Question

What is the wrong step in the integral $ \int {\ln x \over x\sqrt{1-4\ln x -\ln^2 x}}dx $?

score 454 · Answer 1 · 2019-09-30 12:05:07

454

Views

What is the wrong step in the integral $ \int {\ln x \over x\sqrt{1-4\ln x -\ln^2 x}}dx $?

Published on 30 Sep 2019 - 12:05

score 567 · Answer 2 · 2014-03-13 15:52:57

567

Views

Indefinite Integral $\int\frac{1}{1+\tan^{-1}x}\,\text{d}x$

Published on 13 Mar 2014 - 15:52

score 699 · Answer 3 · 2014-03-23 17:10:57

699

Views

Integration of $ \int \frac{dx}{x^2\sqrt{x^2 + 9}} $ using trigonometric substitution

Published on 23 Mar 2014 - 17:10

score 163 · Answer 4 · 2014-04-01 19:10:58

163

Views

How to apply substitution for this integral $\int \frac{dx}{x^2 + 1 + x\sqrt{x^2+2}}$

Published on 01 Apr 2014 - 19:10

score 199 · Answer 5 · 2014-04-11 22:19:22

199

Views

Prove that positive $x,y$ satisfy $\left(\frac{1}{1+x}\right)^2+\left(\frac{1}{1+y}\right)^2\ge\frac{1}{1+xy}$.

Published on 11 Apr 2014 - 22:19

score 5.1k · Answer 6 · 2014-05-26 07:21:22

5.1k

Views

Show that a $-\log$ transformation of a Pareto distribution is exponentially distributed

Published on 26 May 2014 - 7:21

score 970 · Answer 7 · 2026-03-25 07:44:45

970

Views

Prove $\frac{a}{a+bc}+\frac{b}{b+cd}+\frac{c}{c+da}+\frac{d}{d+ab}\ge 2$ for positives $\sum a = 4$

Published on 25 Mar 2026 - 7:44

score 203 · Answer 8 · 2026-03-25 07:46:10

203

Views

Seeking concise proof: $\frac18(a^2+b^2)(b^2+c^2)(c^2+a^2)\ge\frac1{27}(ab+bc+ca)^3$, where $a$, $b$, $c$ are positive numbers

Published on 25 Mar 2026 - 7:46

score 600 · Answer 9 · 2026-03-25 03:04:10

600

Views

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

Published on 25 Mar 2026 - 3:04

score 465 · Answer 10 · 2026-03-25 12:50:50

465

Views

If the sum of cubes of $a,b,c,d$ is $1$, then $\frac{1}{1-bcd}+\frac{1}{1-cda}+\frac{1}{1-dab}+\frac{1}{1-abc}\le \frac{16}{3}$

Published on 25 Mar 2026 - 12:50

score 206 · Answer 11 · 2014-08-19 19:06:02

206

Views

Evaluation of $\int \sec^3 (x)dx$

Published on 19 Aug 2014 - 19:06

score 481 · Answer 12 · 2026-03-25 12:49:43

481

Views

Prove that $\sum\limits_{\mathrm{cyc}}{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$ for $x, y, z > 0$

Published on 25 Mar 2026 - 12:49

score 193 · Answer 13 · 2014-09-11 07:09:21

193

Views

How do I handle $dx$ in $u$-substitution?

Published on 11 Sep 2014 - 7:09

score 659 · Answer 14 · 2014-09-28 18:10:03

659

Views

Evaluate $\int\frac{x^3}{\sqrt{81x^2-16}}dx$ using Trigonometric Substitution

Published on 28 Sep 2014 - 18:10

score 1.4k · Answer 15 · 2026-03-25 12:50:51

1.4k

Views

Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $

Published on 25 Mar 2026 - 12:50

List Question

What is the wrong step in the integral $ \int {\ln x \over x\sqrt{1-4\ln x -\ln^2 x}}dx $?

Indefinite Integral $\int\frac{1}{1+\tan^{-1}x}\,\text{d}x$

Integration of $ \int \frac{dx}{x^2\sqrt{x^2 + 9}} $ using trigonometric substitution

How to apply substitution for this integral $\int \frac{dx}{x^2 + 1 + x\sqrt{x^2+2}}$

Prove that positive $x,y$ satisfy $\left(\frac{1}{1+x}\right)^2+\left(\frac{1}{1+y}\right)^2\ge\frac{1}{1+xy}$.

Show that a $-\log$ transformation of a Pareto distribution is exponentially distributed

Prove $\frac{a}{a+bc}+\frac{b}{b+cd}+\frac{c}{c+da}+\frac{d}{d+ab}\ge 2$ for positives $\sum a = 4$

Seeking concise proof: $\frac18(a^2+b^2)(b^2+c^2)(c^2+a^2)\ge\frac1{27}(ab+bc+ca)^3$, where $a$, $b$, $c$ are positive numbers

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

If the sum of cubes of $a,b,c,d$ is $1$, then $\frac{1}{1-bcd}+\frac{1}{1-cda}+\frac{1}{1-dab}+\frac{1}{1-abc}\le \frac{16}{3}$

Evaluation of $\int \sec^3 (x)dx$

Prove that $\sum\limits_{\mathrm{cyc}}{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$ for $x, y, z > 0$

How do I handle $dx$ in $u$-substitution?

Evaluate $\int\frac{x^3}{\sqrt{81x^2-16}}dx$ using Trigonometric Substitution

Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $

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