Solve the integral of logarithmic functions $\int x\ln\left(x+1\right)dx$

Find the integral

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

Find the integral

$\int\left(Lnx\right)^2dx$

Find the integral

$\int\left(\ln t\right)^2dt$

Find the integral

$\int t\ln\left(t+1\right)dt$

Find the integral

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

Find the integral

$\int\left(x^2sen\left(2x\right)\right)dx$

Find the integral

$\int x^2\ln Xdx$