Integrate the function $\ln\left(x\right)$ from 0 to $e$

Evaluate the integral

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

Evaluate the integral

$\int_0^1xlnxdx$

Evaluate the integral

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

Evaluate the integral

$\int_0^e\left(\ln\left(x\right)\right)dx$

Evaluate the integral

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

Evaluate the integral

$\int_{-\infty}^{\infty}\left(\frac{1}{2x^2\left(x-1\right)}\right)dx$

Evaluate the integral

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