Integrate the function $xe^{\frac{-x}{3}}$ from $-2$ to $\infty $

Evaluate the integral

$\int_{-\infty}^0\left(xe^x\right)dx$

Evaluate the integral

$\int_{-\infty}^0xe^xdx$

Evaluate the integral

$\int_e^{\infty}\left(\frac{1}{x\left(\ln\left(x\right)\right)^3}\right)dx$

Evaluate the integral

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

Evaluate the integral

$\int_0^1\left(\ln\left(1+x\right)\right)dx$

Evaluate the integral

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

Evaluate the integral

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