Question

Substitution in Normal Distribution integral calculation

score 716 · Answer 1 · 2019-09-15 14:01:54

716

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Substitution in Normal Distribution integral calculation

Published on 15 Sep 2019 - 14:01

score 220 · Answer 2 · 2019-09-15 19:28:02

220

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How to solve $\int \frac{\sqrt{x^2-1}}{x^2}dx$ with trig substitution?

Published on 15 Sep 2019 - 19:28

score 284 · Answer 3 · 2019-09-16 11:13:14

284

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How and why do dummy variables work?

Published on 16 Sep 2019 - 11:13

score 93 · Answer 4 · 2019-09-17 08:53:58

93

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If $a+b+c=2$ where $0 \leq {a,b,c} \leq 1$ find the range of $\frac{a}{1-a}\cdot\frac{b}{1-b}\cdot\frac{c}{1-c}$

Published on 17 Sep 2019 - 8:53

score 143 · Answer 5 · 2026-03-25 11:07:02

143

Views

show this inequality $\sum_{cyc}\frac{a^3}{a^2+ab+b^2}\ge\sqrt{\sum a^3}$

Published on 25 Mar 2026 - 11:07

score 55 · Answer 6 · 2019-09-18 19:31:15

55

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Prove or disprove that $ \min\Bigg\{\frac{2x(1+\cos\theta)}{x+y},\frac{2x(1-\cos\theta)}{x-y}\Bigg\}\leq 2.$

Published on 18 Sep 2019 - 19:31

score 30 · Answer 7 · 2026-03-27 06:59:51

30

Views

How to show that two expressions containing 2-dimensional sums with different iterators are equal

Published on 27 Mar 2026 - 6:59

score 148 · Answer 8 · 2026-03-25 03:22:12

148

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Prove that $\sqrt{x^{3} + y^{3}+1} + \sqrt{z^{3} + y^{3}+1} + \sqrt{x^{3} + z^{3}+1} \ge 2 + \sqrt{2(x^{3} + y^{3}+z^{3})+1}$

Published on 25 Mar 2026 - 3:22

score 70 · Answer 9 · 2026-03-25 11:15:54

70

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I can't find the maximum value of P because of some problems in my solution.

Published on 25 Mar 2026 - 11:15

score 57 · Answer 10 · 2019-09-21 17:29:18

57

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Substitution in Linear Algebra

Published on 21 Sep 2019 - 17:29

score 161 · Answer 11 · 2019-09-23 03:34:04

161

Views

Prove inequalities $\frac 34 \le I(a,b) \le 1$

Published on 23 Sep 2019 - 3:34

score 221 · Answer 12 · 2019-09-26 18:55:21

221

Views

If $A+B+C=\pi$, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$

Published on 26 Sep 2019 - 18:55

score 42 · Answer 13 · 2026-03-26 14:26:16

42

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Initial value problem with substitution

Published on 26 Mar 2026 - 14:26

score 227 · Answer 14 · 2019-09-28 12:25:05

227

Views

Given three positive numbers $a,b,c$. Prove that $\sum\limits_{sym}\frac{a+b}{c}\geqq 2\sqrt{(\sum\limits_{sym}a)(\sum\limits_{sym}\frac{a}{bc}})$ .

Published on 28 Sep 2019 - 12:25

score 125 · Answer 15 · 2026-03-25 11:00:47

125

Views

Inequality with square roots conditions

Published on 25 Mar 2026 - 11:00

List Question

Substitution in Normal Distribution integral calculation

How to solve $\int \frac{\sqrt{x^2-1}}{x^2}dx$ with trig substitution?

How and why do dummy variables work?

If $a+b+c=2$ where $0 \leq {a,b,c} \leq 1$ find the range of $\frac{a}{1-a}\cdot\frac{b}{1-b}\cdot\frac{c}{1-c}$

show this inequality $\sum_{cyc}\frac{a^3}{a^2+ab+b^2}\ge\sqrt{\sum a^3}$

Prove or disprove that $ \min\Bigg\{\frac{2x(1+\cos\theta)}{x+y},\frac{2x(1-\cos\theta)}{x-y}\Bigg\}\leq 2.$

How to show that two expressions containing 2-dimensional sums with different iterators are equal

Prove that $\sqrt{x^{3} + y^{3}+1} + \sqrt{z^{3} + y^{3}+1} + \sqrt{x^{3} + z^{3}+1} \ge 2 + \sqrt{2(x^{3} + y^{3}+z^{3})+1}$

I can't find the maximum value of P because of some problems in my solution.

Substitution in Linear Algebra

Prove inequalities $\frac 34 \le I(a,b) \le 1$

If $A+B+C=\pi$, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$

Initial value problem with substitution

Given three positive numbers $a,b,c$. Prove that $\sum\limits_{sym}\frac{a+b}{c}\geqq 2\sqrt{(\sum\limits_{sym}a)(\sum\limits_{sym}\frac{a}{bc}})$ .

Inequality with square roots conditions

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