Question

Find a general solution for $\int_{0}^{\infty} \sin\left(x^n\right)\:dx$

score 490 · Answer 1 · 2026-04-16 06:58:39

490

Views

Find a general solution for $\int_{0}^{\infty} \sin\left(x^n\right)\:dx$

Published on 16 Apr 2026 - 6:58

score 122 · Answer 2 · 2026-04-16 05:18:27

122

Views

Every solution of $x''+x+x^3=0$ is set on $\mathbb{R}$ (proof)

Published on 16 Apr 2026 - 5:18

score 66 · Answer 3 · 2026-04-12 16:51:25

66

Views

Proofreading of a short passage (number theory)

Published on 12 Apr 2026 - 16:51

score 41 · Answer 4 · 2026-04-16 19:03:32

41

Views

Show that $x_n = \left(1+{x\over n}\right)^{n+k}$ is decreasing for $0<x<k$; $n, k\in \mathbb N$

Published on 16 Apr 2026 - 19:03

score 403 · Answer 5 · 2026-04-16 18:54:38

403

Views

Proving $d((x_1,y_1),(x_2,y_2))=\max\{d_1(x_1,x_2),d_2(y_1,y_2)\}$ and $e((x_1,y_1),(x_2,y_2))=d_1(x_1,x_2)+d_2(y_1,y_2)$ are equivalent

Published on 16 Apr 2026 - 18:54

score 371 · Answer 6 · 2026-04-11 20:28:03

371

Views

Proving a decimal expansion is bijective

Published on 11 Apr 2026 - 20:28

score 584 · Answer 7 · 2026-04-15 18:07:40

584

Views

Prove that $\sqrt{2} + \sqrt{17}$ is irrational. Is my proof correct?

Published on 15 Apr 2026 - 18:07

score 106 · Answer 8 · 2026-04-13 17:22:39

106

Views

Is $\{A \in E: A \text{ has distinct eigenvalues}\}$ dense in $E = \{A \in M_n(\mathbb R): \max_i \text{Re}(\lambda_i(A))=0\}$?

Published on 13 Apr 2026 - 17:22

score 243 · Answer 9 · 2026-04-12 13:35:44

243

Views

Show that $30x^n-91$ does not have rational roots

Published on 12 Apr 2026 - 13:35

score 2.2k · Answer 10 · 2026-04-14 23:09:53

2.2k

Views

If $n$ balls are distributed randomly into $k$ buckets, what is the probability that the first bucket contains $j$ balls?

Published on 14 Apr 2026 - 23:09

score 33 · Answer 11 · 2026-03-25 14:29:59

33

Views

Showing a Result Using Cauchy's Generalised Integral Formula

Published on 25 Mar 2026 - 14:29

score 498 · Answer 12 · 2026-03-25 09:28:25

498

Views

Prove the following set of unit vectors is orthogonal.

Published on 25 Mar 2026 - 9:28

score 71 · Answer 13 · 2026-04-09 07:31:20

71

Views

Prove that, $\textrm{LCM}(\textrm{GCD}(m,x),\textrm{GCD}(n,x)) = \textrm{GCD}(\textrm{LCM}(m,n),x)$

Published on 09 Apr 2026 - 7:31

score 68 · Answer 14 · 2026-04-13 19:35:48

68

Views

Could I substitute $i$ in a convergence series?

Published on 13 Apr 2026 - 19:35

score 532 · Answer 15 · 2026-04-09 18:39:06

532

Views

Why Riemannian metric does not depend on the choice of coordinate system

Published on 09 Apr 2026 - 18:39

List Question

Find a general solution for $\int_{0}^{\infty} \sin\left(x^n\right)\:dx$

Every solution of $x''+x+x^3=0$ is set on $\mathbb{R}$ (proof)

Proofreading of a short passage (number theory)

Show that $x_n = \left(1+{x\over n}\right)^{n+k}$ is decreasing for $0<x<k$; $n, k\in \mathbb N$

Proving $d((x_1,y_1),(x_2,y_2))=\max\{d_1(x_1,x_2),d_2(y_1,y_2)\}$ and $e((x_1,y_1),(x_2,y_2))=d_1(x_1,x_2)+d_2(y_1,y_2)$ are equivalent

Proving a decimal expansion is bijective

Prove that $\sqrt{2} + \sqrt{17}$ is irrational. Is my proof correct?

Is $\{A \in E: A \text{ has distinct eigenvalues}\}$ dense in $E = \{A \in M_n(\mathbb R): \max_i \text{Re}(\lambda_i(A))=0\}$?

Show that $30x^n-91$ does not have rational roots

If $n$ balls are distributed randomly into $k$ buckets, what is the probability that the first bucket contains $j$ balls?

Showing a Result Using Cauchy's Generalised Integral Formula

Prove the following set of unit vectors is orthogonal.

Prove that, $\textrm{LCM}(\textrm{GCD}(m,x),\textrm{GCD}(n,x)) = \textrm{GCD}(\textrm{LCM}(m,n),x)$

Could I substitute $i$ in a convergence series?

Why Riemannian metric does not depend on the choice of coordinate system

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