List questions from improper-integrals

Published on 16 Apr 2026 - 8:19

325

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Hard Integral $\frac{1}{(1+x^2+y^2+z^2)^2}$

Published on 14 Apr 2026 - 23:03

285

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Improper integral $\int_0^\infty \sqrt{x}e^{-x}\,dx$

Published on 16 Apr 2026 - 1:17

470

Views

Extended integral over parabola open set

Published on 11 Apr 2026 - 19:02

71

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Determine if the given integral is convergent

Published on 12 Apr 2026 - 12:16

626

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Conditional expectations of the beta distribution in closed form?

Published on 13 Apr 2026 - 6:45

414

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Two-sided improper integral

Published on 13 Apr 2026 - 2:19

4.7k

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A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$

Published on 16 Apr 2026 - 1:08

159

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Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$

Published on 15 Apr 2026 - 23:07

13.2k

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A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$

Published on 16 Apr 2026 - 4:23

88

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How to prove that this integral converges absolutely?

Published on 11 Apr 2026 - 10:31

260

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Difficulties with an elliptic integral (Ahlfors)

Published on 27 Mar 2026 - 3:48

1.1k

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Show that $K=K'$ if and only if $k=(\sqrt{2}-1)^2$ (Ahlfors)

Published on 27 Mar 2026 - 5:38

660

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Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$

Published on 14 Apr 2026 - 22:43

43

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How come the following equality for the integral

Published on 09 Apr 2026 - 8:14

List Question

Solve the following definite integral: $\int_{0}^{\infty}\frac{x^2dx}{({1-x^2})^2}$

Hard Integral $\frac{1}{(1+x^2+y^2+z^2)^2}$

Improper integral $\int_0^\infty \sqrt{x}e^{-x}\,dx$

Extended integral over parabola open set

Determine if the given integral is convergent

Conditional expectations of the beta distribution in closed form?

Two-sided improper integral

A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$

Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$

A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$

How to prove that this integral converges absolutely?

Difficulties with an elliptic integral (Ahlfors)

Show that $K=K'$ if and only if $k=(\sqrt{2}-1)^2$ (Ahlfors)

Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$

How come the following equality for the integral

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