Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

$\int_{-1}^2\frac{3x}{x+4}dx$