New posts in Improper Integrals

Help with closed form of $\int_0^\infty\frac{\tanh(ax)}{e^x-1}dx$

How evaluate $ \int_0^\infty \frac{\ln^2\;\left|\;\tan\left(\frac{ax}{2}-\frac{\pi}{4}\right)\;\right|}{1+x^2} \;dx$

Questions concerning an improper Riemann integrable funciton

Closed form of $\int_0^\infty \left(\frac{\arctan x}{x}\right)^ndx$

Prove that $\int_0^1\,\frac{\ln(x)}{\sqrt{1-x^2}}\,\text{d}x=-\frac{\pi}{2}\,\ln(2)$.

Any special way to integrate $\int_{0}^{\infty}t^2\exp(-t)\sin(t)$ quickly?

Determine whether the integral $ \int^{+\infty}_0\frac{e^{-t}} {\sqrt t} \, dt$ converges or diverges?

Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.

Can we use symmetry rules in improper integrals?

Difficult integral involving $\arctan x$