Question

Is there a clever way to compute $\int \limits_a^b \sqrt[3]{(b-x)(x-a)^2} dx$

score 122 · Answer 1 · 2018-07-25 16:26:56

122

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Is there a clever way to compute $\int \limits_a^b \sqrt[3]{(b-x)(x-a)^2} dx$

Published on 25 Jul 2018 - 16:26

score 413 · Answer 2 · 2026-03-25 03:07:38

413

Views

How to solve equations with both logarithms and square roots, like this: $ax+b\log(x)+c\sqrt{x}+d=0$

Published on 25 Mar 2026 - 3:07

score 258 · Answer 3 · 2018-07-26 20:25:05

258

Views

Find the positive value of $x$ satisfying the given equation

Published on 26 Jul 2018 - 20:25

score 15.9k · Answer 4 · 2026-03-25 13:59:47

15.9k

Views

Conjugate of real number

Published on 25 Mar 2026 - 13:59

score 84 · Answer 5 · 2026-03-25 20:59:49

84

Views

A Question About Square Roots And Exponent Laws

Published on 25 Mar 2026 - 20:59

score 2.2k · Answer 6 · 2026-03-25 04:42:40

2.2k

Views

How to simplify $\int{\sqrt[4]{1-8{{x}^{2}}+8{{x}^{4}}-4x\sqrt{{{x}^{2}}-1}+8{{x}^{3}}\sqrt{{{x}^{2}}-1}}dx}$?

Published on 25 Mar 2026 - 4:42

score 552 · Answer 7 · 2018-08-02 14:52:31

552

Views

Sum of square roots of complex numbers

Published on 02 Aug 2018 - 14:52

score 1.4k · Answer 8 · 2026-03-25 07:50:15

1.4k

Views

Nilpotent Jacobson radical

Published on 25 Mar 2026 - 7:50

score 93 · Answer 9 · 2026-03-25 14:18:15

93

Views

Expanding log problem

Published on 25 Mar 2026 - 14:18

score 357 · Answer 10 · 2026-03-26 01:25:10

357

Views

Prove that inequality $\frac{2ab}{a+b}+\sqrt{\frac{a^2+b^2}{2}}\ge \sqrt{ab}+\frac{a+b}{2}$

Published on 26 Mar 2026 - 1:25

score 367 · Answer 11 · 2026-03-25 13:58:08

367

Views

Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$

Published on 25 Mar 2026 - 13:58

score 177 · Answer 12 · 2018-08-08 03:24:07

177

Views

Solve the equation $\sqrt[3]{x^{2}+4}=\sqrt{x-1}+2x-3$

Published on 08 Aug 2018 - 3:24

score 198 · Answer 13 · 2018-08-08 06:34:31

198

Views

How to prove $1 + \frac{1}{\sqrt{2}} +... +\frac{1}{\sqrt{n}} <\sqrt{n}\ .\left(2n-1\right)^{1/4} $

Published on 08 Aug 2018 - 6:34

score 219 · Answer 14 · 2026-03-25 01:20:32

219

Views

Prove that inequality $1+\frac{1}{2\sqrt{2}}+...+\frac{1}{n\sqrt{n}}<2\sqrt{2}$

Published on 25 Mar 2026 - 1:20

score 182 · Answer 15 · 2026-03-25 12:48:49

182

Views

How to prove AM-GM by induction 3

Published on 25 Mar 2026 - 12:48

List Question

Is there a clever way to compute $\int \limits_a^b \sqrt[3]{(b-x)(x-a)^2} dx$

How to solve equations with both logarithms and square roots, like this: $ax+b\log(x)+c\sqrt{x}+d=0$

Find the positive value of $x$ satisfying the given equation

Conjugate of real number

A Question About Square Roots And Exponent Laws

How to simplify $\int{\sqrt[4]{1-8{{x}^{2}}+8{{x}^{4}}-4x\sqrt{{{x}^{2}}-1}+8{{x}^{3}}\sqrt{{{x}^{2}}-1}}dx}$?

Sum of square roots of complex numbers

Nilpotent Jacobson radical

Expanding log problem

Prove that inequality $\frac{2ab}{a+b}+\sqrt{\frac{a^2+b^2}{2}}\ge \sqrt{ab}+\frac{a+b}{2}$

Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$

Solve the equation $\sqrt[3]{x^{2}+4}=\sqrt{x-1}+2x-3$

How to prove $1 + \frac{1}{\sqrt{2}} +... +\frac{1}{\sqrt{n}} <\sqrt{n}\ .\left(2n-1\right)^{1/4} $

Prove that inequality $1+\frac{1}{2\sqrt{2}}+...+\frac{1}{n\sqrt{n}}<2\sqrt{2}$

How to prove AM-GM by induction 3

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