Question

Prove that $\int_1^{\infty}\frac{dx}{x\sqrt{x^2-1}}=\frac{\pi}{2}$ using complex analysis

score 504 · Answer 1 · 2016-10-07 15:15:35

504

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Prove that $\int_1^{\infty}\frac{dx}{x\sqrt{x^2-1}}=\frac{\pi}{2}$ using complex analysis

Published on 07 Oct 2016 - 15:15

score 56 · Answer 2 · 2026-04-10 02:58:58

56

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Re-arranging terms in Integral

Published on 10 Apr 2026 - 2:58

score 98 · Answer 3 · 2016-10-08 02:24:30

98

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Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?

Published on 08 Oct 2016 - 2:24

score 487 · Answer 4 · 2026-04-11 06:45:49

487

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Measure of Smoothness of a Function

Published on 11 Apr 2026 - 6:45

score 146 · Answer 5 · 2026-04-11 04:23:10

146

Views

Integration involving rational function and exponentials

Published on 11 Apr 2026 - 4:23

score 81 · Answer 6 · 2026-04-11 12:46:59

81

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Intermediate steps needed in integration with substitution

Published on 11 Apr 2026 - 12:46

score 528 · Answer 7 · 2026-04-07 00:24:25

528

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Asymptotics of $\int_0^{\infty} e^{-kx}(\sin(kx)+\cos(kx)) \frac{x^{4}}{\sinh(x^2)} dx$ at large $k$

Published on 07 Apr 2026 - 0:24

score 28 · Answer 8 · 2026-03-30 14:10:45

28

Views

Divergent? $\lim_{x\rightarrow\infty} A\left(\int_{0}^{\frac{x}{B}} te^{-t}\ dt\right)$

Published on 30 Mar 2026 - 14:10

score 178 · Answer 9 · 2016-10-13 09:56:57

178

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How to find $f(c)=\int_{0}^{\infty}\frac{x^2}{e^{cx}-e^x}dx$?

Published on 13 Oct 2016 - 9:56

score 139 · Answer 10 · 2026-04-08 03:38:18

139

Views

A definite integral involving the product of a rational function and a logarithm

Published on 08 Apr 2026 - 3:38

score 27 · Answer 11 · 2026-03-25 19:10:47

27

Views

Which relation between $A$, $B$ and $C$ should be satisfied in order the infinite integral below vanish?

Published on 25 Mar 2026 - 19:10

score 207 · Answer 12 · 2026-04-10 15:26:14

207

Views

How to integrate this improper integral.

Published on 10 Apr 2026 - 15:26

score 101 · Answer 13 · 2016-10-16 12:50:09

101

Views

$ \int\limits_{0}^{\infty} \frac{ dx }{(1+x^{\alpha})^{\alpha}} = 1 $ where $\alpha$ is the golden ratio

Published on 16 Oct 2016 - 12:50

score 28 · Answer 14 · 2026-03-31 15:24:54

28

Views

Is $\int_{-\infty}^{\infty}f_X(z-y)f_Y(y)dy$ a PDF where $f_x,f_Y$ are both PDFS

Published on 31 Mar 2026 - 15:24

score 656 · Answer 15 · 2026-04-10 11:11:47

656

Views

Digamma series Representation

Published on 10 Apr 2026 - 11:11

List Question

Prove that $\int_1^{\infty}\frac{dx}{x\sqrt{x^2-1}}=\frac{\pi}{2}$ using complex analysis

Re-arranging terms in Integral

Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?

Measure of Smoothness of a Function

Integration involving rational function and exponentials

Intermediate steps needed in integration with substitution

Asymptotics of $\int_0^{\infty} e^{-kx}(\sin(kx)+\cos(kx)) \frac{x^{4}}{\sinh(x^2)} dx$ at large $k$

Divergent? $\lim_{x\rightarrow\infty} A\left(\int_{0}^{\frac{x}{B}} te^{-t}\ dt\right)$

How to find $f(c)=\int_{0}^{\infty}\frac{x^2}{e^{cx}-e^x}dx$?

A definite integral involving the product of a rational function and a logarithm

Which relation between $A$, $B$ and $C$ should be satisfied in order the infinite integral below vanish?

How to integrate this improper integral.

$ \int\limits_{0}^{\infty} \frac{ dx }{(1+x^{\alpha})^{\alpha}} = 1 $ where $\alpha$ is the golden ratio

Is $\int_{-\infty}^{\infty}f_X(z-y)f_Y(y)dy$ a PDF where $f_x,f_Y$ are both PDFS

Digamma series Representation

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