Question

Resistant integral $\int_0^1\left(\frac{\ln^2(1-x)\ln^2(1+x)}{1-x}-\frac{\ln^2(2)\ln^2(1-x)}{1-x}\right)\ dx$

score 650 · Answer 1 · 2026-03-26 04:35:08

650

Views

Resistant integral $\int_0^1\left(\frac{\ln^2(1-x)\ln^2(1+x)}{1-x}-\frac{\ln^2(2)\ln^2(1-x)}{1-x}\right)\ dx$

Published on 26 Mar 2026 - 4:35

score 92 · Answer 2 · 2026-03-27 03:42:24

92

Views

Given a, b, c are positive number, $abc=a+b+c$ prove $ab+4bc+9ac≥36$

Published on 27 Mar 2026 - 3:42

score 381 · Answer 3 · 2026-03-27 04:35:13

381

Views

Triple integral $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \frac{dx dy dz}{(1+x^2+y^2+z^2)^2}$

Published on 27 Mar 2026 - 4:35

score 155 · Answer 4 · 2019-07-25 16:18:17

155

Views

Prove or give Counterexample: Is this a Basis (from a more abstract perspective)

Published on 25 Jul 2019 - 16:18

score 65 · Answer 5 · 2019-07-26 00:09:34

65

Views

Proof verification for the set of an intersection of two finite-dimensional subspaces.

Published on 26 Jul 2019 - 0:09

score 172 · Answer 6 · 2026-03-27 20:27:02

172

Views

Proof checking about cardinality of all Real numbers

Published on 27 Mar 2026 - 20:27

score 92 · Answer 7 · 2019-07-28 12:21:52

92

Views

Prove that for all positive integers $x, \ x$ is not divisible by $3 \iff {x^2 - 1} $ is divisible by $3$.

Published on 28 Jul 2019 - 12:21

score 485 · Answer 8 · 2019-07-28 19:15:21

485

Views

If $0<x<1$ and $n$ is a positive integer, then $x^n < 1$

Published on 28 Jul 2019 - 19:15

score 98 · Answer 9 · 2019-07-29 14:54:15

98

Views

Proof confusion or solving strategy?

Published on 29 Jul 2019 - 14:54

score 66 · Answer 10 · 2019-07-29 22:06:00

66

Views

Proof verification: $g\circ f$ injective $\implies$ $f$ injective

Published on 29 Jul 2019 - 22:06

score 658 · Answer 11 · 2019-07-31 04:32:02

658

Views

Is there a geometric proof of $ \sin(3t) = 3\sin(t) - 4\sin^3(t) $

Published on 31 Jul 2019 - 4:32

score 62 · Answer 12 · 2026-03-25 20:35:00

62

Views

Inequality involving integration on the unit square

Published on 25 Mar 2026 - 20:35

score 41 · Answer 13 · 2019-08-02 18:05:46

41

Views

Show that the origin is an attractor point. $F'(0)<1$

Published on 02 Aug 2019 - 18:05

score 38 · Answer 14 · 2019-08-03 10:54:20

38

Views

Is this a valid idea for proving $ S' \subset \text{Span(S)} \implies \text{Span(S')} \subset \text{Span(S)}$?

Published on 03 Aug 2019 - 10:54

score 49 · Answer 15 · 2026-03-26 14:41:58

49

Views

Why is $H/\Gamma$ a Riemann surface with a hyperbolic metric?

Published on 26 Mar 2026 - 14:41

List Question

Resistant integral $\int_0^1\left(\frac{\ln^2(1-x)\ln^2(1+x)}{1-x}-\frac{\ln^2(2)\ln^2(1-x)}{1-x}\right)\ dx$

Given a, b, c are positive number, $abc=a+b+c$ prove $ab+4bc+9ac≥36$

Triple integral $\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \frac{dx dy dz}{(1+x^2+y^2+z^2)^2}$

Prove or give Counterexample: Is this a Basis (from a more abstract perspective)

Proof verification for the set of an intersection of two finite-dimensional subspaces.

Proof checking about cardinality of all Real numbers

Prove that for all positive integers $x, \ x$ is not divisible by $3 \iff {x^2 - 1} $ is divisible by $3$.

If $0<x<1$ and $n$ is a positive integer, then $x^n < 1$

Proof confusion or solving strategy?

Proof verification: $g\circ f$ injective $\implies$ $f$ injective

Is there a geometric proof of $ \sin(3t) = 3\sin(t) - 4\sin^3(t) $

Inequality involving integration on the unit square

Show that the origin is an attractor point. $F'(0)<1$

Is this a valid idea for proving $ S' \subset \text{Span(S)} \implies \text{Span(S')} \subset \text{Span(S)}$?

Why is $H/\Gamma$ a Riemann surface with a hyperbolic metric?

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