Question

Integral $\int_0^\infty\Big[\log\left(1+x^2\right)-\psi\left(1+x^2\right)\Big]dx$

score 853 · Answer 1 · 2026-03-14 08:10:50

853

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Integral $\int_0^\infty\Big[\log\left(1+x^2\right)-\psi\left(1+x^2\right)\Big]dx$

Published on 14 Mar 2026 - 8:10

score 189 · Answer 2 · 2016-01-13 13:52:34

189

Views

Closed form of $\int_{x = 0}^{C} \exp\left(-\frac{x}{A}-\frac{B}{x}\right)\,dx$

Published on 13 Jan 2016 - 13:52

score 201 · Answer 3 · 2016-01-14 00:28:27

201

Views

Simplify $\int_0^\infty \frac{\text{d}{x}}{e^x+x^n}$

Published on 14 Jan 2016 - 0:28

score 295 · Answer 4 · 2016-01-14 11:42:54

295

Views

Non-existence of closed-form solutions

Published on 14 Jan 2016 - 11:42

score 699 · Answer 5 · 2016-01-14 23:52:30

699

Views

Writing sigma notation $\sum^n_{i=1} \frac {i}{2^i}$ in closed form

Published on 14 Jan 2016 - 23:52

score 1.2k · Answer 6 · 2016-01-16 14:32:26

1.2k

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Conjectured closed form for $\sum_{n=-\infty}^\infty\frac{1}{\cosh\pi n+\frac{1}{\sqrt{2}}}$

Published on 16 Jan 2016 - 14:32

score 140 · Answer 7 · 2016-01-17 00:41:06

140

Views

I know the following integral can be computed in closed form, but I can't figure out how ...

Published on 17 Jan 2016 - 0:41

score 125 · Answer 8 · 2016-01-17 08:19:41

125

Views

Closed form or approximation of $\sum\limits_{i=0}^{n-1}\sum\limits_{j=i + 1}^{n-1} \frac{i + j + 2}{(i + 1)(j+1)} (i + 2x)(j +2x)$

Published on 17 Jan 2016 - 8:19

score 57 · Answer 9 · 2016-01-19 08:08:56

57

Views

closed-form of an integral with regard to $a$

Published on 19 Jan 2016 - 8:08

score 2.5k · Answer 10 · 2026-03-26 08:04:36

2.5k

Views

How to know if I can't solve an equation with "standard" methods?

Published on 26 Mar 2026 - 8:04

score 336 · Answer 11 · 2016-01-19 18:58:05

Potential function for an exact closed differential form and a solution of a corresponding linear first order homogeneous differential equation

score 177 · Answer 12 · 2016-01-20 03:20:24

177

Views

Closed-form of a series relating to trigonometric function

Published on 20 Jan 2016 - 3:20

score 171 · Answer 13 · 2016-01-20 09:06:39

171

Views

hunting for the closed form of a series

Published on 20 Jan 2016 - 9:06

score 99 · Answer 14 · 2016-01-21 18:10:01

99

Views

Closed form of $\int_{\delta_1}^{\delta_2}(1+Ax)^{-L}x^{L}\exp\left(-Bx\right)dx$

Published on 21 Jan 2016 - 18:10

score 94 · Answer 15 · 2016-01-22 16:13:50

94

Views

Vandermonde's identity and the close form of $\sum_{k=0}^r C(n,k) C(m,r-k) x^k$

Published on 22 Jan 2016 - 16:13

List Question

Integral $\int_0^\infty\Big[\log\left(1+x^2\right)-\psi\left(1+x^2\right)\Big]dx$

Closed form of $\int_{x = 0}^{C} \exp\left(-\frac{x}{A}-\frac{B}{x}\right)\,dx$

Simplify $\int_0^\infty \frac{\text{d}{x}}{e^x+x^n}$

Non-existence of closed-form solutions

Writing sigma notation $\sum^n_{i=1} \frac {i}{2^i}$ in closed form

Conjectured closed form for $\sum_{n=-\infty}^\infty\frac{1}{\cosh\pi n+\frac{1}{\sqrt{2}}}$

I know the following integral can be computed in closed form, but I can't figure out how ...

Closed form or approximation of $\sum\limits_{i=0}^{n-1}\sum\limits_{j=i + 1}^{n-1} \frac{i + j + 2}{(i + 1)(j+1)} (i + 2x)(j +2x)$

closed-form of an integral with regard to $a$

How to know if I can't solve an equation with "standard" methods?

Potential function for an exact closed differential form and a solution of a corresponding linear first order homogeneous differential equation

Closed-form of a series relating to trigonometric function

hunting for the closed form of a series

Closed form of $\int_{\delta_1}^{\delta_2}(1+Ax)^{-L}x^{L}\exp\left(-Bx\right)dx$

Vandermonde's identity and the close form of $\sum_{k=0}^r C(n,k) C(m,r-k) x^k$

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