Solve the integral of logarithmic functions $\int12x\ln\left(x\right)dx$

Find the integral

$\int x^2\:lnx\:dx$

Find the integral

$\int\:x\:ln\:2x\:dx$

Find the integral

$\int xLnxdx$

Find the integral

$\int\left(x^3\right)\log x^2dx$

Find the integral

$\int x^3\log\left(x\right)dx$

Find the integral

$\int x^{2}\ln xdx$

Find the integral

$\int x^3ln\left(x^3\right)dx$