Questions in indefinite-integration

Select	Question
	If $\int{x{{e}^{2x}}\,\,dx}$ is equal to ${{e}^{2x}}f(x)+C$ where C is constant of integration, then f(x) is
	If $\frac{d}{dx}f(x)=x\cos x+\sin x$ and $f(0)=2$, then $f(x)=$
	$\int{{{\cos }^{-1}}\left( \frac{1}{x} \right)\,\,dx}$
	$\int{{{x}^{3}}\log x\,\,dx=}$
	$\int{\cos ({{\log }_{e}}x)\,dx}$ is equal to
	$\int_{{}}^{{}}{{{e}^{x}}(1+\tan x)\sec x\ dx=}$
	$\int_{{}}^{{}}{\frac{x{{e}^{x}}}{{{(1+x)}^{2}}}dx=}$
	$\int_{{}}^{{}}{{{e}^{x}}[\tan x-\log (\cos x)]\ dx=}$
	$\int_{{}}^{{}}{{{e}^{x}}\sin x(\sin x+2\cos x)}\ dx=$
	$\int_{{}}^{{}}{{{e}^{2x}}\frac{1+\sin 2x}{1+\cos 2x}}\ dx=$