Integrate the function $\frac{8}{x^2+1}$ from $1$ to $\infty $

Evaluate the integral

$\int_2^{\infty}\left(\frac{1}{x^2+6x+5}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{\sqrt{x}+x^2}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{x}{1+x^3}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{x}{x^3+1}\right)dx$

Evaluate the integral

$\int_4^{\infty}\left(\frac{x+18}{x^2+x-12}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{x^2}{1+x^4}\right)dx$

Evaluate the integral

$\int_3^{\infty}4e^{\left(2x-4\right)}dx$