Question

Evaluate the indefinite integral $\int\left(1-\left(1-x^{\frac{1}{a}}\right)^a\right)\mathrm dx\,$

score 125 · Answer 1 · 2023-07-05 18:02:08

125

Views

Evaluate the indefinite integral $\int\left(1-\left(1-x^{\frac{1}{a}}\right)^a\right)\mathrm dx\,$

Published on 05 Jul 2023 - 18:02

score 21 · Answer 2 · 2023-07-06 17:45:54

21

Views

Need help in detailing the proof of the existence of the test function

Published on 06 Jul 2023 - 17:45

score 61 · Answer 3 · 2023-07-08 17:56:23

61

Views

How to compute $\int_{-\infty}^{\infty} 1/(x^2+1)^s dx$?

Published on 08 Jul 2023 - 17:56

score 176 · Answer 4 · 2023-07-18 14:01:04

176

Views

How to solve this definite integral? $\int_0^1\frac{1}{\sqrt{1+x^4}}\,{\rm d}x$

Published on 18 Jul 2023 - 14:01

score 17 · Answer 5 · 2023-07-26 22:21:22

17

Views

Natural two parameter probability distribution for a one-sided interval

Published on 26 Jul 2023 - 22:21

score 114 · Answer 6 · 2023-08-07 11:48:59

114

Views

Challenging integral evaluation

Published on 07 Aug 2023 - 11:48

score 66 · Answer 7 · 2023-08-09 13:35:59

66

Views

Integration: "partial" Beta function?

Published on 09 Aug 2023 - 13:35

score 30 · Answer 8 · 2023-08-12 22:45:28

30

Views

Express the following $\int \cdots \int \prod_i AR_i ^{\alpha_i-s_i}dR_{k-1} \cdots dR_1$ in binomial form

Published on 12 Aug 2023 - 22:45

score 41 · Answer 9 · 2023-08-16 16:11:51

41

Views

Expansion of Beta function near negative integers

Published on 16 Aug 2023 - 16:11

score 61 · Answer 10 · 2023-08-27 02:13:17

61

Views

Is there a way to express $ \sum_{n=0}^\infty \frac{(-1)^n}{2n+1}\,\,B_{\frac{1}{2}}\left(n+\frac{1}{2},\frac{1}{2}\right)$

Published on 27 Aug 2023 - 2:13

score 67 · Answer 11 · 2023-08-27 10:21:55

67

Views

Solve for $\int_0^1 t^{s+a-1}(1-t)^{a-1}(2t-1)^{-1}dt$

Published on 27 Aug 2023 - 10:21

score 76 · Answer 12 · 2026-03-26 12:54:01

76

Views

"Legendre-type" integrals involving $\frac{dt}{\sqrt{t^2-2t\cos(\theta)+1}}$

Published on 26 Mar 2026 - 12:54

score 46 · Answer 13 · 2023-09-04 07:32:22

46

Views

To evaluate some Complex integral by using Beta function

Published on 04 Sep 2023 - 7:32

score 154 · Answer 14 · 2023-09-09 11:45:14

154

Views

How to find the limit $\left (\int_0^{\frac{\pi}{2}}\sin^n xdx\right)^{\frac{1}{n}}$

Published on 09 Sep 2023 - 11:45

score 167 · Answer 15 · 2023-09-11 09:34:43

167

Views

Analytic continuation of Dirichlet beta funcion

Published on 11 Sep 2023 - 9:34

List Question

Evaluate the indefinite integral $\int\left(1-\left(1-x^{\frac{1}{a}}\right)^a\right)\mathrm dx\,$

Need help in detailing the proof of the existence of the test function

How to compute $\int_{-\infty}^{\infty} 1/(x^2+1)^s dx$?

How to solve this definite integral? $\int_0^1\frac{1}{\sqrt{1+x^4}}\,{\rm d}x$

Natural two parameter probability distribution for a one-sided interval

Challenging integral evaluation

Integration: "partial" Beta function?

Express the following $\int \cdots \int \prod_i AR_i ^{\alpha_i-s_i}dR_{k-1} \cdots dR_1$ in binomial form

Expansion of Beta function near negative integers

Is there a way to express $ \sum_{n=0}^\infty \frac{(-1)^n}{2n+1}\,\,B_{\frac{1}{2}}\left(n+\frac{1}{2},\frac{1}{2}\right)$

Solve for $\int_0^1 t^{s+a-1}(1-t)^{a-1}(2t-1)^{-1}dt$

"Legendre-type" integrals involving $\frac{dt}{\sqrt{t^2-2t\cos(\theta)+1}}$

To evaluate some Complex integral by using Beta function

How to find the limit $\left (\int_0^{\frac{\pi}{2}}\sin^n xdx\right)^{\frac{1}{n}}$

Analytic continuation of Dirichlet beta funcion

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