On this integral $\int_0^1 \ln\left(\zeta(s)\right)ds$
93581
On questions about the integral of the logarithm of the Riemann zeta function II
117751
An integral of a rational function of logarithm and nonlinear arguments
39524
Integral Representation of the Zeta Function: $\zeta(s)=\frac1{\Gamma(s)}\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$
17996
Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
26444
How can I integrate $\ln \left( x+\sqrt{1+x^2} \right) $?
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
25797
Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
115198
Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$
87395
Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$
139784
Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
33392
Proving that $ \ln\left(\frac{49}{50}\right)<\sum^{98}_{k=1}\int^{k+1}_{k}\frac{k+1}{x(x+1)}dx<\ln(99)$
44059
Evaluating $\int_{-1}^{1}\frac{\arctan{x}}{1+x}\ln{\left(\frac{1+x^2}{2}\right)}dx$
150971
If $f$ is Riemann integrable on $[0,1]$ then $\lim\limits_{n\rightarrow\infty}\frac{1}{n}\sum f\left(\frac{k}{n}\right)=\int\limits_{0}^{1} f(x)dx$
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
84178
On the Maclaurin expansion of the Riemann zeta function and a related sequence.
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$