Why does $\int\limits_0^1 {\dfrac{{x - 1}}{{\ln x}}} \;\text{d}x=\ln2$?
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
125506
Why can I get two different results when calculating $\int \ln(z) \,dz$?
25652
Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
83851
Why does my professor say that writing $\int \frac 1x \mathrm{d}x = \ln|x| + C$ is wrong?
139784
Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
80710
Does $\int_{-1}^1 \frac 1 x dx$ equal zero?
88154
Proving $\int_{0}^1\frac{x-1}{\log x}dx=\log 2$ and $\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$
128953
Why $\frac{\log(x)}{\log(y)}$ gives the same value as $\frac{\ln(x)}{\ln(y)}$
15821
$\ln(x^2)$ vs $2\ln x$
96505
Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
98838
How to evaluate $\int_0^1 \frac{\ln(x+1)}{x^2+1} dx$
70790
Evaluation of $\lim_{q \to 0} (\int_0^1 |f|^q)^{1/q} $ for $f \in L^1([0,1])$.
102649
Prove that $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx=\frac{\pi^2}{96}+\frac{\ln^2 2}{8}$
31964
Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
84413
Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?
55577
Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$?
19514
$\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?