Question

Compute $\int_{-\infty}^{+\infty}(1+\frac{1}{v^2})\exp(-\frac{u^2}{2\sigma_1^2\sigma_2^2}(\sigma_2v+\frac{\sigma_1}{v})^2)\,dv$

score 220 · Answer 1 · 2026-03-25 19:11:38

220

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Compute $\int_{-\infty}^{+\infty}(1+\frac{1}{v^2})\exp(-\frac{u^2}{2\sigma_1^2\sigma_2^2}(\sigma_2v+\frac{\sigma_1}{v})^2)\,dv$

Published on 25 Mar 2026 - 19:11

score 39 · Answer 2 · 2026-04-09 11:53:59

39

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score 43 · Answer 3 · 2026-04-04 18:59:11

43

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70

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How to evaluate the integral , $\int_0^y\sqrt{\log(1+1/x)}dx$ as $y$ tens to zero.?

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120

Views

$\int_0^\infty \frac{\ln(x^2+1)}{x^{\alpha+1}}dx, 0<\alpha <2 $ using Residue and IBP

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List Question

Compute $\int_{-\infty}^{+\infty}(1+\frac{1}{v^2})\exp(-\frac{u^2}{2\sigma_1^2\sigma_2^2}(\sigma_2v+\frac{\sigma_1}{v})^2)\,dv$

Integration of following integral

Divergence-example of a non-negative function with $\lim_{x\to0} f(x)=0$ and $\int^1_0 \frac{f(x)}{x} dx = \infty$

A question about definition of uniform convergence

Explicit transformation between conjugate harmonic functions: Bäcklund/Hilbert/Riesz transform

How does $1/e^{(1/\infty)}$ equal $1$?

Need help with an exercise (Improper integral).

How to integrate a highly oscillatory function

How to evaluate integral using complex analysis

How to evaluate the integral , $\int_0^y\sqrt{\log(1+1/x)}dx$ as $y$ tens to zero.?

How to evaluate the integral defined below analytically,

Evaluate $\int_0^1 \frac{\log(1+x)}{x}$

Finding normalizing constant of joint density function

Failure of Abel's and Dirichlet's test?

$\int_0^\infty \frac{\ln(x^2+1)}{x^{\alpha+1}}dx, 0<\alpha <2 $ using Residue and IBP

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