Question

Definite integral containing 2 trig functions and a square root function

score 152 · Answer 1 · 2019-05-09 23:36:37

152

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Definite integral containing 2 trig functions and a square root function

Published on 09 May 2019 - 23:36

score 103 · Answer 2 · 2026-03-25 06:04:27

103

Views

show this $\sum_{cyc}\frac{x}{x^2-x+1}\le\frac{8}{3}$

Published on 25 Mar 2026 - 6:04

score 36 · Answer 3 · 2026-03-25 18:53:41

36

Views

Question about using substitution + Jacobian for integration in a concrete example

Published on 25 Mar 2026 - 18:53

score 203 · Answer 4 · 2026-03-24 22:08:44

203

Views

Given three positive numbers $a,b,c$. Prove that $\prod\limits_{sym}(\!a+\frac{1}{a}\!)\geqq\frac{4}{3}\sum\limits_{sym}\frac{b+c}{a}$ .

Published on 24 Mar 2026 - 22:08

score 302 · Answer 5 · 2019-05-10 12:46:41

302

Views

Maclaurin series degree 6 involving substitution

Published on 10 May 2019 - 12:46

score 200 · Answer 6 · 2026-03-25 06:06:51

200

Views

Given three positive numbers $a,b,c$ so that $8abc\geqq a+b+c+5$. Prove that $\frac{1}{a+2b}+\frac{1}{b+ 2c}+\frac{1}{c+2a}\leqq1$ .

Published on 25 Mar 2026 - 6:06

score 219 · Answer 7 · 2026-03-25 06:13:08

219

Views

Prove that $k=0$ is the only $constant$ so $(\sum\limits_{cyc}a^{3}-\sum\limits_{cyc}a^{2}b)-k(a-b)(a-c)(b+c)\geqq0$ .

Published on 25 Mar 2026 - 6:13

score 30 · Answer 8 · 2019-05-11 18:06:13

30

Views

Using substitution for definite integral

Published on 11 May 2019 - 18:06

score 118 · Answer 9 · 2019-05-13 05:33:28

118

Views

Find maximize of the function $\frac{a}{1+a^2}+\frac{b}{1+b^2}-\frac{1}{c^2+1}$

Published on 13 May 2019 - 5:33

score 163 · Answer 10 · 2026-03-25 06:07:01

163

Views

Find $f(x)$ so that $\sum\limits_{cyc}a^{2}-f(x)\left(\prod_{sym}a-\prod_{sym}(1-a)\right)\geqq3(\frac{x}{2})^{2}$ .

Published on 25 Mar 2026 - 6:07

score 949 · Answer 11 · 2019-05-14 16:53:30

949

Views

Evaluating $\int_0^1 \frac{3x}{\sqrt{4-3x}} dx$

Published on 14 May 2019 - 16:53

score 59 · Answer 12 · 2019-05-14 19:41:46

59

Views

Why can we let $x = 2\cos t\ $ in the solution for the following system of equations

Published on 14 May 2019 - 19:41

score 135 · Answer 13 · 2019-05-18 04:24:04

135

Views

Problem with integrating $\int_0^{\pi/2}\frac{\cos^6x}{\cos^6x+\sin^6x}dx$

Published on 18 May 2019 - 4:24

score 297 · Answer 14 · 2026-03-25 06:07:04

297

Views

Given three positve numbers $a,b,c$. Prove that $\sum\limits_{cyc}\frac{a}{\sqrt{b(a+b)}}\geqq \sum\limits_{cyc}\frac{a}{\sqrt{b(c+a)}}$ .

Published on 25 Mar 2026 - 6:07

score 4.9k · Answer 15 · 2019-05-19 20:14:21

4.9k

Views

Why is this integration method not valid?

Published on 19 May 2019 - 20:14

List Question

Definite integral containing 2 trig functions and a square root function

show this $\sum_{cyc}\frac{x}{x^2-x+1}\le\frac{8}{3}$

Question about using substitution + Jacobian for integration in a concrete example

Given three positive numbers $a,b,c$. Prove that $\prod\limits_{sym}(\!a+\frac{1}{a}\!)\geqq\frac{4}{3}\sum\limits_{sym}\frac{b+c}{a}$ .

Maclaurin series degree 6 involving substitution

Given three positive numbers $a,b,c$ so that $8abc\geqq a+b+c+5$. Prove that $\frac{1}{a+2b}+\frac{1}{b+ 2c}+\frac{1}{c+2a}\leqq1$ .

Prove that $k=0$ is the only $constant$ so $(\sum\limits_{cyc}a^{3}-\sum\limits_{cyc}a^{2}b)-k(a-b)(a-c)(b+c)\geqq0$ .

Using substitution for definite integral

Find maximize of the function $\frac{a}{1+a^2}+\frac{b}{1+b^2}-\frac{1}{c^2+1}$

Find $f(x)$ so that $\sum\limits_{cyc}a^{2}-f(x)\left(\prod_{sym}a-\prod_{sym}(1-a)\right)\geqq3(\frac{x}{2})^{2}$ .

Evaluating $\int_0^1 \frac{3x}{\sqrt{4-3x}} dx$

Why can we let $x = 2\cos t\ $ in the solution for the following system of equations

Problem with integrating $\int_0^{\pi/2}\frac{\cos^6x}{\cos^6x+\sin^6x}dx$

Given three positve numbers $a,b,c$. Prove that $\sum\limits_{cyc}\frac{a}{\sqrt{b(a+b)}}\geqq \sum\limits_{cyc}\frac{a}{\sqrt{b(c+a)}}$ .

Why is this integration method not valid?

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