List questions from improper-integrals

Published on 01 Jan 2015 - 7:22

59

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How do I test the convergence/divergence of the following improper integral?

Published on 01 Jan 2015 - 14:40

202

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Convergence of $ \int_{-\infty}^\infty \cos(x\log(\lvert x\lvert ))\,dx $

Published on 02 Jan 2015 - 2:59

422

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Evaluate $\lim_{n \to \infty}\Bigl[\bigl(\prod_{k=1}^{n}{\frac{2k}{2k-1}}\bigr)\bigl(\int_{-1}^{\infty}\frac{(\cos{x})^{2n}}{2^x}\,dx\bigr)\Bigr]$

Published on 02 Jan 2015 - 5:26

2.5k

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Convergence of $\int_0^\infty $sin$ (x^p) dx$

Published on 02 Jan 2015 - 22:34

76

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Evaluate the following infinite sum with parameter

Published on 29 Mar 2026 - 13:49

81

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Identity about integral of logarithm

Published on 03 Oct 2019 - 12:18

81

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Improper integral from expectation

Published on 29 Mar 2026 - 16:54

922

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Integrate $\int_0^\infty\frac{\cos(\alpha x) - \cos(\beta x)}{x}dx$

Published on 08 Oct 2019 - 2:40

404

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Integral related to the softplus function

Published on 26 Mar 2026 - 6:19

248

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For $\alpha>0$, evaluate $\int^{+\infty}_0xe^{-x}\cos x\cos(x^2/\alpha)\,dx$

Published on 31 Mar 2026 - 5:18

65

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Integral Test can it be used here

Published on 09 Oct 2019 - 21:23

129

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Evaluate $\int^{\infty}_0\frac{x^c}{c^x}\,dx$ with $c>1$

Published on 29 Mar 2026 - 20:20

86

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If the improper integral exists, must the limit exist if the function is continuous and differentiable?

Published on 28 Mar 2026 - 11:53

289

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How to calculate this double integral in probability?

Published on 11 Oct 2019 - 19:42

List Question

Definite integral of a function containing max()

How do I test the convergence/divergence of the following improper integral?

Convergence of $ \int_{-\infty}^\infty \cos(x\log(\lvert x\lvert ))\,dx $

Evaluate $\lim_{n \to \infty}\Bigl[\bigl(\prod_{k=1}^{n}{\frac{2k}{2k-1}}\bigr)\bigl(\int_{-1}^{\infty}\frac{(\cos{x})^{2n}}{2^x}\,dx\bigr)\Bigr]$

Convergence of $\int_0^\infty $sin$ (x^p) dx$

Evaluate the following infinite sum with parameter

Identity about integral of logarithm

Improper integral from expectation

Integrate $\int_0^\infty\frac{\cos(\alpha x) - \cos(\beta x)}{x}dx$

Integral related to the softplus function

For $\alpha>0$, evaluate $\int^{+\infty}_0xe^{-x}\cos x\cos(x^2/\alpha)\,dx$

Integral Test can it be used here

Evaluate $\int^{\infty}_0\frac{x^c}{c^x}\,dx$ with $c>1$

If the improper integral exists, must the limit exist if the function is continuous and differentiable?

How to calculate this double integral in probability?

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