List questions from substitution

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Prove the inequality $\sum_{cyc} {{a+abc} \over {1+ab+abcd}} \ge {{10} \over {3}}$ with Cauchy-Schwarz

Published on 11 Jan 2019 - 6:49

207

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Inequality. $\sum_{cyc}(\frac{1}{a+b+\sqrt{2a+2c}})^3 \le \frac{8}{9}$

Published on 11 Jan 2019 - 8:11

181

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Solving $8x-3+\sqrt{x+2}-\sqrt{x-1}=7 \sqrt{x^2+x-2}$

Published on 23 Mar 2026 - 3:10

54

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Inequality triangle Radon substitutions

Published on 25 Mar 2026 - 9:31

142

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Primitive of a function with $\sin \frac{1}{x}$

Published on 16 Jan 2019 - 20:19

80

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Prove $\frac{1}{3}(a+b+c)^2\leq a^2 + b^2 + c^2 + 2(a-b+1).$

Published on 17 Jan 2019 - 7:21

459

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Very Hard System of Equations

Published on 18 Jan 2019 - 2:44

111

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Stuck with Integration by Substitution

Published on 21 Jan 2019 - 0:19

415

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What's the answer to $\int \frac{\cos^2x \sin x}{\sin x - \cos x} dx$?

Published on 21 Jan 2019 - 17:22

172

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to prove this inequality $\sum a^3b+3\ge 2(ab+bc+ca)$

Published on 25 Mar 2026 - 9:38

216

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Inequality. ${{\sqrt{a}+\sqrt{b}+\sqrt{c}} \over {2}} \ge {{1} \over {\sqrt{a}}} + {{1} \over {\sqrt{b}}} + {{1} \over {\sqrt{c}}}$

Published on 25 Mar 2026 - 7:44

25

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Solving the reccurence method by using substitution

Published on 25 Jan 2019 - 3:05

64

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How do I solve $\int \frac{x\cos^2x + \sin x}{\cos^2x} e^{\sin x} dx$?

Published on 27 Jan 2019 - 7:00

93

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Show that solution $(0,0)$ is unique

Published on 28 Jan 2019 - 18:11

788

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integration by substitution of multiple variables

Published on 28 Jan 2019 - 21:06

List Question

Prove the inequality $\sum_{cyc} {{a+abc} \over {1+ab+abcd}} \ge {{10} \over {3}}$ with Cauchy-Schwarz

Inequality. $\sum_{cyc}(\frac{1}{a+b+\sqrt{2a+2c}})^3 \le \frac{8}{9}$

Solving $8x-3+\sqrt{x+2}-\sqrt{x-1}=7 \sqrt{x^2+x-2}$

Inequality triangle Radon substitutions

Primitive of a function with $\sin \frac{1}{x}$

Prove $\frac{1}{3}(a+b+c)^2\leq a^2 + b^2 + c^2 + 2(a-b+1).$

Very Hard System of Equations

Stuck with Integration by Substitution

What's the answer to $\int \frac{\cos^2x \sin x}{\sin x - \cos x} dx$?

to prove this inequality $\sum a^3b+3\ge 2(ab+bc+ca)$

Inequality. ${{\sqrt{a}+\sqrt{b}+\sqrt{c}} \over {2}} \ge {{1} \over {\sqrt{a}}} + {{1} \over {\sqrt{b}}} + {{1} \over {\sqrt{c}}}$

Solving the reccurence method by using substitution

How do I solve $\int \frac{x\cos^2x + \sin x}{\cos^2x} e^{\sin x} dx$?

Show that solution $(0,0)$ is unique

integration by substitution of multiple variables

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