Prove the trigonometric identity $\left(1-\sin\left(\infty \right)\right)\left(\sec\left(\infty \right)+\tan\left(\infty \right)\right)=\cos\left(\infty \right)$

Find the integral

$\int x^2\ln Xdx$

Find the integral

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

Find the integral

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

Find the integral

$\int xLnxdx$

Find the integral

$\int x\:ln\left(2x\right)dx$

Find the integral

$\int\sqrt{x}\ln xdx$

Find the integral

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