Question

Closed form of $\int \frac{1}{\sqrt{(x-a) (x-b) (x-c) (x-d) (x-e)}} \, \rm{d}x$

score 156 · Answer 1 · 2022-05-24 05:08:29

156

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Closed form of $\int \frac{1}{\sqrt{(x-a) (x-b) (x-c) (x-d) (x-e)}} \, \rm{d}x$

Published on 24 May 2022 - 5:08

score 444 · Answer 2 · 2022-05-26 05:15:33

444

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Integral of $\sqrt{\cosh(x)}$ with respect to x

Published on 26 May 2022 - 5:15

score 107 · Answer 3 · 2026-03-27 22:57:33

107

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how to prove this identity $s = 2 \int_{- \pi}^{\pi} | \frac{\sin (t) - i}{(\sin (t) + i)^2} | dt = 2 K (- 1) = 2.62206...$

Published on 27 Mar 2026 - 22:57

score 50 · Answer 4 · 2026-03-27 22:57:31

50

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What is the argument of the quarter period $iK^\prime(k)$ when $|k| = 1$, i.e. $k = e^{i\alpha}$? (Is it $\frac{\pi-\alpha}{2}$?)

Published on 27 Mar 2026 - 22:57

score 71 · Answer 5 · 2022-06-20 14:43:07

71

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prove the definite Integral

Published on 20 Jun 2022 - 14:43

score 115 · Answer 6 · 2026-03-28 02:06:35

Simplifications of the Elliptic integral $\displaystyle J_n(r)=\int^r_{r_0}\frac{x^n}{\sqrt{(x-x_1)(x-x_2)(x-x_3)}}$ for specific values of $n$.

score 111 · Answer 7 · 2022-06-26 00:54:46

111

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Any hint for evaluating $\int_0^\theta \sec^2(\phi)\cdot\sqrt{\sec2\phi}\,d\phi\;$?

Published on 26 Jun 2022 - 0:54

score 148 · Answer 8 · 2022-06-28 11:04:52

148

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Elliptic integrals of complex argument and parameter

Published on 28 Jun 2022 - 11:04

score 129 · Answer 9 · 2022-06-29 17:56:23

129

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Assistance with solving the integral

Published on 29 Jun 2022 - 17:56

score 63 · Answer 10 · 2022-07-02 16:22:50

63

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Product of elliptic integrals given by inverse ellipses

Published on 02 Jul 2022 - 16:22

score 72 · Answer 11 · 2022-07-17 07:20:49

72

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Differential Equations with Special Functions: Are analytical solutions possible?

Published on 17 Jul 2022 - 7:20

score 96 · Answer 12 · 2026-03-26 11:03:49

96

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An integral Identity about the Elliptic Integrals and Ellipsoids

Published on 26 Mar 2026 - 11:03

score 250 · Answer 13 · 2022-07-29 12:43:09

250

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Reduction of elliptic integrals to Legendre's normal form

Published on 29 Jul 2022 - 12:43

score 330 · Answer 14 · 2022-08-06 11:24:15

330

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Circle Deformation

Published on 06 Aug 2022 - 11:24

score 175 · Answer 15 · 2022-08-09 15:16:01

175

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The lemniscate of Euler's $\textit{elastica}$: precise determination of a characteristic constant

Published on 09 Aug 2022 - 15:16

List Question

Closed form of $\int \frac{1}{\sqrt{(x-a) (x-b) (x-c) (x-d) (x-e)}} \, \rm{d}x$

Integral of $\sqrt{\cosh(x)}$ with respect to x

how to prove this identity $s = 2 \int_{- \pi}^{\pi} | \frac{\sin (t) - i}{(\sin (t) + i)^2} | dt = 2 K (- 1) = 2.62206...$

What is the argument of the quarter period $iK^\prime(k)$ when $|k| = 1$, i.e. $k = e^{i\alpha}$? (Is it $\frac{\pi-\alpha}{2}$?)

prove the definite Integral

Simplifications of the Elliptic integral $\displaystyle J_n(r)=\int^r_{r_0}\frac{x^n}{\sqrt{(x-x_1)(x-x_2)(x-x_3)}}$ for specific values of $n$.

Any hint for evaluating $\int_0^\theta \sec^2(\phi)\cdot\sqrt{\sec2\phi}\,d\phi\;$?

Elliptic integrals of complex argument and parameter

Assistance with solving the integral

Product of elliptic integrals given by inverse ellipses

Differential Equations with Special Functions: Are analytical solutions possible?

An integral Identity about the Elliptic Integrals and Ellipsoids

Reduction of elliptic integrals to Legendre's normal form

Circle Deformation

The lemniscate of Euler's $\textit{elastica}$: precise determination of a characteristic constant

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