New posts in Improper Integrals

Show convergence of $\int_1^\infty{\frac{dx}{\sqrt{x^3-x}}}$

There is $f$ such that $\int_0^1 f dx = \lim_{c \downarrow 0} \int_c^1 fdx$, but for $|f|$ this limit does not exist. How is that possible?

Integral $\int_0^\infty \frac{1-e^{-x}\cos bx}{x} dx$

How can I prove $\frac{\gamma}{2}=\int_{0}^{\infty}\frac{e^{-x^{2}}-e^{-x}}{x}\text{d}x$?

A lucky proof for the Basel problem.

If $\int_ {0}^ \infty (\frac{ \sin x}{x})^3 = A$, then $\int_ {0}^ \infty \frac{ x- \sin x}{x^3} = ??$

Recurrence relation for $\int_{0}^{\infty} \frac{1}{(1+x^2/a)^n}dx$

Frullani integral $\int_0^\infty \frac{\text{csch}(x)-\frac1x}{x} {\rm d}x$

Fresnel integral $\int\limits_0^\infty\sin(x^2) dx$ calculation

Integral $\int_{-\infty}^{\infty} \arctan(e^x) \arctan(e^{-x})dx=\frac{7}{4}\zeta(3)$