List questions from closed-form

Published on 14 Dec 2014 - 12:55

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Finding a closed-form formula for a sequence that is defined recursively

Published on 14 Dec 2014 - 23:13

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Evaluating $\int_{0}^{\pi/2}\frac{x\sin x\cos x\;dx}{(a^{2}\cos^{2}x+b^{2}\sin^{2}x)^{2}}$

Published on 15 Dec 2014 - 3:46

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Closed form of $\int_0^\infty \ln \left( \frac{x^2+2kx\cos b+k^2}{x^2+2kx\cos a+k^2}\right) \;\frac{\mathrm dx}{x}$

Published on 15 Dec 2014 - 16:59

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How to find a recursive formula for some sequence

Published on 16 Dec 2014 - 22:12

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Recursively appending mean to list: Is there a closed form?

Published on 18 Dec 2014 - 8:14

274

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How to calculate the series?

Published on 19 Dec 2014 - 8:54

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How to calculate the series in the modified form?

Published on 19 Dec 2014 - 9:12

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Multiple integrals involving product of gamma functions

Published on 29 Mar 2026 - 18:50

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Closed form of $\int_0^1\int_0^1\int_0^1\frac{\left(1-x^y\right)\left(1-x^z\right)\ln x}{(1-x)^3}\,\mathrm dx\;\mathrm dy\;\mathrm dz$

Published on 20 Dec 2014 - 15:49

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Closed form of $\int_{0}^{\eta}\cos nt\log\left(\frac{\cos(t/2)+\sqrt{\cos^2(t/2) -\cos^2(\eta/2)}}{\cos(\eta/2)}\right) dt$

Published on 20 Dec 2014 - 17:09

544

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Finding $ \int_0^1 \frac {\ln x}{1+x^2}\mathrm dx $

Published on 20 Dec 2014 - 18:26

72

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Given a closed form for a series, what can be said about the sum of the squares of its terms?

Published on 27 Mar 2026 - 6:16

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The sequence of improper integrals of the form $\int\frac{dx}{1+x^{2n}}$

Published on 21 Dec 2014 - 13:50

1.1k

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Evaluate $\int \ln(1 + e^x)\ \mathrm dx$

Published on 21 Dec 2014 - 17:43

List Question

Closed form of a series

Finding a closed-form formula for a sequence that is defined recursively

Evaluating $\int_{0}^{\pi/2}\frac{x\sin x\cos x\;dx}{(a^{2}\cos^{2}x+b^{2}\sin^{2}x)^{2}}$

Closed form of $\int_0^\infty \ln \left( \frac{x^2+2kx\cos b+k^2}{x^2+2kx\cos a+k^2}\right) \;\frac{\mathrm dx}{x}$

How to find a recursive formula for some sequence

Recursively appending mean to list: Is there a closed form?

How to calculate the series?

How to calculate the series in the modified form?

Multiple integrals involving product of gamma functions

Closed form of $\int_0^1\int_0^1\int_0^1\frac{\left(1-x^y\right)\left(1-x^z\right)\ln x}{(1-x)^3}\,\mathrm dx\;\mathrm dy\;\mathrm dz$

Closed form of $\int_{0}^{\eta}\cos nt\log\left(\frac{\cos(t/2)+\sqrt{\cos^2(t/2) -\cos^2(\eta/2)}}{\cos(\eta/2)}\right) dt$

Finding $ \int_0^1 \frac {\ln x}{1+x^2}\mathrm dx $

Given a closed form for a series, what can be said about the sum of the squares of its terms?

The sequence of improper integrals of the form $\int\frac{dx}{1+x^{2n}}$

Evaluate $\int \ln(1 + e^x)\ \mathrm dx$

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