List questions from improper-integrals

Published on 16 Apr 2026 - 17:17

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What to do when an improper integral returns infinity-infinity

Published on 11 Apr 2026 - 12:35

88

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Hypergeometric Quadratic Transformations

Published on 15 Apr 2026 - 10:50

239

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A question about $\int_{0}^{\pi/2} \ln(\sec^{2}(x) + \tan^{4}(x)) \mathrm{d}x$

Published on 14 Apr 2026 - 2:11

80

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$I = \int_{1}^{+\infty} f(x) dx $ exist iff exist $\lim_{n \to +\infty} \int_{1}^{n} f(x) dx$

Published on 17 Apr 2026 - 5:57

118

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For what values of $a$ does $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\cos{x})^a \ dx$ converge?

Published on 15 Apr 2026 - 11:38

229

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Is there a closed form of $\int_0^{+\infty} t^n \cos (\pi t) e^{-m t}dt$ for any non-negative integer $n$ and $m>0$?

Published on 15 Apr 2026 - 21:16

328

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How to evaluate $\int_0^1 \frac{dx}{\sqrt{x + \sqrt{x^2 + \sqrt{x^3}}}}?$

Published on 15 Apr 2026 - 12:52

120

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Can you pull out the sign-function out of the integral?

Published on 14 Apr 2026 - 10:59

80

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Evaluating the integral of a double power law

Published on 25 Mar 2026 - 9:37

94

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Evaluate $\Gamma(-\frac{1}{2})$ directly from the definition of $\Gamma()$

Published on 14 Apr 2026 - 16:47

133

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Solving the integral $\int\limits^{\infty}_{1}\frac{x-\sqrt{\lfloor x^2\rfloor}}{x}dx$

Published on 15 Apr 2026 - 23:14

89

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convergence of $\int_{0}^{\infty} \cos(x^3-x)\, dx$

Published on 17 Apr 2026 - 2:39

49

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Necessary condition for convergence of improper integrals

Published on 11 Apr 2026 - 23:41

41

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Integral representation of Meijer G function

Published on 12 Apr 2026 - 19:20

List Question

Evaluate integral $\int_0^1\sin(\pi \sqrt{-\ln x})\,dx$

What to do when an improper integral returns infinity-infinity

Hypergeometric Quadratic Transformations

A question about $\int_{0}^{\pi/2} \ln(\sec^{2}(x) + \tan^{4}(x)) \mathrm{d}x$

$I = \int_{1}^{+\infty} f(x) dx $ exist iff exist $\lim_{n \to +\infty} \int_{1}^{n} f(x) dx$

For what values of $a$ does $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\cos{x})^a \ dx$ converge?

Is there a closed form of $\int_0^{+\infty} t^n \cos (\pi t) e^{-m t}dt$ for any non-negative integer $n$ and $m>0$?

How to evaluate $\int_0^1 \frac{dx}{\sqrt{x + \sqrt{x^2 + \sqrt{x^3}}}}?$

Can you pull out the sign-function out of the integral?

Evaluating the integral of a double power law

Evaluate $\Gamma(-\frac{1}{2})$ directly from the definition of $\Gamma()$

Solving the integral $\int\limits^{\infty}_{1}\frac{x-\sqrt{\lfloor x^2\rfloor}}{x}dx$

convergence of $\int_{0}^{\infty} \cos(x^3-x)\, dx$

Necessary condition for convergence of improper integrals

Integral representation of Meijer G function

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