Integrate the function $\sin\left(\frac{1}{x}\right)$ from $1$ to $\infty $

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

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

Evaluate the integral

$\int_0^1xln\left(x\right)dx$

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

$\int_1^exlnx\:dx$