List questions from improper-integrals

Published on 09 Apr 2026 - 16:44

41

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limit of the integral $\int_0^A \frac{1}{n!} [\log(\frac Bx)]^n~dx$ where $A,B$ are positive constants

Published on 15 Apr 2026 - 14:04

40

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How to prove an integral inequality in a ball

Published on 16 Apr 2026 - 16:44

91

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Do $\int_{1}^{\infty}\frac{\cos(x) dx}{1+x^2}$ and $\int_{1}^{\infty}\frac{\sin(x) dx}{1+x^2}$ converge?

Published on 16 Apr 2026 - 16:12

69

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Leading-order approximation of $\int_0^{\infty} e^{t-z(t^4-2t^2)}\sin^2(2\pi\nu t)~dt$

Published on 16 Apr 2026 - 17:58

98

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Asymptotic expansion of $\int_{\xi}^{\infty}\frac{e^{-\alpha t}}{t}dt$

Published on 10 Apr 2026 - 23:00

77

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Conditional distribution given density function

Published on 10 Apr 2026 - 17:19

137

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Tricky Integral with parameter with difficult limits

Published on 09 Apr 2026 - 2:25

50

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Ratio of a function and its integral inequalities

Published on 13 Apr 2026 - 19:26

136

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Evaluate $\int^\infty_0\frac{x^{s-1}\arctan{x}}{\sqrt{1+x^2}}\ dx$

Published on 17 Apr 2026 - 7:46

90

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why integral converges

Published on 13 Apr 2026 - 20:31

106

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improper integral-integral test for convergence:$\displaystyle\int_0^{+\infty}\frac{\cos (\ln x)}{\sqrt{x^4+1}} \mathrm dx$

Published on 16 Apr 2026 - 18:28

93

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Integral of a piecewise continuous function - is this correct?

Published on 25 Mar 2026 - 22:09

187

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Curious improper integral:$\displaystyle\int_0^\infty\dfrac{\sin(x^3)}{x^2}dx$

Published on 16 Apr 2026 - 17:10

565

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Evaluation of $\int_0^1\frac{\ln ^2\left( 1-x \right) \text{Li}_2\left( \dfrac{1+x}{2} \right)}{x}\text{d}x$

Published on 16 Apr 2026 - 18:55

List Question

Integral of indirectly defined function

limit of the integral $\int_0^A \frac{1}{n!} [\log(\frac Bx)]^n~dx$ where $A,B$ are positive constants

How to prove an integral inequality in a ball

Do $\int_{1}^{\infty}\frac{\cos(x) dx}{1+x^2}$ and $\int_{1}^{\infty}\frac{\sin(x) dx}{1+x^2}$ converge?

Leading-order approximation of $\int_0^{\infty} e^{t-z(t^4-2t^2)}\sin^2(2\pi\nu t)~dt$

Asymptotic expansion of $\int_{\xi}^{\infty}\frac{e^{-\alpha t}}{t}dt$

Conditional distribution given density function

Tricky Integral with parameter with difficult limits

Ratio of a function and its integral inequalities

Evaluate $\int^\infty_0\frac{x^{s-1}\arctan{x}}{\sqrt{1+x^2}}\ dx$

why integral converges

improper integral-integral test for convergence:$\displaystyle\int_0^{+\infty}\frac{\cos (\ln x)}{\sqrt{x^4+1}} \mathrm dx$

Integral of a piecewise continuous function - is this correct?

Curious improper integral:$\displaystyle\int_0^\infty\dfrac{\sin(x^3)}{x^2}dx$

Evaluation of $\int_0^1\frac{\ln ^2\left( 1-x \right) \text{Li}_2\left( \dfrac{1+x}{2} \right)}{x}\text{d}x$

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