Question

Closed form of $\mathscr{R}=\int_0^{\pi/2}\sin^2x\,\ln\big(\sin^2(\tan x)\big)\,\,dx$

score 1.9k · Answer 1 · 2014-11-04 17:14:53

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Closed form of $\mathscr{R}=\int_0^{\pi/2}\sin^2x\,\ln\big(\sin^2(\tan x)\big)\,\,dx$

Published on 04 Nov 2014 - 17:14

score 139 · Answer 2 · 2014-11-04 19:19:10

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$\displaystyle\int_0^{\infty} \dfrac{\mathrm{d}x}{(x^4+ax^3+bx^2+cx+d)^m}$

Published on 04 Nov 2014 - 19:19

score 2.2k · Answer 3 · 2014-11-05 13:05:09

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How to solve integrals using series?

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score 1.4k · Answer 4 · 2014-11-06 00:50:23

1.4k

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An infinite exponential sum

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score 187 · Answer 5 · 2014-11-06 02:23:14

187

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Closed form of a "harmonic" alternating dilogarithm sum

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score 42 · Answer 6 · 2026-03-27 19:33:45

42

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List of functions $\chi_{s,a}(n)$ defined on a Group such that $\chi_{s,a}(n)\in{s,a}$ and depending on the parity

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score 77 · Answer 7 · 2014-11-07 16:13:26

77

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Closed form for certain trigonometric integral

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score 433 · Answer 8 · 2026-03-28 11:37:24

433

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score 405 · Answer 9 · 2014-11-08 15:54:20

405

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How to find closed-form of $\int_{0}^{+\infty} \operatorname{sech}^2 (x^2)\,dx$

Published on 08 Nov 2014 - 15:54

score 347 · Answer 10 · 2014-11-11 10:17:54

347

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score 76 · Answer 11 · 2026-03-25 11:53:23

76

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score 154 · Answer 12 · 2014-11-12 18:39:48

154

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General Solution of $y'(x)+p(x)e^{r(x) y(x)}=q(x)$

Published on 12 Nov 2014 - 18:39

score 287 · Answer 13 · 2014-11-13 11:21:40

287

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Closed-form formula for the $n^{\rm th}$ term of ${1,1,1,1,\ldots, 1}, {2,2,2,2,\ldots, 2},\ldots, {k-1, k-1}, k.$

Published on 13 Nov 2014 - 11:21

score 130 · Answer 14 · 2014-11-14 00:40:14

130

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what's the summation of this finite sequence?

Published on 14 Nov 2014 - 0:40

score 349 · Answer 15 · 2014-11-14 05:08:10

349

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An integral $\int^\infty_0\frac{\tanh{x}}{x(1-2\cosh{2x})^2}{\rm d}x$

Published on 14 Nov 2014 - 5:08

List Question

Closed form of $\mathscr{R}=\int_0^{\pi/2}\sin^2x\,\ln\big(\sin^2(\tan x)\big)\,\,dx$

$\displaystyle\int_0^{\infty} \dfrac{\mathrm{d}x}{(x^4+ax^3+bx^2+cx+d)^m}$

How to solve integrals using series?

An infinite exponential sum

Closed form of a "harmonic" alternating dilogarithm sum

List of functions $\chi_{s,a}(n)$ defined on a Group such that $\chi_{s,a}(n)\in{s,a}$ and depending on the parity

Closed form for certain trigonometric integral

New identity for sums of Bessel functions?

How to find closed-form of $\int_{0}^{+\infty} \operatorname{sech}^2 (x^2)\,dx$

Solving a 2 independent variables (2nd degree) recurrence relation

Help in simplifying this nasty expression obtained after binomial expnasion

General Solution of $y'(x)+p(x)e^{r(x) y(x)}=q(x)$

Closed-form formula for the $n^{\rm th}$ term of ${1,1,1,1,\ldots, 1}, {2,2,2,2,\ldots, 2},\ldots, {k-1, k-1}, k.$

what's the summation of this finite sequence?

An integral $\int^\infty_0\frac{\tanh{x}}{x(1-2\cosh{2x})^2}{\rm d}x$

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