New posts in Improper Integrals

Trig Subsitution When There's No Square Root

Calculate the value for the following improper integral

Proving $\int_0^\infty x^ne^{-tx}\frac{\sin x}xdx=\frac{\sin n\theta}{(1+t^2)^{n/2}}(n-1)!$, where $\theta=\arcsin\frac1{\sqrt{1+t^2}}$

How to do integral $\int_{0}^{\infty} \frac{x^4 e^{x}}{(e^x-1)^2}\,dx$

Find positive $K$ such that $\int_0^\infty\left(\frac{1}{\sqrt{2x^2+1}}-\frac{K}{x+1}\right)dx$ converges

General formula for $\int_0^{\pi/2} \tan^{\alpha}(x) dx$?

$\int_{1}^{\infty}\frac{\ln x}{x^2-1}dx=\frac{\pi^2}{8}$

On the evalution of an infinite sum

Compute $\int_0^{\infty} \frac {1}{x^{1/3}(1+x^2)}dx$

Evaluate $\int_0^1 \frac{\ln (1 - x) \ln (1 + x)}{x} \, dx$