List questions from substitution

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If $\frac {1}{2+a} + \frac {1}{2+b} + \frac {1}{2+c} = 1$, prove $\sqrt{ab} + \sqrt{ac} + \sqrt{bc} \leq 3$

Published on 08 Mar 2015 - 5:59

153

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How can I integrate $\frac{1}{x^2-x-1}$?

Published on 28 Mar 2026 - 22:55

2.3k

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Given $a,b,c,d>0$ and $a^2+b^2+c^2+d^2=1$, prove $a+b+c+d\ge a^3+b^3+c^3+d^3+ab+ac+ad+bc+bd+cd$

Published on 26 Mar 2026 - 11:00

331

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Finding $\int\frac{1}{x^{11}+4x^6}dx$

Published on 29 Mar 2026 - 2:17

26

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About equal substitutions

Published on 27 May 2015 - 7:29

47

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What's my mistake in this integral transformation?

Published on 27 May 2015 - 19:26

87

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Help with definite integral using U-subsitution

Published on 01 Jun 2015 - 9:04

1.8k

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Indefinite Integral of Floor Function Integration by Substitution

Published on 04 Jun 2015 - 16:30

139

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Square rooting to make quadratic function

Published on 07 Jun 2015 - 20:45

70

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Substitutions as mappings from the set of Propositional Variables to the set of Formulas

Published on 09 Jun 2015 - 11:26

92

Views

Problem in substitution

Published on 11 Jun 2015 - 6:00

274

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Solving the integral $\int x\sqrt{1+x}\ dx $

Published on 16 Jun 2015 - 14:21

49

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Help understanding variable substitutions

Published on 18 Jun 2015 - 21:05

464

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Non bijective substitution in integral of a piecewise continuous function

Published on 19 Jun 2015 - 16:22

137

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Substitution needed for calculating integral $\int \frac{1}{x \sqrt{x^4+x^2+1}}dx$

Published on 21 Jun 2015 - 17:51

List Question

If $\frac {1}{2+a} + \frac {1}{2+b} + \frac {1}{2+c} = 1$, prove $\sqrt{ab} + \sqrt{ac} + \sqrt{bc} \leq 3$

How can I integrate $\frac{1}{x^2-x-1}$?

Given $a,b,c,d>0$ and $a^2+b^2+c^2+d^2=1$, prove $a+b+c+d\ge a^3+b^3+c^3+d^3+ab+ac+ad+bc+bd+cd$

Finding $\int\frac{1}{x^{11}+4x^6}dx$

About equal substitutions

What's my mistake in this integral transformation?

Help with definite integral using U-subsitution

Indefinite Integral of Floor Function Integration by Substitution

Square rooting to make quadratic function

Substitutions as mappings from the set of Propositional Variables to the set of Formulas

Problem in substitution

Solving the integral $\int x\sqrt{1+x}\ dx $

Help understanding variable substitutions

Non bijective substitution in integral of a piecewise continuous function

Substitution needed for calculating integral $\int \frac{1}{x \sqrt{x^4+x^2+1}}dx$

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