$$\int_\limits2^5 2[\mathrm{x}] \mathrm{dx}=\{\text { where }[\mathrm{x}] \text { denotes the greatest integer function } \leq \mathrm{x}\}$$

$$\int_\limits0^\pi x \sin x \cos ^4 x d x=$$

$$\int_\limits0^4 x[x] d x=$$ (where $$[\mathrm{x}]$$ denotes greatest integer function not greater than $$\mathrm{x}]$$

$$\int_\limits0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x=$$