New posts in Riemann Zeta

How to integrate $\int_0^{\infty} \frac{x}{e^x+1} dx$

How to solve $\int\limits_0^x {x^n \over{1 + e^x}} dx$?

Improving an approximation for the inverse of the Riemann–Siegel θ-function

Prove $\int_0^{\infty }\frac1{\sqrt{x}}\left(\frac{\cos(\pi x^2)}{\sinh (\pi x)}-\frac1{\pi x}\right)dx=\frac{1}{\sqrt{2}}\zeta(\frac{1}{2})$

Evaluate the following integral $ \int_1^{\infty} \frac{\lbrace x\rbrace-\frac{1}2}{x} dx$

Question about $f(x)=\sum_{k=1}^\infty (-1)^{k+1}\sin (\frac{x}{k}) $

What's the generalization for $\zeta(2n)$?

How to find $I=\int_0^1\frac{\arctan^2x}{1+x}\left(\frac{\ln x}{1-x}+\ln(1+x)\right)dx$

Prove $\int_0^1\frac{\ln x\ln(1+x)}{1-x}\ dx=\zeta(3)-\frac32\ln2\zeta(2)$

Is the sum of the reciprocals of imaginary parts of the zeros of the zeta function divergent?