12

111

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Why is this integral $\int_{-\infty}^{+\infty} F(f(x)) - F(x) dx = 0$?

Published on 15 Dec 2014 - 23:42

score 669 · Answer 10 · 2026-04-04 04:38:04

669

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Evaluate $\int_1^\infty \frac {dx}{x^3+1}$

Published on 04 Apr 2026 - 4:38

score 2.1k · Answer 11 · 2014-12-16 19:09:47

2.1k

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Is it OK to evaluate improper integrals this way?

Published on 16 Dec 2014 - 19:09

score 40 · Answer 12 · 2026-04-03 00:50:33

40

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Volume of a solid formed as vertical limit goes to infinity

Published on 03 Apr 2026 - 0:50

score 59 · Answer 13 · 2026-03-30 10:42:25

59

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$E(g(X)), E(g'(X)) <\infty $ implies $\lim_{x\rightarrow \infty} f(x)g(x)= 0$ ($f$ is the density of $X$)?

Published on 30 Mar 2026 - 10:42

score 106 · Answer 14 · 2014-12-18 08:22:14

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Does $\int_0^\infty |f'(x)| dx < \infty$ conclude $\lim_{x\to \infty} f(x)<\infty $

Published on 18 Dec 2014 - 8:22

score 4.3k · Answer 15 · 2014-12-18 14:27:20

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Proving $\int_{0}^{\infty}\frac{x}{(x^2+1)(e^{2\pi x}+1)} dx=1-\frac{\gamma}{2}-\ln2$

Published on 18 Dec 2014 - 14:27

List Question

Evaluate $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}} \,\mathrm dx$

Is it possible to evaluate $\int_0^1 \sin(\frac{1}{t})\,dt\,$?

Evaluation of an improper integral

How to evaluate $\int_{0}^{\infty}\frac{(x^2-1)\ln{x}}{1+x^4}dx$?

The integral of $e^{-x^2}$

For what $p$ does the surface of revolution for $x^p$ have finite surface area?

How to prove that $\int_{0}^{\infty}\sin{x}\arctan{\frac{1}{x}}\,\mathrm dx=\frac{\pi }{2} \big(\frac{e-1}e\big)$

Closed form of $\int_0^\infty \ln \left( \frac{x^2+2kx\cos b+k^2}{x^2+2kx\cos a+k^2}\right) \;\frac{\mathrm dx}{x}$

Why is this integral $\int_{-\infty}^{+\infty} F(f(x)) - F(x) dx = 0$?

Evaluate $\int_1^\infty \frac {dx}{x^3+1}$

Is it OK to evaluate improper integrals this way?

Volume of a solid formed as vertical limit goes to infinity

$E(g(X)), E(g'(X)) <\infty $ implies $\lim_{x\rightarrow \infty} f(x)g(x)= 0$ ($f$ is the density of $X$)?

Does $\int_0^\infty |f'(x)| dx < \infty$ conclude $\lim_{x\to \infty} f(x)<\infty $

Proving $\int_{0}^{\infty}\frac{x}{(x^2+1)(e^{2\pi x}+1)} dx=1-\frac{\gamma}{2}-\ln2$

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