Question

$\lim_{x\rightarrow\infty}f(x)=0$ given that f is continuously differentiable, $f'(x)$ is bounded and $\int_{a}^{\infty}\left|f(x)\right|dx$ exists

score 109 · Answer 1 · 2026-03-27 00:10:08

109

Views

$\lim_{x\rightarrow\infty}f(x)=0$ given that f is continuously differentiable, $f'(x)$ is bounded and $\int_{a}^{\infty}\left|f(x)\right|dx$ exists

Published on 27 Mar 2026 - 0:10

score 195 · Answer 2 · 2026-02-23 10:00:08

195

Views

Improper integral of an odd function

Published on 23 Feb 2026 - 10:00

score 230 · Answer 3 · 2026-03-29 20:38:46

230

Views

Evaluating improper integral $\lim_{\epsilon \rightarrow 0} \int_{0}^{1} (\frac{\phi(x)}{x+i\epsilon}- \frac{\phi(x)}{x-i\epsilon}) dx$

Published on 29 Mar 2026 - 20:38

score 223 · Answer 4 · 2026-03-25 23:53:02

223

Views

Calculating $\int_0^\infty\frac{\ln^3x\ln(1+x)}{x(1+x)}\ dx$ using the Beta function

Published on 25 Mar 2026 - 23:53

score 173 · Answer 5 · 2020-02-08 16:27:05

173

Views

For which values of $p$ the improper integral $\int_0^1 \frac{dx}{x^p~\ln(x)} $ converges?

Published on 08 Feb 2020 - 16:27

score 1.3k · Answer 6 · 2026-03-30 06:49:25

1.3k

Views

The Hankel Integral Representation for $\Gamma(z)$

Published on 30 Mar 2026 - 6:49

score 45 · Answer 7 · 2026-04-01 03:13:08

45

Views

Computing the characteristic function of a Rice Random Variable

Published on 01 Apr 2026 - 3:13

score 72 · Answer 8 · 2026-04-05 16:42:37

72

Views

How can I use complex analysis to compute the integral of $\int_0^\infty \frac{x^\alpha}{1 + (kx)^\beta} dx$

Published on 05 Apr 2026 - 16:42

score 72 · Answer 9 · 2026-03-30 01:47:56

72

Views

How to evaluate this integral $\int_0^\infty\frac{\sin^2(ax)}{(ax)^2\sqrt{x^2+bi}} dx$?

Published on 30 Mar 2026 - 1:47

score 200 · Answer 10 · 2020-02-12 22:01:33

200

Views

Evaluate $\int\limits_0^{+\infty}\frac{e^{-ax^2}-e^{-bx^2}}{x}dx$

Published on 12 Feb 2020 - 22:01

score 37 · Answer 11 · 2026-03-25 14:33:38

37

Views

Distributional integral involving $\frac{e^{i\omega x}}{\omega}$

Published on 25 Mar 2026 - 14:33

score 187 · Answer 12 · 2026-04-01 03:45:41

187

Views

Proving $\int\limits^{\infty}_{-\infty}\frac{\sin(2n\arctan(x))}{\left(x^2+1\right)^n\left( e^{x\pi}+1\right)}dx=\eta(2n)-\zeta(2n)$

Published on 01 Apr 2026 - 3:45

score 345 · Answer 13 · 2020-02-15 12:27:24

345

Views

Gaussian integral convergence

Published on 15 Feb 2020 - 12:27

score 118 · Answer 14 · 2020-02-15 14:17:33

118

Views

Integral $\int_0^\infty \frac{u^\alpha}{1+u} du$ for $\alpha<-1$

Published on 15 Feb 2020 - 14:17

score 949 · Answer 15 · 2020-02-16 02:43:34

949

Views

What is the area under a PDF for a normal distrubution?

Published on 16 Feb 2020 - 2:43

List Question

$\lim_{x\rightarrow\infty}f(x)=0$ given that f is continuously differentiable, $f'(x)$ is bounded and $\int_{a}^{\infty}\left|f(x)\right|dx$ exists

Improper integral of an odd function

Evaluating improper integral $\lim_{\epsilon \rightarrow 0} \int_{0}^{1} (\frac{\phi(x)}{x+i\epsilon}- \frac{\phi(x)}{x-i\epsilon}) dx$

Calculating $\int_0^\infty\frac{\ln^3x\ln(1+x)}{x(1+x)}\ dx$ using the Beta function

For which values of $p$ the improper integral $\int_0^1 \frac{dx}{x^p~\ln(x)} $ converges?

The Hankel Integral Representation for $\Gamma(z)$

Computing the characteristic function of a Rice Random Variable

How can I use complex analysis to compute the integral of $\int_0^\infty \frac{x^\alpha}{1 + (kx)^\beta} dx$

How to evaluate this integral $\int_0^\infty\frac{\sin^2(ax)}{(ax)^2\sqrt{x^2+bi}} dx$?

Evaluate $\int\limits_0^{+\infty}\frac{e^{-ax^2}-e^{-bx^2}}{x}dx$

Distributional integral involving $\frac{e^{i\omega x}}{\omega}$

Proving $\int\limits^{\infty}_{-\infty}\frac{\sin(2n\arctan(x))}{\left(x^2+1\right)^n\left( e^{x\pi}+1\right)}dx=\eta(2n)-\zeta(2n)$

Gaussian integral convergence

Integral $\int_0^\infty \frac{u^\alpha}{1+u} du$ for $\alpha<-1$

What is the area under a PDF for a normal distrubution?

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