show $ \ln(1+\frac{1}{x})−\frac{1}{x+1}>0 $
117262
Proving a logarithm inequality
87055
How to prove $\frac{x}{1+x^2}0$?
63956
Evaluate $\int_0^{\infty}\frac{\ln x}{x^a(x+1)}dx$ where $0<a<1$
91000
Prove that $\frac{1}{a+1}0$
102639
How to receive the result of the integral $ \int\frac{1}{x}dx$ is $\ln|x|$?
138107
Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
93408
Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$
132452
Integral $\int_{\frac{1}{2}}^1 \frac{\ln x}{\sqrt{x^2+1}}dx$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
68990
Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
150565
Prove $(a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}$
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
126762
taylor series of $\ln(1+x)$?
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
74170
Prove that $\lim_{x \to +\infty} \frac{f(x)}{x} = L$ if $\lim_{x \to +\infty} [f(x+1) - f(x)] = L \space$