New posts in Improper Integrals

Closed form of $\int_0^\infty \sin(x)\sin\left(\frac{1}{x}\right)dx$?

i know application but want proof of following definite integration property .

Evaluating an improper integral $\int_{0}^{\infty}\frac{x^2}{(x^4+1)^2}dx$

Ways to prove that $\int_0^\infty \frac{x^2 \ln(x)}{(1+x^2)^3} {\rm d}x = 0$.

How to prove $\int_0^\infty \ln(1+\frac{z}{\cosh(x)})dx=\frac{\pi^2}{8}+\frac{(\cosh^{-1}(z))^2}{2},z\ge1$ and a closed form for $-1<z<1$?

Closed form of an improper integral to solve the period of a dynamical system

Solving $\int_{0}^{\infty} \frac{\sin(x)}{x^3}dx$

Evaluating $\int_{0}^{2\pi}x^2\ln^2(1-\cos x)dx$

Way to solve $\int\limits _0^\limits\infty \frac{x^{-t}}{1+x}\ dx$

Evaluating $\int_{0}^{\infty} \frac{1}{a_{n}x^{n} + ... + a_{2}x^{2} + a_{o}}dx$ via Residue Theory?