Integrate the function $\cos\left(\pi x\right)$ from $- \infty $ to $\infty $

Evaluate the integral

$\int_2^{\infty}\left(\frac{lnx}{x}\right)dx$

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

$\int_0^1\left(\frac{ln\left(x\right)}{x}\right)dx$

Evaluate the integral

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

Evaluate the integral

$\int_0^{\infty}\left(xe^{-x}\right)dx$