User TheSimpliFire

6 votes

Find all functions $f:\mathbb{R}^+\to \mathbb{R}$ such that $xf(xf(x)-4)-1=4x$

answered Jul 23, 2020 at 7:33

6 votes

Proving Fibonacci Identity

answered Mar 20, 2018 at 7:23

6 votes

Find $\frac{\tan 54-\tan 2}{\frac{\sin 2}{\cos 6}+\frac{\sin 6}{\cos 18}+\frac{\sin 18}{\cos 54}}$

answered Apr 16, 2018 at 10:57

6 votes

Accepted

If $a|b$ and $c|d$ then $ac|bd$?

answered Apr 24, 2018 at 9:57

6 votes

Integral with constant u-substitution

answered Apr 23, 2018 at 19:12

6 votes

Accepted

$5$-digit number from $0-9$

answered Mar 10, 2018 at 10:04

6 votes

New bound for Am-Gm of 2 variables

answered Jun 8, 2019 at 16:16

6 votes

Finding the sum of squares of the real roots

answered Sep 17, 2018 at 19:00

6 votes

Accepted

Finding the value of $\frac{13}{a-13}+\frac{23}{b-23}+\frac{42}{c-42} $ given a system of three equations

answered Aug 30, 2018 at 17:23

6 votes

Evaluate $\sum_{r=2}^{\infty} \frac{2-r}{r(r+1)(r+2)}$

answered Dec 31, 2018 at 15:53

6 votes

Accepted

Manipulating this $\frac{x-y}{z-y}$ to $1+\frac{x-z}{z-y}$

answered Jan 6, 2019 at 19:17

6 votes

If I don't have a computer at hand (or an app), how can I know that $1637$ is prime?

answered Jun 6, 2018 at 14:40

5 votes

Calculate integral $\int_0^{\pi/2} \frac{\cos^3x}{\sin^2x + \cos^3x}dx$.

answered Jan 29, 2021 at 11:38

5 votes

Accepted

Evaluate $\int_{-1}^1 \frac{x^2e^{\arctan x}}{\sqrt{{1+x^2}}}\ \mathrm{d}x$

answered Apr 24, 2021 at 11:10

5 votes

$\int_0^\infty \log\left(1 - \frac{x}{\sinh x}\right)\,dx$ and generalisations

answered Nov 2, 2022 at 0:10

5 votes

Number of zeros of $f(x)= \frac{1}{2} E\left[ \tanh \left( \frac{x+Z}{2} \right) \right]-\tanh(x)+\frac{x}{2}$ where $Z$ is standard normal

answered Jan 8, 2022 at 22:03

5 votes

Accepted

Is there a slick argument to prove that, for $n>6$, $2(n-2)!=2^kk!(n-2k)! \implies k=1$?

answered Oct 8, 2021 at 19:58

5 votes

Accepted

Asymptotics for $f(\lambda)=\int_1^\infty\frac{1}{\sqrt{x}(\lambda+1)^x}dx$ as $\lambda\to0^+$.

answered May 23, 2021 at 15:08

5 votes

Analogs of $\sum_{n\ge1}\frac{n^{13}}{e^{2\pi n}-1}=\frac{1}{24}$

answered Aug 2, 2022 at 20:30

5 votes

Accepted

Evaluate indefinite integral $\int \tan(\frac{x}{3}) \, dx$

answered Jun 1, 2018 at 15:10

5 votes

What does the equal sign mean in mathematics?

answered Jun 4, 2018 at 9:54

5 votes

Accepted

How to simplify of $\sin\left(\frac{\cos^{-1}\theta}2\right)$?

answered Apr 26, 2018 at 18:49

5 votes

Is there a formula for $(x+y+z)^n$?

answered May 9, 2018 at 7:52

5 votes

Integration of $ \int_1^2 \frac{3x^3 + 3x^2 - 5x + 4}{3x^3 - 2x^2 +3x -2} \mathrm dx$

answered May 16, 2018 at 18:12

5 votes

A problem related with limit and continuity.

answered Aug 7, 2018 at 14:44

5 votes

Accepted

Sum of roots of equation $x^4 - 2x^2 \sin^2(\displaystyle {\pi x}/2) +1 =0$ is

answered Aug 26, 2018 at 14:11

5 votes

Accepted

Is $\sqrt[0]{0}$ defined?

answered Jul 15, 2018 at 10:41

5 votes

Accepted

Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

answered Dec 1, 2018 at 19:00

5 votes

Accepted

What is the maximum value of $\ln(x+\ln(x+\ln(x+\cdots)))-\ln x$?

answered Nov 9, 2018 at 16:06

5 votes

Accepted

Differentiate $\tan^3(x^2)$

answered Aug 26, 2018 at 18:35

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808 Answers

Find all functions $f:\mathbb{R}^+\to \mathbb{R}$ such that $xf(xf(x)-4)-1=4x$

Proving Fibonacci Identity

Find $\frac{\tan 54-\tan 2}{\frac{\sin 2}{\cos 6}+\frac{\sin 6}{\cos 18}+\frac{\sin 18}{\cos 54}}$

If $a|b$ and $c|d$ then $ac|bd$?

Integral with constant u-substitution

$5$-digit number from $0-9$

New bound for Am-Gm of 2 variables

Finding the sum of squares of the real roots

Finding the value of $\frac{13}{a-13}+\frac{23}{b-23}+\frac{42}{c-42} $ given a system of three equations

Evaluate $\sum_{r=2}^{\infty} \frac{2-r}{r(r+1)(r+2)}$

Manipulating this $\frac{x-y}{z-y}$ to $1+\frac{x-z}{z-y}$

If I don't have a computer at hand (or an app), how can I know that $1637$ is prime?

Calculate integral $\int_0^{\pi/2} \frac{\cos^3x}{\sin^2x + \cos^3x}dx$.

Evaluate $\int_{-1}^1 \frac{x^2e^{\arctan x}}{\sqrt{{1+x^2}}}\ \mathrm{d}x$

$\int_0^\infty \log\left(1 - \frac{x}{\sinh x}\right)\,dx$ and generalisations

Number of zeros of $f(x)= \frac{1}{2} E\left[ \tanh \left( \frac{x+Z}{2} \right) \right]-\tanh(x)+\frac{x}{2}$ where $Z$ is standard normal

Is there a slick argument to prove that, for $n>6$, $2(n-2)!=2^kk!(n-2k)! \implies k=1$?

Asymptotics for $f(\lambda)=\int_1^\infty\frac{1}{\sqrt{x}(\lambda+1)^x}dx$ as $\lambda\to0^+$.

Analogs of $\sum_{n\ge1}\frac{n^{13}}{e^{2\pi n}-1}=\frac{1}{24}$

Evaluate indefinite integral $\int \tan(\frac{x}{3}) \, dx$

What does the equal sign mean in mathematics?

How to simplify of $\sin\left(\frac{\cos^{-1}\theta}2\right)$?

Is there a formula for $(x+y+z)^n$?

Integration of $ \int_1^2 \frac{3x^3 + 3x^2 - 5x + 4}{3x^3 - 2x^2 +3x -2} \mathrm dx$

A problem related with limit and continuity.

Sum of roots of equation $x^4 - 2x^2 \sin^2(\displaystyle {\pi x}/2) +1 =0$ is

Is $\sqrt[0]{0}$ defined?

Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

What is the maximum value of $\ln(x+\ln(x+\ln(x+\cdots)))-\ln x$?

Differentiate $\tan^3(x^2)$