Question

how to calculuate $\int_0^ \pi \sqrt{1+x^2 \sin^2x}dx$

score 392 · Answer 1 · 2014-10-01 15:57:57

392

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how to calculuate $\int_0^ \pi \sqrt{1+x^2 \sin^2x}dx$

Published on 01 Oct 2014 - 15:57

score 237 · Answer 2 · 2014-10-03 13:59:58

237

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A closed form for $\sum_{n=1}^{\infty}(-1)^{n-1}\arctan\left(\frac{1}{n}\right)\ln(n^2+1) $

Published on 03 Oct 2014 - 13:59

score 266 · Answer 3 · 2014-10-04 05:50:26

266

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Sums with squares of binomial coefficients multiplied by a polynomial

Published on 04 Oct 2014 - 5:50

score 509 · Answer 4 · 2026-03-25 07:44:50

509

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Generalized FoxTrot Series $F(a,b,q,x) = \sum_{k=q}^{\infty} \dfrac {(-1)^{k+1} k^a}{k^b+x}$

Published on 25 Mar 2026 - 7:44

score 3.5k · Answer 5 · 2014-10-05 00:08:50

3.5k

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Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $

Published on 05 Oct 2014 - 0:08

score 212 · Answer 6 · 2014-10-05 04:04:08

212

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How to derive the closed form of this recurrence?

Published on 05 Oct 2014 - 4:04

score 76 · Answer 7 · 2014-10-05 15:39:39

76

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How to find this integral $I=\int_{0}^{1} t^{-1/2}\left(1-\frac{t}{1+4y}\right)^{-1/2-ix}dt$

Published on 05 Oct 2014 - 15:39

score 8.4k · Answer 8 · 2014-10-06 09:37:12

8.4k

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A long nasty limit problem: $\lim_{x \to \infty}\left[8e\,\sqrt[\Large x]{x^{x+1}(x-1)!}- 8x^2-4x \ln x - \ln^2 x - (4x + 2 \ln x) \ln 2\pi\right]$

Published on 06 Oct 2014 - 9:37

score 231 · Answer 9 · 2026-03-25 07:43:50

231

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Double series of Harmonic Numbers

Published on 25 Mar 2026 - 7:43

score 1.2k · Answer 10 · 2026-03-28 01:08:35

1.2k

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Prove ${_2F_1}\left({{\tfrac16,\tfrac23}\atop{\tfrac56}}\middle|\,\frac{80}{81}\right)=\frac 35 \cdot 5^{1/6} \cdot 3^{2/3}$

Published on 28 Mar 2026 - 1:08

score 179 · Answer 11 · 2014-10-08 02:32:39

179

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How to write in closed form this nasty expression?

Published on 08 Oct 2014 - 2:32

score 2.1k · Answer 12 · 2014-10-08 22:48:45

2.1k

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Integral $\int_0^1\frac{x^{42}}{\sqrt{x^4-x^2+1}}\operatorname d \!x$

Published on 08 Oct 2014 - 22:48

score 225 · Answer 13 · 2026-03-25 16:01:55

225

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Is there a finite set comprising the solutions to indefinite integrals of common functions?

Published on 25 Mar 2026 - 16:01

score 107 · Answer 14 · 2026-03-27 04:22:29

107

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Integral involving the error function

Published on 27 Mar 2026 - 4:22

score 485 · Answer 15 · 2026-03-26 14:40:41

485

Views

Any way to get a Recursive function from its closed form?

Published on 26 Mar 2026 - 14:40

List Question

how to calculuate $\int_0^ \pi \sqrt{1+x^2 \sin^2x}dx$

A closed form for $\sum_{n=1}^{\infty}(-1)^{n-1}\arctan\left(\frac{1}{n}\right)\ln(n^2+1) $

Sums with squares of binomial coefficients multiplied by a polynomial

Generalized FoxTrot Series $F(a,b,q,x) = \sum_{k=q}^{\infty} \dfrac {(-1)^{k+1} k^a}{k^b+x}$

Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $

How to derive the closed form of this recurrence?

How to find this integral $I=\int_{0}^{1} t^{-1/2}\left(1-\frac{t}{1+4y}\right)^{-1/2-ix}dt$

A long nasty limit problem: $\lim_{x \to \infty}\left[8e\,\sqrt[\Large x]{x^{x+1}(x-1)!}- 8x^2-4x \ln x - \ln^2 x - (4x + 2 \ln x) \ln 2\pi\right]$

Double series of Harmonic Numbers

Prove ${_2F_1}\left({{\tfrac16,\tfrac23}\atop{\tfrac56}}\middle|\,\frac{80}{81}\right)=\frac 35 \cdot 5^{1/6} \cdot 3^{2/3}$

How to write in closed form this nasty expression?

Integral $\int_0^1\frac{x^{42}}{\sqrt{x^4-x^2+1}}\operatorname d \!x$

Is there a finite set comprising the solutions to indefinite integrals of common functions?

Integral involving the error function

Any way to get a Recursive function from its closed form?

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