List questions from improper-integrals

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Integrating Planck's function between 0 and infinity

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If $E(X^2)$ is finite then $xP(X>x)$ is eventually decreasing?

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Solving a non-linear, improper integral equation

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Evaluate $\int_0^\infty\left\{ \frac{1}{t} \right\}^{kn}t^{s-1}dt$ for positive integers $n,k$ and $0<\Re s<1$

Published on 25 Mar 2026 - 13:13

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$\int_0^{\infty} \frac{x^{\frac{1}{4}}}{1+x^3} dx = \frac{\pi}{3 \sin\left( \frac{5\pi}{12} \right)}$

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Suggested Integration Technique for $\text{sinc}^2(x)/\sqrt{x^2+c^2}$?

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Improper integral quotient in a limit statement

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Evaluation of an improper integral: $\int_0^\infty \frac{t\sin{t}}{u^2+t^2\,}dt$

Published on 07 Nov 2016 - 16:47

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Expected value from CDF calculation - passing the limit through the integral

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Double improper integral , how to see if it diverge

Published on 07 Nov 2016 - 21:52

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When does this integral equality hold (Fubini's theorem)?

Published on 08 Nov 2016 - 16:58

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close form solution needed for following integration

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Advanced integral, calculus

Published on 09 Nov 2016 - 21:33

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Help solving improper integral

Published on 11 Apr 2026 - 0:43

List Question

Evaluating $ \int_{-\infty}^{\infty} \frac{e^{-ix}}{\sqrt{x+2i} + \sqrt{x+5i}}dx$

Integrating Planck's function between 0 and infinity

If $E(X^2)$ is finite then $xP(X>x)$ is eventually decreasing?

Solving a non-linear, improper integral equation

Evaluate $\int_0^\infty\left\{ \frac{1}{t} \right\}^{kn}t^{s-1}dt$ for positive integers $n,k$ and $0<\Re s<1$

$\int_0^{\infty} \frac{x^{\frac{1}{4}}}{1+x^3} dx = \frac{\pi}{3 \sin\left( \frac{5\pi}{12} \right)}$

Suggested Integration Technique for $\text{sinc}^2(x)/\sqrt{x^2+c^2}$?

Improper integral quotient in a limit statement

Evaluation of an improper integral: $\int_0^\infty \frac{t\sin{t}}{u^2+t^2\,}dt$

Expected value from CDF calculation - passing the limit through the integral

Double improper integral , how to see if it diverge

When does this integral equality hold (Fubini's theorem)?

close form solution needed for following integration

Advanced integral, calculus

Help solving improper integral

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