List questions from substitution

Published on 05 Aug 2012 - 13:50

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Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$

Published on 25 Mar 2026 - 21:49

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Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$

Published on 26 Mar 2026 - 14:23

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How to prove this inequality $\sqrt{\frac{ab+bc+cd+da+ac+bd}{6}}\geq \sqrt[3]{{\frac{abc+bcd+cda+dab}{4}}}$

Published on 26 Mar 2026 - 14:23

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A inequality proposed at Zhautykov Olympiad 2008

Published on 25 Mar 2026 - 13:59

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Integrate $e^{\frac{x-y}{x+y}}$ over the triangle bounded by $x=0$, $y=0$, and $y=1-x$

Published on 29 Mar 2026 - 4:26

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Integrate $\frac{1}{(1+\sqrt{x})^4}$ via Substitution

Published on 06 Dec 2012 - 4:55

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How is the Taylor expansion for $f(x + h)$ derived?

Published on 09 Dec 2012 - 19:24

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Showing that: $(\frac{a}{b+c})^2+(\frac{b}{a+c})^2+(\frac{c}{a+b})^2+\frac{10abc}{(a+b)(b+c)(c+a)}\ge 2$

Published on 26 Mar 2026 - 14:23

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bound for $a,b,c$ in $|ax^2+bx+c| \leq 1\;\forall x\in \left[0,1\right]$

Published on 26 Feb 2013 - 8:01

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Prove that $\frac 1 {x+y}+\frac 1 {y+z}+\frac 1 {z+x}\geq \frac 5 2$.

Published on 26 Mar 2026 - 14:22

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How to prove this inequality? $ab+ac+ad+bc+bd+cd\le a+b+c+d+2abcd$

Published on 26 Mar 2026 - 14:20

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Arc length of function - confused about particular u-substitution in integral

Published on 27 Mar 2026 - 23:48

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Evalution of a function where $t = x + \frac{1}{x}$

Published on 04 Aug 2020 - 13:42

58

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Help with substitution

Published on 30 Mar 2026 - 1:43

List Question

How to integrate $\frac{1}{\sqrt{1+x^2}}$ using substitution?

Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$

Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$

How to prove this inequality $\sqrt{\frac{ab+bc+cd+da+ac+bd}{6}}\geq \sqrt[3]{{\frac{abc+bcd+cda+dab}{4}}}$

A inequality proposed at Zhautykov Olympiad 2008

Integrate $e^{\frac{x-y}{x+y}}$ over the triangle bounded by $x=0$, $y=0$, and $y=1-x$

Integrate $\frac{1}{(1+\sqrt{x})^4}$ via Substitution

How is the Taylor expansion for $f(x + h)$ derived?

Showing that: $(\frac{a}{b+c})^2+(\frac{b}{a+c})^2+(\frac{c}{a+b})^2+\frac{10abc}{(a+b)(b+c)(c+a)}\ge 2$

bound for $a,b,c$ in $|ax^2+bx+c| \leq 1\;\forall x\in \left[0,1\right]$

Prove that $\frac 1 {x+y}+\frac 1 {y+z}+\frac 1 {z+x}\geq \frac 5 2$.

How to prove this inequality? $ab+ac+ad+bc+bd+cd\le a+b+c+d+2abcd$

Arc length of function - confused about particular u-substitution in integral

Evalution of a function where $t = x + \frac{1}{x}$

Help with substitution

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