Solve the integral of logarithmic functions $\int\frac{\sqrt{\ln\left(x\right)}}{x}dx$

Find the integral

$\int\frac{ln\left(x+1\right)}{2\left(x+1\right)}dx$

Find the integral

$\int \frac { \operatorname { ln } x } { x } d x$

Find the integral

$\int\ln\left(\sqrt{x}+\sqrt{1+x}\right)dx$

Find the integral

$\int\left(x^3+2\right)^23x^2dx$

Find the integral

$\int x^2\ln Xdx$

Find the integral

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

Find the integral

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