User Claude Leibovici

120 votes

Accepted

Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$

answered May 25, 2014 at 11:34

53 votes

How to test whether I am suitable to pursue mathematics?

soft-question advice

answered Jan 25, 2014 at 13:13

43 votes

Can a chemical engineer become a self-taught mathematician?

soft-question self-learning education research

answered Jun 29, 2018 at 5:20

41 votes

Accepted

How do you determine which representation of a function to use for Newton's method?

linear-algebra numerical-methods

answered Sep 16, 2019 at 5:53

32 votes

Accepted

How can I find this limit involving thrice-iterated logarithm?

calculus limits logarithms

answered Sep 10, 2014 at 5:55

29 votes

Is there a better way to find the closest point on a line?

calculus derivatives optimization

answered Jul 28, 2016 at 2:21

28 votes

Finding x in an Olympiad simultaneous equation

contest-math systems-of-equations

answered Sep 7, 2015 at 7:20

26 votes

Accepted

An integral for which I don't trust WolframAlpha

integration complex-analysis proof-verification

answered Jun 26, 2017 at 3:37

25 votes

Find the value of $(\log_{a}b + 1)(\log_{b}c + 1)(\log_{c}a+1)$ if $\log_{b}a+\log_{c}b+\log_{a}c=13$ and $\log_{a}b+\log_{b}c+\log_{c}a=8$

logarithms contest-math systems-of-equations

answered Apr 16, 2017 at 5:38

24 votes

Accepted

Evaluate $\int_0^{1/\sqrt{3}}\sqrt{x+\sqrt{x^2+1}}\,dx$

calculus integration definite-integrals

answered Apr 19, 2015 at 4:45

22 votes

Solve $x\sqrt{x\sqrt{x\sqrt{x\dots}}} = 4$

sequences-and-series radicals nested-radicals

answered Jun 24, 2014 at 13:16

22 votes

How to straighten a parabola?

calculus geometry functions analytic-geometry quadratics

answered Jul 29, 2021 at 9:44

21 votes

If $f(x) = \frac{x^3}{3} -\frac{x^2}{2} + x + \frac{1}{12}$, then $\int_{\frac{1}{7}}^{\frac{6}{7}}f(f(x))\,dx =\,$?

calculus integration functions definite-integrals

answered Jun 10, 2021 at 14:15

20 votes

What is an example of real application of cubic equations?

algebra-precalculus applications cubics

answered Jun 8, 2014 at 12:06

19 votes

Accepted

Approximation of the Gamma function for small value

inequality reference-request gamma-function

answered Oct 27, 2016 at 13:57

19 votes

Accepted

Is there an approximation to the natural log function at large values?

logarithms taylor-expansion approximation

answered Oct 17, 2014 at 6:37

18 votes

How to find an approximation to $1 - \left( \frac{13999}{14000}\right )^{14000}$?

approximation

answered Aug 6, 2015 at 3:54

18 votes

A closed form for: $\int_{0}^{\infty} \frac{1}{(x-\log x)^2}dx$

calculus integration definite-integrals problem-solving closed-form

answered Jun 29, 2019 at 13:26

17 votes

Accepted

given $2f(x) + f(1-x) = x^2$ find $f(-5)$

contest-math functional-equations

answered Jul 26, 2015 at 8:11

15 votes

Accepted

Please explain the logic behind $d(xy) = y(dx) + x(dy)$

calculus physics

answered Jun 10, 2014 at 9:21

15 votes

Conjecture: $\frac1\pi=\sum_{n=0}^\infty\left((n+1)\frac{C_n^3}{2^{6n}}\sum_{k=0}^n(-1)^k{n\choose k}{\frac{(n-k)(k-1)}{(2k-1)(2k+1)}}\right)$

sequences-and-series number-theory generating-functions pi catalan-numbers

answered Jun 13 at 5:34

14 votes

Accepted

Why can we linearize the exponential regression?

calculus statistics optimization nonlinear-optimization regression

answered Apr 25, 2021 at 4:46

14 votes

Accepted

Fun logarithm question

logarithms exponentiation

answered Jan 16, 2014 at 13:31

14 votes

Accepted

How to find the solutions to $\frac{11}{2} x - \cos x = 0$?

trigonometry

answered Aug 19, 2016 at 5:22

14 votes

Euler-Mascheroni constant in Bessel function integral

definite-integrals bessel-functions euler-mascheroni-constant

answered Jun 10 at 9:22

14 votes

Accepted

Solving a quintic function for zero

problem-solving

answered Mar 8, 2015 at 6:04

14 votes

Accepted

Solve the system of equations for $\sqrt{xy}$

linear-algebra systems-of-equations

answered Jan 3, 2021 at 2:10

13 votes

Finding the limit of a difficult exponential function

limits

answered Jun 1, 2016 at 6:00

13 votes

Accepted

How to simplify $\lim_{n\to \infty}\sum_{r=1}^n \tan^{-1} \dfrac{2r+1}{r^4+2r^3+r^2+1}$

limits trigonometry summation

answered Jan 30, 2016 at 7:48

13 votes

Accepted

How to compute $\int_0^\infty \frac{1}{(1+x^{\varphi})^{\varphi}}\,dx$?

calculus integration definite-integrals closed-form golden-ratio

answered Jun 17, 2015 at 5:48

Stack Exchange Network

current community

your communities

more stack exchange communities

11,343 Answers

Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$

How to test whether I am suitable to pursue mathematics?

Can a chemical engineer become a self-taught mathematician?

How do you determine which representation of a function to use for Newton's method?

How can I find this limit involving thrice-iterated logarithm?

Is there a better way to find the closest point on a line?

Finding x in an Olympiad simultaneous equation

An integral for which I don't trust WolframAlpha

Find the value of $(\log_{a}b + 1)(\log_{b}c + 1)(\log_{c}a+1)$ if $\log_{b}a+\log_{c}b+\log_{a}c=13$ and $\log_{a}b+\log_{b}c+\log_{c}a=8$

Evaluate $\int_0^{1/\sqrt{3}}\sqrt{x+\sqrt{x^2+1}}\,dx$

Solve $x\sqrt{x\sqrt{x\sqrt{x\dots}}} = 4$

How to straighten a parabola?

If $f(x) = \frac{x^3}{3} -\frac{x^2}{2} + x + \frac{1}{12}$, then $\int_{\frac{1}{7}}^{\frac{6}{7}}f(f(x))\,dx =\,$?

What is an example of real application of cubic equations?

Approximation of the Gamma function for small value

Is there an approximation to the natural log function at large values?

How to find an approximation to $1 - \left( \frac{13999}{14000}\right )^{14000}$?

A closed form for: $\int_{0}^{\infty} \frac{1}{(x-\log x)^2}dx$

given $2f(x) + f(1-x) = x^2$ find $f(-5)$

Please explain the logic behind $d(xy) = y(dx) + x(dy)$

Conjecture: $\frac1\pi=\sum_{n=0}^\infty\left((n+1)\frac{C_n^3}{2^{6n}}\sum_{k=0}^n(-1)^k{n\choose k}{\frac{(n-k)(k-1)}{(2k-1)(2k+1)}}\right)$

Why can we linearize the exponential regression?

Fun logarithm question

How to find the solutions to $\frac{11}{2} x - \cos x = 0$?

Euler-Mascheroni constant in Bessel function integral

Solving a quintic function for zero

Solve the system of equations for $\sqrt{xy}$

Finding the limit of a difficult exponential function

How to simplify $\lim_{n\to \infty}\sum_{r=1}^n \tan^{-1} \dfrac{2r+1}{r^4+2r^3+r^2+1}$

How to compute $\int_0^\infty \frac{1}{(1+x^{\varphi})^{\varphi}}\,dx$?