List questions from improper-integrals

Published on 08 Apr 2026 - 18:37

89

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Find out if $\int _1^{\infty }\:\left(\frac{2+\sin^2\left(x+1\right)}{x^2e^x}\right)dx$ converges

Published on 10 Feb 2017 - 0:39

775

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The Cauchy Principal value of a rational function with only real poles

Published on 12 Apr 2026 - 8:18

820

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Cauchy principal value example

Published on 25 Mar 2026 - 16:07

484

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Generalization of Improper Integral

Published on 31 Mar 2026 - 22:43

129

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The value of $\int_0^{+\infty} \frac{\sin ax}{x^2+1}dx$

Published on 10 Feb 2017 - 22:35

55

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Simplifing integral with known function

Published on 08 Apr 2026 - 19:36

1.3k

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The principal value of an integral

Published on 25 Mar 2026 - 16:08

168

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Existence of certain smooth function with divergent integral

Published on 11 Apr 2026 - 12:45

44

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Prove or disprove the convergence of improper integral

Published on 13 Feb 2017 - 14:22

3.2k

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Finding constant to make integrals converge

Published on 09 Apr 2026 - 3:10

1.3k

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Find the value $C$ such that $\int^{\infty}_{0}(\frac{x}{x^2+1} - \frac{C}{3x+1})dx$ converges

Published on 14 Feb 2017 - 2:36

147

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Is there a quicker way to evaluate $\int_{0}^{\infty} \frac{1-x^2}{x^4+3x^2+1}\ dx$?

Published on 14 Feb 2017 - 7:07

214

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What's about functions $f:[0,\infty)\to\mathbb{R}$ satisfying $\int_0^\infty f(x)(\log x)dx=1$?

Published on 14 Feb 2017 - 12:49

255

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Is this (exotic) integral well defined and convergent (always)? and the bound correct?

Published on 15 Feb 2017 - 14:19

List Question

Integrating a function against a complex measure

Find out if $\int _1^{\infty }\:\left(\frac{2+\sin^2\left(x+1\right)}{x^2e^x}\right)dx$ converges

The Cauchy Principal value of a rational function with only real poles

Cauchy principal value example

Generalization of Improper Integral

The value of $\int_0^{+\infty} \frac{\sin ax}{x^2+1}dx$

Simplifing integral with known function

The principal value of an integral

Existence of certain smooth function with divergent integral

Prove or disprove the convergence of improper integral

Finding constant to make integrals converge

Find the value $C$ such that $\int^{\infty}_{0}(\frac{x}{x^2+1} - \frac{C}{3x+1})dx$ converges

Is there a quicker way to evaluate $\int_{0}^{\infty} \frac{1-x^2}{x^4+3x^2+1}\ dx$?

What's about functions $f:[0,\infty)\to\mathbb{R}$ satisfying $\int_0^\infty f(x)(\log x)dx=1$?

Is this (exotic) integral well defined and convergent (always)? and the bound correct?

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