Newbetuts

Evaluating $\int_0^{\Large\frac{\pi}{2}}\left(\frac{1}{\log(\tan x)}+\frac{1}{1-\tan(x)}\right)^3dx$

The Fermat prime 257 and binomial sum $\sum_{n=0}^\infty \frac{(-1)^n}{\binom {8n}{4n}}$?

A Binet-like integral $\int_{0}^{1} \left(\frac{1}{\ln x} + \frac{1}{1-x} -\frac{1}{2} \right) \frac{x^s }{1-x}\mathrm{d}x$

What is $\int_0^1 \ln (1-x) \ln \left(\ln \left(\frac{1}{x}\right)\right) \, dx$?

What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?

Is log the only choice for measuring information?

An Intriguing Identity: $\cos(2x) \overset{?}{=} \log_{\cos(1)}\frac{\cos(\cos(x))}{\cos(\sin(x))}$

What is the fastest algorithm for finding the natural logarithm of a big number?

About irrational logarithms

Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$

Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$

Convergence N'th Harmonic number minus the Natural Logarithm of N. [duplicate]

Inequalities from Taylor expansions of $\log$ functions

$\ln(x^2)$ vs $2\ln x$

On irrationality of natural logarithm

How $a^{\log_b x} = x^{\log_b a}$?

How do I calculate $\lim_{x\rightarrow 0} x\ln x$

New posts in logarithms

The differential equation $y' = \frac{\ln(x^2+y^2)}{x^2 + y^2}$

Closed form for ${\large\int}_0^1\frac{\ln^3x}{\sqrt{x^2-x+1}}dx$

About the inequality $\left(\ln\left(\frac{4+x}{2x+2}\right)\right)^{2}\leq x!$

Evaluating $\int_0^{\Large\frac{\pi}{2}}\left(\frac{1}{\log(\tan x)}+\frac{1}{1-\tan(x)}\right)^3dx$

The Fermat prime 257 and binomial sum $\sum_{n=0}^\infty \frac{(-1)^n}{\binom {8n}{4n}}$?

A Binet-like integral $\int_{0}^{1} \left(\frac{1}{\ln x} + \frac{1}{1-x} -\frac{1}{2} \right) \frac{x^s }{1-x}\mathrm{d}x$

What is $\int_0^1 \ln (1-x) \ln \left(\ln \left(\frac{1}{x}\right)\right) \, dx$?

What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?

Is log the only choice for measuring information?

An Intriguing Identity: $\cos(2x) \overset{?}{=} \log_{\cos(1)}\frac{\cos(\cos(x))}{\cos(\sin(x))}$

What is the fastest algorithm for finding the natural logarithm of a big number?

About irrational logarithms

Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$

Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$

Convergence N'th Harmonic number minus the Natural Logarithm of N. [duplicate]

Inequalities from Taylor expansions of $\log$ functions

$\ln(x^2)$ vs $2\ln x$

On irrationality of natural logarithm

How $a^{\log_b x} = x^{\log_b a}$?

How do I calculate $\lim_{x\rightarrow 0} x\ln x$